2020
12
3
0
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1

NonLinear Response of Torsional Buckling Piezoelectric Cylindrical Shell Reinforced with DWBNNTs Under Combination of ElectroThermoMechanical Loadings in Elastic Foundation
http://jsm.iauarak.ac.ir/article_677536.html
10.22034/jsm.2019.581546.1365
1
Nanocomposites provide new properties and exploit unique synergism between materials. Polyvinylidene fluoride (PVDF) is an ideal piezoelectric matrix applicable in nanocomposites in a broad range of industries from oil and gas to electronics and automotive. And boron nitride nanotubes (BNNTs) show high mechanical, electrical and chemical properties. In this paper, the critical torsional load of a composite tube made of PVDF reinforced with doublewalled BNNTs is investigated, under a combination of electrothermomechanical loading. First, a nanocomposite smart tube is modeled as an isotropic cylindrical shell in an elastic foundation. Next, employing the classical shell theory, straindisplacement equations are derived so loads and moments are obtained. Then, the total energy equation is determined, consisting of strain energy of shell, energy due to external work, and energy due to elastic foundation. Additionally, equilibrium equations are derived in cylindrical coordinates as triply orthogonal, utilizing Euler equations; subsequently, stability equations are developed through the equivalent method in adjacent points. The developed equations are solved using the wave technique to achieve critical torsional torque. Results indicated that critical torsional buckling load occurred in axial halfwave number m = 24 and circumferential wave number n = 1, for the investigated cylindrical shell. The results also showed that with the increase in the lengthtoradius ratio and in the radiustoshell thickness ratio, the critical torsional buckling load increased and decreased, respectively. Lastly, results are compared in various states through a numerical method. Moreover, stability equations are validated via comparison with the shell and sheet equations in the literature.
0

505
520


M
Sarvandi
Department of Mechanical Engineering, Arak Branch, Islamic Azad University, Arak, Iran
Iran


M.M
Najafizadeh
Department of Mechanical Engineering, Arak Branch, Islamic Azad University, Arak, Iran
Iran


H
Seyyedhasani
School of Plant and Environmental Sciences, Virginia Polytechnic Institute and State University, Blacksburg, Virginia, USA
U.S.A
seyyedhasani12@vt.edu
Torsional Buckling
Piezoelectric
Electrothermomechanic
Elastic foundation
Cylindrical shell
[[1] Brockmann T.H., 2009, Theory of Adaptive Fiber Composites: From Piezoelectric Material Behavior to Dynamics of Rotating Structures, Springer Science & Business Media.##[2] Uzun B., Numanoglu H., Civalek O., 2018, Free vibration analysis of BNNT with different crossSections via nonlocal FEM, Journal of Computational Applied Mechanics 49(2): 252260.##[3] Sofiyev A., 2010, Buckling analysis of FGM circular shells under combined loads and resting on the Pasternak type elastic foundation, Mechanics Research Communications 37(6): 539544.##[4] Miraliyari O., Najafizadeh M.M., Rahmani A.R., Momeni Hezaveh A., 2011, Thermal and mechanical buckling of short and long functionally graded cylindrical shells using third order shear deformation theory, World Academy of Science, Engineering and Technology International Journal of Mechanical and Mechatronics Engineering 5(2): 518522.##[5] Bagherizadeh E., Kiani Y., Eslami M., 2011, Mechanical buckling of functionally graded material cylindrical shells surrounded by Pasternak elastic foundation, Composite Structures 93(11): 30633071.##[6] Najafizadeh M.M., Hasani A., Khazaeinejad P., 2009, Mechanical stability of functionally graded stiffened cylindrical shells, Applied Mathematical Modelling 33(2): 11511157.##[7] Sheng G., Wang X., 2010, Thermoelastic vibration and buckling analysis of functionally graded piezoelectric cylindrical shells, Applied Mathematical Modelling 34(9): 26302643.##[8] Shen H.S., Yang J., Kitipornchai S., 2010, Postbuckling of internal pressure loaded FGM cylindrical shells surrounded by an elastic medium, European Journal of MechanicsA/Solids 29(3): 448460.##[9] Najafizadeh M.M., Khazaeinejad P., 2011, Buckling of nonhomogeneous cylindrical shells under torsion using first order shear deformation theory, National Conference on New Technologies in Mechanical Engineering, Iran.##[10] Hassani H.S., 2010, Transient heat transfer analysis of hydraulic system for JD 955 harvester combine by finite element method, Journal of Food, Agriculture & Environment 8(2): 382385.##[11] Arani A.G., 2012, Electrothermomechanical buckling of DWBNNTs embedded in bundle of CNTs using nonlocal piezoelasticity cylindrical shell theory, Composites Part B: Engineering 43(2): 195203.##[12] Shadmehri F., Hoa S., Hojjati M., 2012, Buckling of conical composite shells, Composite Structures 94(2): 787792.##[13] Arani A.G., 2011, Semianalytical solution of timedependent electrothermomechanical creep for radially polarized piezoelectric cylinder, Computers & Structures 89(15): 14941502.##[14] Khazaeinejad P., 2010, On the buckling of functionally graded cylindrical shells under combined external pressure and axial compression, Journal of Pressure Vessel Technology 132(6): 064501.##[15] Zargaripoor A., 2018, Free vibration analysis of nanoplates made of functionally graded materials based on nonlocal elasticity theory using finite element method, Journal of Computational Applied Mechanics 49(1): 86101.##[16] Moradi A., 2018, Magnetothermo mechanical vibration analysis of FG nanoplate embedded on Visco Pasternak foundation, Journal of Computational Applied Mechanics 49(2): 395407.##[17] Mohammadi M., 2013, Temperature effect on vibration analysis of annular graphene sheet embedded on viscoPasternak foundation, Journal of Solid Mechanics 5(3): 305323.##[18] Goodarzi M., 2014, Investigation of the effect of prestressed on vibration frequency of rectangular nanoplate based on a viscoPasternak foundation, Journal of Solid Mechanics 6(1): 98121.##[19] Shen H.S., Zhang C.L., 2010, Torsional buckling and postbuckling of doublewalled carbon nanotubes by nonlocal shear deformable shell model, Composite Structures 92(5): 10731084.##[20] Mantari J., Oktem A., Soares C.G., 2012, A new higher order shear deformation theory for sandwich and composite laminated plates, Composites Part B: Engineering 43(3): 14891499.##[21] Hassani H.S., 2011, Fatigue analysis of hydraulic pump gears of JD 1165 harvester combine through finite element method, Trends in Applied Sciences Research 6(2): 174.##[22] Arani A.G., Kolahchi R., Barzoki A.M., 2011, Effect of material inhomogeneity on electrothermomechanical behaviors of functionally graded piezoelectric rotating shaft, Applied Mathematical Modelling 35(6): 27712789.##[23] Arani A.G., 2013, Electrothermotorsional buckling of an embedded armchair DWBNNT using nonlocal shear deformable shell model, Composites Part B: Engineering 51: 291299.##[24] Arani A.G., 2012, Electrothermomechanical nonlinear nonlocal vibration and instability of embedded microtube reinforced by BNNT, conveying fluid, Physica E: LowDimensional Systems and Nanostructures 45: 109121.##[25] Ansari R., Rouhi S., Ahmadi M., 2018, On the thermal conductivity of carbon nanotube/polypropylene nanocomposites by finite element method, Journal of Computational Applied Mechanics 49(1): 7085.##[26] Barzoki A.M., 2012, Electrothermomechanical torsional buckling of a piezoelectric polymeric cylindrical shell reinforced by DWBNNTs with an elastic core, Applied Mathematical Modelling 36(7): 29832995.##[27] Kargarnovin M., Shahsanami M., 2012, Buckling analysis of a composite cylindrical shell with fiber’s material properties changing lengthwise using firstorder shear deformation theory, International Conference on Mechanical, Automotive and Materials Engineering.##[28] Barzoki A.M., 2013, Nonlinear buckling response of embedded piezoelectric cylindrical shell reinforced with BNNT under electro–thermomechanical loadings using HDQM, Composites Part B: Engineering 44(1): 722727.##[29] Tan P., Tong L., 2001, Microelectromechanics models for piezoelectricfiberreinforced composite materials, Composites Science and Technology 61(5): 759769.##[30] Brush D.O., Almroth O., 1975, Buckling of Bars, Plates and Shells, New York, McGraw Hill.##]
1

The Effects of Initial InPlane Loads on the Response of CompositeSandwich Plates Subjected to Low Velocity Impact: Using a New Systematic Iterative Analytical Process
http://jsm.iauarak.ac.ir/article_677457.html
10.22034/jsm.2019.573380.1320
1
A new systematic iterative analytical procedure is presented to predict the dynamic response of composite sandwich plates subjected to lowvelocity impact phenomenon with/without initial inplane forces. In this method, the interaction between indenter and sandwich panel is modeled with considering the exponential equation similar to the Hertzian contact law and using the principle of minimum potential energy and the energybalance model. In accordance with the mentioned procedure and considering initial inplane forces, the unknown coefficients of the exponential equation are obtained analytically. Accordingly, the traditional Hertzian contact law is modified for use in the composite sandwich panel with the flexible core under biaxial prestresses. The maximum contact force using the twodegreesoffreedom (2DOF) springmass model is calculated through an iterative systematic analytical process. Using the present method, in addition to reducing the runtime, the problemsolving process is carried out with appropriate convergence. The numerical results of the analysis are compared with the published experimental and theoretical results. The effects of some important geometrical and physical parameters on contact force history are examined in details.
0

521
538


K
Malekzadeh Fard
Department of Aerospace Engineering, MalekeAshtar University of Technology, Tehran, Iran
Iran
kmalekzadeh@mut.ac.ir


A
Azarnia
Department of Aerospace Engineering, MalekeAshtar University of Technology, Tehran, Iran
Iran
Lowvelocity Impact
Composite sandwich plate
New analytical contact law
Initial inplane force
[[1] Koller M.G., 1986, Elastic impact of spheres on sandwich plates, Zeitschrift für Angewandte Mathematik und Physik (ZAMP) 37(2): 256269.##[2] Lee L.J.,Huang K.Y., Fann Y.J., 1993,Dynamic responses of composite sandwich plate impacted by a rigid ball, Journal of Composite Materials 27(13): 12381256.##[3] Yang S.H., Sun C.T., 1982,Indentation law for composite laminates, ASTM STP 787: 425449.##[4] Olsson R., McManus H.L., 1996, Improved theory for contact indentation of sandwich panels, AIAA 34(6): 12381244.##[5] Liou W.J., 1997,Contact laws of carbon/Epoxy laminated Composite plates, Journal of Reinforced Plastics and Composites 16: 155166.##[6] Hoo Fatt M.S., Park K.S., 2001, Dynamic models for lowvelocity impact damage of composite sandwich panelspart A: Deformation, Composite Structure 52: 335351.##[7] Sburlati R., 2002,The effect of a slow impact on sandwich plates, Journal of Composite Materials 36(9): 10791092.##[8] Choi I.H.,Lim C.H., 2004, Low velocity impact analysis of composite laminates using linearized contact law, Composite Structures 66: 125132.##[9] Kiratisaevee H., Cantwell W.J., 2005, Lowvelocity impact response of highperformance aluminum foam sandwich structures, Journal of Reinforced Plastics and Composites 24(10): 10571072.##[10] Malekzadeh K.,Khalili M.R.,Mittal R.K., 2006, Response of inplane linearly prestressed composite sandwich panels with transversely flexible core to lowvelocity impact, Journal of Sandwich and Materials 8: 157181.##[11] Choi I.H., 2008, Lowvelocity impact analysis of composite laminates under initial inplane load, Journal of Composite Structures 86: 251257.##[12] Hossini M.,Khalili M.R.,Malekzadeh K., 2011,Indentation analysis of inplane prestress composite sandwich plates: An improved contact law, Key Engineering Materials 471472: 11591164.##[13] Khalili M.R.,Hosseini M.,Malekzadeh K., Forooghgy S.H., 2013, Static indentation response of an inplane prestressed composite sandwich plate subjected to a rigid blunted indenter, European Journal of Mechanics A/Solids 38: 5969.##[14] Shariyat M.,Hosseini S.H., 2014, Eccentric impact analysis of prestressed composite sandwich plates with viscoelastic cores: A novel global–local theory and a refined contact law, Composite Structures 117: 333345.##[15] Zhou D.W.,Stronge W.J., 2006, Low velocity impact denting of HSSA lightweight sandwich panel, International Journal of Mechanical Sciences 48: 10311045.##[16] Azarnia A.H.,Malekzadeh K., 2018, Analytical modeling to predict dynamic response of FiberMetal Laminated Panel subjected to low velocity impact, Journal of Science and Technology of Composite 5(3): 331342.##[17] Shokrieh M.M.,Fakhar M.N., 2012, Experimental, analytical, and numerical studies of composite sandwich panels under lowvelocity impact loadings, Mechanics of Composite Materials 47(6): 643658.##]
1

On the Optimum Die Shape in Rod Drawing Process Considering WorkHardening Effect of Material
http://jsm.iauarak.ac.ir/article_674302.html
10.22034/jsm.2019.585582.1400
1
The assessment of the influence of the workhardening of material on the optimum die profile and drawing force in rod drawing process is the main objective of the present paper. The upper bound solution, based on the assumption of perfect plasticity, has been extended to consider the workhardening of the material during the rod drawing process through curved dies. Analytical results of drawing forces for rod drawing process through four different types of streamlined die profiles are compared with the finite element simulation data using the finite element code, DEFORM 2D. It is shown that as the workhardening exponent increases, the optimum die length increases, the required drawing force decreases and maximum possible reduction in area increases. Based on this proposed modeling technique, drawing process of real materials through various curved dies can be optimized.
0

539
550


M.M
Mahdavi
Mechanical Engineering Department, Razi University, Kermanshah, Iran
Iran


H
Haghighat
Mechanical Engineering Department, Razi University, Kermanshah, Iran
Iran
hhaghighat@razi.ac.ir
Rod drawing
Workhardening
Upper bound analysis
[[1] Avitzur B., 1963, Analysis of wire drawing and extrusion through conical dies of small cone angle, ASME Journal of Engineering for Industry 85: 8996.##[2] Avitzur B., 1964, Analysis of wire drawing and extrusion through conical dies of large cone angle, ASME Journal of Engineering for Industry 86: 305316.##[3] Chen C.T., Ling F.F., 1968, Upper bound solutions to axisymmetric extrusion problems, International Journal of Mechanical Sciences 10: 863879.##[4] Chen C.C., Oh S.I., Kobayashi S., 1977, Ductile fracture in axisymmetric extrusion and drawingPart I: Deformation mechanics of extrusion and drawing metal, ASME Journal of Engineering for Industry 101: 369377.##[5] Chevalier L., 1992, Prediction of defects in metal forming: application to wire drawing, Journal of Materials Processing Technology 32: 145153.##[6] Devenpeck M.L., Richmond O., 1965, Strip drawing experiments with a sigmoidal die profile, ASME Journal of Engineering for Industry 87: 425428.##[7] Chen D.C., Huang J.Y., 2007, Design of brass alloy drawing process using Taguchi method, Materials Science and Engineering 464: 135140.##[8] Gordon W. A., Van Tyne C. J., Moon Y. H., 2007a, Axisymmetric extrusion through adaptable diesPart 1: Flexible velocity fields and power terms, International Journal of Mechanical Sciences 49: 8695.##[9] Gordon W. A., Van Tyne C. J., Moon Y. H., 2007b, Axisymmetric extrusion through adaptable dies Part 2: Comparison of velocity fields, International Journal of Mechanical Sciences 49: 96103.##[10] Gordon W.A., Van Tyne C. J., Moon Y. H., 2007c, Axisymmetric extrusion through adaptable diesPart 3: Minimum pressure streamlined die shapes, International Journal of Mechanical Sciences 49: 104115.##[11] Gonzalez R.H.A., Calvet J.V., Bubnovich V.I., 2008, A new analytical solution for prediction of forward tension in the drawing process, Journal of Materials Processing Technology 198: 9398.##[12] Gunasekera J.S., Gegel H.L., Malas J.C., Doraivelu S.M., Barker D., 1984, CAD/CAM of streamlined extrusion dies, Journal of Applied Metalworking 4: 4349.##[13] Liu T.S., Chung N.L., 1990, Extrusion analysis and workability prediction using finite element method, Computers and Structures 36: 369377.##[14] Lu Y.H., Lo S.W., 1999, An advanced model of designing controlled strain rate dies for axisymmetric extrusion, Journal of Materials and Engineering Performance 8: 5160.##[15] Luis C.J., Leon J., Luri R., 2005, Comparison between finite element method and analytical methods for studying wire drawing processes, Journal of Materials Processing Technology 164165:12181225.##[16] Nagpal V., 1974, General kinematically admissible velocity fields for some axisymmetric metal forming problems, ASME Journal of Engineering for Industry 96: 11971201.##[17] Ponalagusamy R., Narayanasamy R., Srinivasan P., 2005, Design and development of streamlined extrusion dies: A Bezier curve approach, Journal of Materials Processing Technology 161: 375380.##[18] Panteghini A., Genna F., 2010, An engineering analytical approach to the design of cold wire drawing processes for strainhardening materials, International Journal of Materials Forming 3: 279289##[19] Panteghini A., 2014, An analytical solution for the estimation of the drawing force in three dimensional plate drawing processes, International Journal of Mechanical Sciences 84: 147157.##[20] Rubio Alvir E.M., Sebastian P.M.A., Sanz L.A., 2003, Mechanical solutions for drawing processes under plane strain conditions by the upper bound method, Journal of Materials Processing Technology 143144: 539545.##[21] Rubio Alvir E.M., Mariin M., Domingo R., Sebastian P.M.A., 2009, Analysis of plate drawing processes by the upper bound method using theoretical workhardening materials, International Journal of Advanced Manufacturing Technology 40: 261269.##[22] Richmond O., Devenpeck M. L., 1962, A die profile for maximum efficiency in strip drawing, Proceedings of the Fourth US National Congress of Applied Mechanics ASME1962, New York.##[23] Yang D.Y., Han C.H., Lee B.C., 1985, The use of generalized deformation boundaries for the analysis of axisymmetric extrusion through curved dies, International Journal of Mechanical Sciences 27: 653663.##[24] Yang D.Y., Han C.H., 1987, A new formulation of generalized velocity field for axisymmetric forward extrusion through arbitrarily curved dies, ASME Journal of Engineering for Industry 109: 161168.##[25] Zhao D.W., Zhao H.J., Wang G.D., 1995, Curvilinear integral of the velocity field of drawing and extrusion through elliptic die profile, Transaction of Nonferrous Metals Society of China 5: 7983.##[26] Zhang S.H., Chen X.D., Zhou J., Zhao D.W., 2016, Upper bound analysis of wire drawing through a twin parabolic die, Meccanica 51: 20992110.##]
1

Fatigue Life Prediction of Rivet Joints
http://jsm.iauarak.ac.ir/article_677572.html
10.22034/jsm.2019.1867882.1436
1
Strength reduction in structures like an aircraft could be resulted as cyclic loads over a period of time and is an important factor for structural life prediction. Service loads are emphasized at the regions of stress concentration, mostly at the connection of components. The initial flaw prompting the service life was expected by using the Equivalent Initial Flaw Size (EIFS) which has been recognized as a powerful design tool for life prediction of engineering structures. This method was introduced 30 years ago in an attempt to study the initial quality of structural details. In this paper, the prediction of life based on failure mechanics in a riveted joint has been addressed through the concept of EIFS. For estimation of initial crack length by EIFS, extrapolation method has been used. The EIFS value is estimated using the coefficient of cyclic intensity (ΔK) and using the cyclic integral (ΔJ), and the results are compared with each other. The simulation results show that the if the coefficient of tension been used in EIFS estimation, which based on the Paris law, the EIFS value will be dependent on the loading domain, while the use of the JCyclic integral in the EIFS decrease its dependence on the load domain dramatically.
0

551
558


M. M
Amiri
Research Institute of Petroleum Industry, Islamic Republic of, Tehran, Iran
Iran
amirimm@ripi.ir
Fatigue
Riveted joints
Life prediction
Fracture
[[1] Newman J.C., Phillips E.P., Swain M.H., 1999, Fatiguelife prediction methodology using smallcrack theory, International Journal of Fatigue 21: 109119.##[2] Lim J.Y., Hong S.G., Lee S.B., 2005, Application of local stress–strain approaches in the prediction of fatigue crack initiation life for cyclically nonstabilized and nonMasing steel, International Journal of Fatigue 27: 16531660.##[3] Pugno N., Ciavarella M., Cornetti P., Carpinteri A., 2006, A generalized Paris’ law for fatigue crack growth, Journal of the Mechanics and Physics of Solids 54: 13331349.##[4] Kim S.T., Tadjiev D., Yang H.T., 2006, Fatigue life prediction under random loading conditions in 7475T7351 aluminum alloy using the RMS model, International Journal of Damage Mechanics 15: 89102.##[5] Dowling Norman E., 1999, Mechanical Behavior of Materials, PrenticeHall, New Jersey.##[6] Newman J.C.Jr., 1998, The merging of fatigue and fracture mechanics concepts, Progress in Aerospace Sciences 34: 347390.##[7] Liu Y., Mahadovan S., 2009, Probabilistic fatigue life prediction using an equivalent initial flaw size distribution, International Journal of Fatigue 31(3): 476487.##[8] Amanullah M., Siddiqui N.A., Umar A., Abbas H., 2002, Fatigue reliability analysis of welded joints of a TLP tether system, Steel & Composite Structures 2(5): 331354.##[9] Kim J., Zi G., Van S., Jeong M., Kong J., Kim M., 2011, Fatigue life prediction of multiple site damage based on probabilistic equivalent initial flaw model, Structural Engineering and Mechanics 38(4): 443457.##[10] Shahani A. R., Moayeri Kashani H., 2013, Assessment of equivalent initial flaw size estimation methods in fatigue life prediction using compact tension specimen tests, Engineering Fracture Mechanics 99: 4861.##[11] Suna J., Dinga Z., Huang Q., 2019, Development of EIFSbased corrosion fatigue life prediction approach for corroded RC beams, Engineering Fracture Mechanics 209: 116.##[12] Gallagher J.P., Molent L., 2015, The equivalence of EPS and EIFS based on the same crack growth life data, International Journal of Fatigue 80: 162170.##[13] Newman J.C.Jr., 1981, A crack closure model for predicting fatigue crackgrowth under aircraft spectrum loading, NASA Technical Memorandum 81941: 5384.##[14] Molent L., SUN Q., Green A.J., 2006, Characterisation of equivalent initial flaw sizes in 7050 aluminium alloy, Fatigue & Fracture of Engineering Materials & Structures 29: 916937.##[15] Yongming Liu, Sankaran Mahadevan, 2009, Probabilistic fatigue life prediction using an equivalent initial flaw size distribution, International Journal of Fatigue 31: 476487.##[16] Moreira P., Matos P., Camanho P., Pastrama P., Castro P., 2007, Stress intensity factor and load transfer analysis of a cracked riveted lap joint, Materials and Design 28(4): 12631270.##]
1

A New Approach for Stress State  Dependent Flow Localization Failure Bounded Through Ductile Damage in Dynamically Loaded Sheets
http://jsm.iauarak.ac.ir/article_677562.html
10.22034/jsm.2019.1869860.1449
1
In this paper, a new approach is proposed for stress state  dependent flow localization in bifurcation failure model bounded through ductile damage in dynamically loaded sheets. Onset of localized necking is considered in phenomenological way for different strain rates to draw the forming limit diagram (FLD). Using a strain metal hardening exponent in the Vertex theory related to the strain rate helps investigate rate dependent metal forming limits. Besides, the paper utilizes the model of ductile damage as a function of strain condition, stress states (triaxiality and Lode parameters), and the symbols of stiffness strain to predict the onset of the necking. It is worth noting that updated level of elasticity modulus in the plastic deforming is attributed as an essential index for the ductile damage measuring. According to original formulations, a UMAT subroutine is developed in the finite element simulation by ABAQUS code to analyze and connect the related constitutive models. Results reveal that the FLD levels increase for St 13 material through enhancing the strain rate.
0

559
569


F
Hosseini Mansoub
Department of Mechanical Engineering, University Campus, University of Guilan, Rasht, Iran
Iran


A
Basti
Department of Mechanical Engineering, University of Guilan, Rasht, Iran
Iran
basti@guilan.ac.ir


A
Darvizeh
Department of Mechanical Engineering, University of Guilan, Rasht, Iran
Iran


A
Zajkani
Department of Mechanical Engineering, Imam Khomeini International University, Qazvin, Iran
Iran
Ductile damage
Stress State
Strain rate
Forming Limit
Localized necking
[[1] Aboutalebi F.H., Farzin M., Poursina M., 2011, Numerical simulation and experimental validation of a ductile damage model for DIN 1623 St14 steel, The International Journal of Advanced Manufacturing Technology 53: 157165.##[2] Ma X., Li F., Li J., 2015, Analysis of forming limits based on a new ductile damage criterion in St14 steel sheets, Materials & Design 68: 134145.##[3] Hill R., 1952, On discontinuous plastic states, with special reference to localized necking in thin sheets, Journal of the Mechanics and Physics of Solids 1:1930.##[4] Hill R., 1958, A general theory of uniqueness and stability in elasticplastic solids, Journal of the Mechanics and Physics of Solids 6: 236249.##[5] Borré G., Maier G., 1989, On linear versus nonlinear flow rules in strain localization analysis, Meccanica 24: 3641.##[6] Thomas W.M., 1991, Friction stir butt welding, International Patent Application No PCT/GB92/0220.##[7] Chow C.L., Jie M., Wu X., 2005, Localized necking criterion for strainsoftening materials, Journal of Engineering Materials and Technology 127: 273278.##[8] Neilsen M.K., Schreyer H.L., 1993, Bifurcations in elasticplastic materials, International Journal of Solids and Structures 30: 521544.##[9] Chow C.L., Jie M., Wu X., 2007, A damagecoupled criterion of localized necking based on acoustic tensor, International Journal of Damage Mechanics 16: 265281.##[10] Szabó L., 2000, Comments on loss of strong ellipticity in elastoplasticity, International Journal of Solids and Structures 37: 37753806.##[11] Bigoni D., Hueckel T., 1991, Uniqueness and localization—I. Associative and nonassociative elastoplasticity, International Journal of Solids and Structures 28: 197213.##[12] Rudnicki J.W., Rice J.R., 1975, Condition for the localization of deformation in pressuresensitive dilatant materials, Journal of the Mechanics and Physics of Solids 23(6): 371394.##[13] Xue L., Wierzbicki T., 2008, Ductile fracture initiation and propagation modeling using damage plasticity theory, Engineering Fracture Mechanics 75: 32763293.##[14] Marciniak Z., Kuczyński K., 1967, Limit strains in the processes of stretchforming sheet metal, International Journal of Mechanical Sciences 9(9): 609612.##[15] Marciniak Z., Kuczyński K., Pokora T., 1973, Influence of the plastic properties of a material on the forming limit diagram for sheet metal in tension, International Journal of Mechanical Sciences 15: 789800.##[16] Mirfalah S.M., Basti A., Hashemi R., Darvizeh A., 2018, Effects of normal and throughthickness shear stresses on the forming limit curves of AA3104H19 using advanced yield criteria, International Journal of Mechanical Sciences 137: 1523.##[17] Erfanian M., Hashemi R., 2018, A comparative study of the extended forming limit diagrams considering strain path, throughthickness normal and shear stress, International Journal of Mechanical Sciences 148: 316326.##[18] Zajkani A., Bandizaki A., 2017, An efficient model for diffuse to localized necking transition in ratedependent bifurcation analysis of metallic sheets, International Journal of Mechanical Sciences 133: 794803.##[19] Zajkani A., Bandizaki A., 2017, A pathdependent necking instability analysis of the thin substrate composite plates considering nonlinear reinforced layer effects, The International Journal of Advanced Manufacturing Technology 95: 759774.##[20] Stören S., Rice J.R., 1975, Localized necking in thin sheets, Journal of the Mechanics and Physics of Solids 23: 421441.##[21] Zajkani A., Bandizaki A., 2018, Stability and instability analysis of the substrate supported panels in the forming process based on perturbation growth and bifurcation threshold models, Journal of Manufacturing Processes 31: 703711.##[22] Xue L., 2007, Ductile Fracture modelingTheory, Experimental Investigation and Numerical Verification, Thesis Ph. D., Massachusetts Institute of Technology.##[23] Bai Y., Wierzbicki T., 2008, A new model of metal plasticity and fracture with pressure and Lode dependence, International Journal of Plasticity 24: 10711096.##[24] Simha C.H.M., Xu S., Tyson W.R., 2014, Nonlocal phenomenological damagemechanicsbased modeling of the DropWeight Tear Test, Engineering Fracture Mechanics 118: 6682.##[25] Campos H.B., Butuc M.C., Grácio J.J., 2006, Theorical and experimental determination of the forming limit diagram for the AISI 304 stainless steel, Journal of Materials Processing Technology 179: 5660.##[26] Kim S.B., Huh H., Bok H.H., Moon M.B., 2011, Forming limit diagram of autobody steel sheets for highspeed sheet metal forming, Journal of Materials Processing Technology 211: 851862.##[27] Mosavi F., Hashemi R., Madoliat R., 2018, Measurement of directional anisotropy coefficients for AA7020T6 tubes and prediction of forming limit curve, International Journal of Advanced Manufacturing Technology 96: 10151023.##[28] Balasubramanian S., Anand L., 2002, Elastoviscoplastic constitutive equations for polycrystalline fcc materials at low homologous temperatures, Journal of the Mechanics and Physics of Solids 50: 101126.##[29] Brünig M., Gerke S., 2011, Simulation of damage evolution in ductile metals undergoing dynamic loading conditions, International Journal of Plasticity 27: 15981617.##[30] Shojaei A., Voyiadjis G.Z., Tan P.J., 2013, Viscoplastic constitutive theory for brittle to ductile damage in polycrystalline materials under dynamic loading, International Journal of Plasticity 48: 125151.##[31] Huh J., Huh H., Lee C.S., 2013, Effect of strain rate on plastic anisotropy of advanced high strength steel sheets, International Journal of Plasticity 44: 2346.##[32] Johnson G.R., Cook W.H., 1983, A constitutive model and data for metals subjected to large strains, high strain rates and high temperatures, 7th International Symposium on Ballistics, The Hague.##[33] Clausen A.H., Børvik T., Hopperstad O.S., Benallal A., 2004, Flow and fracture characteristics of aluminium alloy AA5083–H116 as function of strain rate, temperature and triaxiality, Materials Science and Engineering 364: 260272.##[34] Erice B., Gálvez F., Cendón D.A., SánchezGálvez V., 2012, Flow and fracture behaviour of FV535 steel at different triaxialities, strain rates and temperatures, Engineering Fracture Mechanics 79: 117.##[35] Kajberg J., Sundin KG., 2013, Material characterisation using hightemperature Split Hopkinson pressure bar, Journal of Materials Processing Technology 213: 522531.##[36] Smerd R., Winkler S., Salisbury C., 2005, High strain rate tensile testing of automotive aluminum alloy sheet, International Journal of Impact Engineering 32: 541560.##[37] Verleysen P., Peirs J., Van Slycken J., 2011, Effect of strain rate on the forming behaviour of sheet metals, Journal of Materials Processing Technology 211:14571464.##[38] Mohr D., Dunand M., Kim KH., 2010, Evaluation of associated and nonassociated quadratic plasticity models for advanced high strength steel sheets under multiaxial loading, International Journal of Plasticity 26: 939956.##[39] Kim J.H., Sung J.H., Piao K., Wagoner R.H., 2011, The shear fracture of dualphase steel, International Journal of Plasticity 27: 16581676.##[40] Lou Y., Yoon J.W., Huh H., 2014, Modeling of shear ductile fracture considering a changeable cutoff value for stress triaxiality, International Journal of Plasticity 54: 5680.##[41] Sun X., Choi K.S., Liu W.N., Khaleel M.A., 2009, Predicting failure modes and ductility of dual phase steels using plastic strain localization, International Journal of Plasticity 25: 18881909.##[42] Gruben G., Fagerholt E., Hopperstad O.S., Børvik T., 2011, Fracture characteristics of a coldrolled dualphase steel, European Journal of Mechanics 30: 204218.##[43] Chung K., Ma N., Park T., 2011, A modified damage model for advanced high strength steel sheets, International Journal of Plasticity 27: 14851511.##[44] Huh H., Kim SB., Song JH., Lim JH., 2008, Dynamic tensile characteristics of TRIPtype and DPtype steel sheets for an autobody, International Journal of Mechanical Sciences 50: 918931.##[45] Curtze S., Kuokkala VT., Hokka M., Peura P., 2009, Deformation behavior of TRIP and DP steels in tension at different temperatures over a wide range of strain rates, Materials Science and Engineering 507: 124131.##[46] Roth C.C., Mohr D., 2014, Effect of strain rate on ductile fracture initiation in advanced high strength steel sheets: Experiments and modeling, International Journal of Plasticity 56: 1944.##[47] Mirfalah S.M., Basti A., Hashemi R., 2016, Forming limit curves analysis of aluminum alloy considering the throughthickness normal stress, anisotropic yield functions and strain rate, International Journal of Mechanical Sciences 117: 93101.##[48] Jie M., Cheng C.H., Chan L.C., Chow C.L., 2009, Forming limit diagrams of strainratedependent sheet metals, International Journal of Mechanical Sciences 51: 269275.##[49] Saradar M., Basti A., Zaeimi M., 2015, Numerical study of the effect of strain rate on damage prediction by dynamic forming limit diagram in high velocity sheet metal forming, Modares Mechanical Engineering 14: 212222.##[50] Wu HY., Sun PH., Chen HW., Chiu CH., 2012, Rate and orientation dependence of formability in finegrained AZ31BO Mg alloy thin sheet, Journal of Materials Engineering and Performance 21: 21242130.##[51] Kim D., Kim H., Kim J.H., 2015, Modeling of forming limit for multilayer sheets based on strainrate potentials, International Journal of Plasticity 75: 6399.##[52] Fakir O. El., Wang L., Balint D., 2014, Predicting effect of temperature, strain rate and strain path changes on forming limit of lightweight sheet metal alloys, Procedia Engineering 81: 736741.##]
1

Vibration Analysis of SizeDependent Piezoelectric Nanobeam Under MagnetoElectrical Field
http://jsm.iauarak.ac.ir/article_677310.html
10.22034/jsm.2019.1864682.1446
1
The damping vibration characteristics of magnetoelectroviscoelastic (MEV) nanobeam resting on viscoelastic foundation based on nonlocal strain gradient elasticity theory (NSGT) is studied in this article. For this purpose, by considering the effects of WinklerPasternak, the viscoelastic medium consists of linear and viscous layers. with respect to the displacement field in accordance with the refined shear deformable beam theory (RSDT) and the KelvinVoigt viscoelastic damping model, the governing equations of motion are obtained using Hamilton’s principle based on nonlocal strain gradient theory (NSGT). Using Fourier Series Expansion, The Galerkin’s method adopted to solving differential equations of nanobeam with both of simply supported and clamped boundary conditions. Numerical results are obtained to show the influences of nonlocal parameter, the length scale parameter, slenderness ratio and magnetoelectromechanical loadings on the vibration behavior of nanobeam for both types of boundary conditions. It is found that by increasing the magnetic potential, the dimensionless frequency can be increased for any value of the damping coefficient and vice versa. Moreover, negative/positive magnetic potential decreases/increases the vibration frequencies of thinner nanobeam. Also, the vibrating frequency decreases and increases with increasing nonlocal parameter and length scale parameter respectively.
0

570
585


M
Ghadiri
Department of Mechanics, Imam Khomeini International University, Qazvin, Iran
Iran
ghadiri@eng.ikiu.ac.ir


M
Karimi Asl
Department of Mechanics, Imam Khomeini International University, Qazvin, Iran
Iran


M
Noroozi
Department of Mechanics, Imam Khomeini International University, Qazvin, Iran
Iran
Piezoelectric nanobeam
Vibration analysis
Viscoelastic damping
Nonlocal strain gradient
Magnetoelectroviscoelastic
[[1] Eringen A., 1968, Mechanics of micromorphic continua, Mechanics of Generalized Continua 104: 1835.##[2] Leissa A.W., 1969, Vibration of Plates, Ohio State University Columbus.##[3] Eringen A., 1972, Nonlocal polar elastic continua, International Journal of Engineering Science 10:116.##[4] Van den Boomgard J., Terrell D.R., Born R.A.J., 1974, An in situ grown eutectic magnetoelectric composite material, Journal of Materials Science 9: 17051709.##[5] Eringen A., 1976, Nonlocal Micropolar Field Theory, In Continuum Physics, Academic Press, New York.##[6] Eringen A., 1983, On differential equations of nonlocal elasticity and solutions of screw dislocation and surface waves, Journal of Applied Physics 54(9): 47034710.##[7] Eringen A., 2002, Nonlocal Continuum Field Theories, Springer, New York.##[8] Lam D.C.C., Yang F., Chong A.C.M., Wang J., Tong P., 2003, Experiments and theory in strain gradient elasticity, Journal of the Mechanics and Physics of Solids 51(8): 14771508.##[9] Peddieson J., Buchanan G.R., McNitt R.P., 2003, Application of nonlocal continuum models to nanotechnology, International Journal of Engineering Science 41(35): 305312.##[10] Zheng H.,Wang J., Lofland S.E., 2004, Multiferroic BaTiO3CoFe2O4 nanostructures, Science 303: 661663.##[11] Wang Q., 2005, Wave propagation in carbon nanotubes via nonlocal continuum mechanics, Journal of Applied Physics 98: 124301.##[12] Eringen A., 2006, Nonlocal continuum mechanics based on distributions, International Journal of Engineering Science 44(3): 141147.##[13] Martin L.W., Crane S.P., Chu Y.H., 2008, Multiferroics and magnetoelectrics: Thin films and nanostructures, Journal of Physics: Condensed Matter 20: 434220.##[14] Wang C.M., Kitipornchai S., Lim C.W., Eisenberger M., 2008, Beam bending solutions based on nonlocal Timoshenko beam theory, Journal of Engineering Mechanics 134: 475481.##[15] Murmu T., Pradhan S.C., 2009, Buckling analysis of a singlewalled carbon nanotube embedded in an elastic medium based on nonlocal elasticity and Timoshenko beam theory and using DQM, Physica E: LowDimensional Systems and Nanostructures 41(7): 12321239.##[16] Yang J., Ke L.L., Kitipornchai S., 2010, Nonlinear free vibration of singlewalled carbon nanotubes using nonlocal Timoshenko beam theory, Physica E: LowDimensional Systems and Nanostructures 42(5): 17271735.##[17] Wang Y., Hu J.M., Lin Y.H., 2010, Multiferroic magnetoelectric composite nanostructures, NPG Asia Materials 2: 6168.##[18] Civalek O., Demir C., 2011, Bending analysis of microtubules using nonlocal Euler–Bernoulli beam theory, Applied Mathematical Modelling 35: 20532067.##[19] Roque C.M.C., Ferreira A.J.M., Reddy J.N., 2011, Analysis of Timoshenko nanobeams with a nonlocal formulation and meshless method, International Journal of Engineering Science 49(9): 976984. ##[20] Prashanthi K., Shaibani P.M., Sohrabi A., 2012, Nanoscale magnetoelectric coupling in multiferroic BiFeO3 nanowires, Physica Status Solidi 6: 244246.##[21] Zenkour A.M., Sobhy M., 2013, Nonlocal elasticity theory for thermal buckling of nanoplates lying on Winkler–Pasternak elastic substrate medium, Physica E: LowDimensional Systems and Nanostructures, 53: 251259.##[22] Şimşek M., Yurtcu H.H., 2013, Analytical solutions for bending and buckling of functionally graded nanobeams based on the nonlocal Timoshenko beam theory, Composite Structures 97: 378386.##[23] Ke L.L., Wang Y.S., Yang J., Kitipornchai S., 2014, Free vibration of sizedependent magnetoelectroelastic nanoplates based on the nonlocal theory, Acta Mechanica Sinica 30(4): 516525.##[24] Ke L.L., Wang Y.S., 2014, Free vibration of sizedependent magnetoelectroelastic nanobeams based on the nonlocal theory, Physica E: LowDimensional Systems and Nanostructures 63: 5261.##[25] Mantari J.L., Bonilla E.M., Soares C.G., 2014, A new tangentialexponential higher order shear deformation theory for advanced composite plates, Composites Part B: Engineering 60: 319328.##[26] Li L., Hu Y., Ling L., 2015, Flexural wave propagation in smallscaled functionally graded beams via a nonlocal strain gradient theory, Composite Structures 133: 10791092.##[27] Ebrahimi F., Salari E., 2015a, Effect of various thermal loadings on buckling and vibrational characteristics of nonlocal temperaturedependent FG nanobeams, Mechanics of Advanced Materials and Structures 23: 13791397.##[28] Arefi M., Zenkour A.M., 2016, A simplified shear and normal deformations nonlocal theory for bending of functionally graded piezomagnetic sandwich nanobeams in magnetothermoelectric environment, Journal of Sandwich Structures & Materials 18(5): 624651.##[29] Ebrahimi F., Barati M.R., 2016, Vibration analysis of smart piezoelectrically actuated nanobeams subjected to magnetoelectrical field in thermal environment, Journal of Vibration and Control 24: 549564.##[30] Ebrahimi F., Barati M.R., 2016, Buckling analysis of nonlocal thirdorder shear deformable functionally graded piezoelectric nanobeams embedded in 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1

An Analytical Solution on Size Dependent Longitudinal Dynamic Response of SWCNT Under Axial Moving Harmonic Load
http://jsm.iauarak.ac.ir/article_677314.html
10.22034/jsm.2019.1875642.1476
1
The main purposes of the present work are devoted to the investigation of the free axial vibration, as well as the timedependent and forced axial vibration of a SWCNT subjected to a moving load. The governing equation is derived through using Hamilton's principle. Eringen’s nonlocal elasticity theory has been utilized to analyze the nonlocal behaviors of SWCNT. A Galerkin method based on a closedform solution is applied to solve the governing equation. The boundary conditions are considered as clampedclamped (CC) and clampedfree (CF). Firstly, the nondimensional natural frequencies are calculated, as well as the influence of the nonlocal parameter on them are explained. The results of both boundary conditions are compared together, and both of them are compared to the results of another study to verify the accuracy and efficiency of the present results. The novelty of this work is related to the study of the dynamic forced axial vibration due to the axial moving harmonic force in the time domain. The previously forced vibration studies were devoted to the transverse vibrations. The effect of the geometrical parameters, velocity of the moving load, excitation frequency, as well as the smallscale effect, are explained and discussed in this context. According to the lack of accomplished studies in this field, the present work has the potential to be used as a benchmark for future works.
0

586
599


F
Khosravi
Department of Aerospace Engineering, K.N. Toosi University of Technology, Tehran, Iran
Iran


M
Simyari
Department of Mechanical Engineering, University of Tehran, Tehran, Iran
Iran


S. A
Hosseini
Department of Industrial, Mechanical and Aerospace Engineering, Buein Zahra Technical University, Buein Zahra, Qazvin, Iran
Iran
hosseini@bzte.ac.ir


M
Ghadiri
Faculty of Engineering, Department of Mechanics, Imam Khomeini International University, Qazvin, Iran
Iran
ghadiri@ikiu.ac.ir
Moving load
size dependent
Axial vibration
Free vibration
Forced vibration
Galerkin Method
Harmonic load
[Kroto H.W., 1985, C60: Buckminsterfullerene, Nature 318: 162163.##[2] Krätschmer W., 1990, Solid C60: a new form of carbon, Nature 347: 354358.##[3] Iijima S., 1991, Synthesis of Carbon Nanotubes, Nature 354: 5658.##[4] Iijima S., Ichihashi T., 1993, Singleshell carbon nanotubes of 1nm diameter, Nature 363: 603605.##[5] Iijima S., 1991, Helical microtubules of graphitic carbon, Nature 354: 5658.##[6] Lu X., Chen Z., 2005, Curved piconjugation, aromaticity, and the related chemistry of small fullerenes (< C60) and singlewalled carbon nanotubes, Chemical Reviews 105(10): 36433696.##[7] Dresselhaus M., 2004, Electronic, thermal and mechanical properties of carbon nanotubes. Philosophical Transactions of the Royal Society of London, Series A: Mathematical, Physical and Engineering Sciences 362: 20652098.##[8] Hong S., Myung S., 2007, Nanotube electronics: A flexible approach to mobility, Nature Nanotechnology 2(4): 207208.##[9] Bethune D., 1993, Cobaltcatalysed growth of carbon nanotubes with singleatomiclayer walls, Nature 363: 605607.##[10] Dai H., 2002, Carbon nanotubes: opportunities and challenges, Surface Science 500 (13): 218241.##[11] De Volder M.F., 2013, Carbon nanotubes: present and future commercial applications, Science 339: 535539.##[12] Esawi A.M., Farag M.M., 2007, Carbon nanotube reinforced composites: potential and current challenges, Materials & Design 28(9): 23942401.##[13] Mubarak N., 2014, An overview on methods for the production of carbon nanotubes, Journal of Industrial and Engineering Chemistry 20(4): 11861197.##[14] Lei Z., Zhang L., Liew K., 2015, Free vibration analysis of laminated FGCNT reinforced composite rectangular plates using the kpRitz method, Composite Structures 127: 245259.##[15] Zhang L., Song Z., Liew K., 2015, Statespace Levy method for vibration analysis of FGCNT composite plates subjected to inplane loads based on higherorder shear deformation theory, Composite Structures 134: 9891003.##[16] Natarajan S., Haboussi M., Manickam G., 2014, Application of higherorder structural theory to bending and free vibration analysis of sandwich plates with CNT reinforced composite facesheets, Composite Structures 113: 197207.##[17] Wang Z.X., Shen H.S., 2012, Nonlinear vibration and bending of sandwich plates with nanotubereinforced composite face sheets, Composites Part B: Engineering 43(2): 411421.##[18] Ma J., 2010, Diameters of singlewalled carbon nanotubes (SWCNTs) and related nanochemistry and nanobiology, Frontiers of Materials Science in China 4(1): 1728.##[19] Sethuraman A., Stroscio M.A., Dutta M., 2004, Potential Applications of Carbon Nanotubes in Bioengineering, Springer.##[20] Chen Y., Zhang J., 2014, Chemical vapor deposition growth of singlewalled carbon nanotubes with controlled structures for nanodevice applications, Accounts of Chemical Research 47(8): 22732281.##[21] Fukuda T., Arai F., Dong L., 2003, Assembly of nanodevices with carbon nanotubes through nanorobotic manipulations, Proceedings of the IEEE 91(11): 18031818.##[22] Ma P.C., 2010, Dispersion and functionalization of carbon nanotubes for polymerbased nanocomposites: a review, Composites Part A: Applied Science and Manufacturing 41(10): 13451367.##[23] Sahoo N.G., 2010, Polymer nanocomposites based on functionalized carbon nanotubes, Progress in Polymer Science 35(7): 837867.##[24] Zarepour M., Hosseini S.A., Ghadiri M., 2017, Free vibration investigation of nano mass sensor using differential transformation method, Applied Physics A 123(3): 181.##[25] Namvar M., 2017, Experimental and analytical investigations of vibrational behavior of Ushaped atomic force microscope probe considering thermal loading and the modified couple stress theory, The European Physical Journal Plus 132(6): 247.##[26] Sourki R., Hosseini S.A., 2017, Coupling effects of nonlocal and modified couple stress theories incorporating surface energy on analytical transverse vibration of a weakened nanobeam, The European Physical Journal Plus 132(4): 184.##[27] Refaeinejad V., Rahmani O., Hosseini S.A., 2017, Evaluation of nonlocal higher order shear deformation models for the vibrational analysis of functionally graded nanostructures, Mechanics of Advanced Materials and Structures 24(13): 11161123.##[28] Rahmani O., Hosseini S.A., Parhizkari M., 2017, Buckling of double functionallygraded nanobeam system under axial load based on nonlocal theory: an analytical approach, Microsystem Technologies 23(7): 27392751.##[29] Hayati H., Hosseini S.A., Rahmani O.,2016, Coupled twist–bending static and dynamic behavior of a curved singlewalled carbon nanotube based on nonlocal theory, Microsystem Technologies 23: 23932401.##[30] Eringen A.C., Edelen D., 1972, On nonlocal elasticity, International Journal of Engineering Science 10(3): 233248.##[31] Eringen A.C., 1983, On differential equations of nonlocal elasticity and solutions of screw dislocation and surface waves, Journal of Applied Physics 54(9): 47034710.##[32] Kahrobaiyan M., 2010, Investigation of the sizedependent dynamic characteristics of atomic force microscope microcantilevers based on the modified couple stress theory, International Journal of Engineering Science 48(12): 19851994.##[33] Ansari R., 2015, Surface stress effect on the vibration and instability of nanoscale pipes conveying fluid based on a sizedependent Timoshenko beam model, Acta Mechanica Sinica 31(5): 708719.##[34] Farajpour M.R., 2016, Vibration of piezoelectric nanofilmbased electromechanical sensors via higherorder nonlocal strain gradient theory, Micro & Nano Letters 11(6): 302307.##[35] Behrouz S.J., Rahmani O., Hosseini S.A., 2019, On nonlinear forced vibration of nano cantileverbased biosensor via couple stress theory, Mechanical Systems and Signal Processing 128: 1936.##[36] Hosseini S.A., Rahmani O., 2018, Modeling the size effect on the mechanical behavior of functionally graded curved micro/nanobeam, Thermal Science and Engineering 1(2): 120.##[37] Rahmani O., 2018, Size dependent bending analysis of micro/nano sandwich structures based on a nonlocal high order theory, Steel and Composite Structures 27(3): 371388.##[38] Rahmani O., 2018, Free vibration of deep curved FG nanobeam based on modified couple stress theory, Steel and Composite Structures 26(5): 607620.##[39] Rahmani O., 2018, Dynamic response of a singlewalled carbon nanotube under a moving harmonic load by considering modified nonlocal elasticity theory, The European Physical Journal Plus 133(2): 42.##[40] Ghadiri M., 2018, InPlane and out of plane free vibration of Ushaped AFM probes based on the nonlocal elasticity, Journal of Solid Mechanics 10(2): 285299.##[41] Hosseini S.A., Rahmani O., 2018, Bending and vibration analysis of curved FG nanobeams via nonlocal Timoshenko model, Smart Construction Research 2(2): 117.##[42] Xu K., Guo X., Ru C., 2006, Vibration of a doublewalled carbon nanotube aroused by nonlinear intertube van der Waals forces, Journal of Applied Physics 99(6): 064303.##[43] Lee H.L., Chang W.J., 2009, Vibration analysis of a viscousfluidconveying singlewalled carbon nanotube embedded in an elastic medium, Physica E: LowDimensional Systems and Nanostructures 41(4): 529532.##[44] MoradiDastjerdi R., 2014, Vibration analysis of functionally graded nanocomposite cylinders reinforced by wavy carbon nanotube based on meshfree method, Journal of Composite Materials 48(15): 19011913.##[45] Pourseifi M., Rahmani O., Hoseini S.A., 2015, Active vibration control of nanotube structures under a moving nanoparticle based on the nonlocal continuum theories, Meccanica 50(5): 13511369.##[46] Mahdavi M., Jiang L., Sun X., 2011, Nonlinear vibration of a doublewalled carbon nanotube embedded in a polymer matrix, Physica E: LowDimensional Systems and Nanostructures 43(10): 18131819.##[47] Kiani K., 2010, Free longitudinal vibration of tapered nanowires in the context of nonlocal continuum theory via a perturbation technique, Physica E: LowDimensional Systems and Nanostructures 43(1): 387397.##[48] Askari H., Esmailzadeh E., Zhang D., 2014, Nonlinear vibration analysis of nonlocal nanowires, Composites Part B: Engineering 67: 607613.##[49] Ansari R., Torabi J., Shojaei M.F., 2017, Buckling and vibration analysis of embedded functionally graded carbon nanotubereinforced composite annular sector plates under thermal loading, Composites Part B: Engineering 109: 197213.##[50] Yas M., Heshmati M., 2012, Dynamic analysis of functionally graded nanocomposite beams reinforced by randomly oriented carbon nanotube under the action of moving load, Applied Mathematical Modelling 36(4): 13711394.##[51] Şimşek M., 2010, Vibration analysis of a singlewalled carbon nanotube under action of a moving harmonic load based on nonlocal elasticity theory, Physica E: LowDimensional Systems and Nanostructures 43(1): 182191.##[52] Malekzadeh P., Zarei A., 2014, Free vibration of quadrilateral laminated plates with carbon nanotube reinforced composite layers, ThinWalled Structures 82: 221232.##[53] Joshi A.Y., Harsha S., Sharma S.C., 2010, Vibration signature analysis of single walled carbon nanotube based nanomechanical sensors, Physica E: LowDimensional Systems and Nanostructures 42(8): 21152123.##[54] Aydogdu M., 2012, Axial vibration analysis of nanorods (carbon nanotubes) embedded in an elastic medium using nonlocal elasticity, Mechanics Research Communications 43: 3440.##[55] Aydogdu M., 2015, A nonlocal rod model for axial vibration of doublewalled carbon nanotubes including axial van der Waals force effects, Journal of Vibration and Control 21(16): 31323154.##[56] Murmu T., Adhikari S., 2010, Nonlocal effects in the longitudinal vibration of doublenanorod systems, Physica E: LowDimensional Systems and Nanostructures 43(1): 415422.##[57] Şimşek M., 2012, Nonlocal effects in the free longitudinal vibration of axially functionally graded tapered nanorods, Computational Materials Science 61: 257265.##[58] Murmu T., Adhikari S., 2011, Axial instability of doublenanobeamsystems, Physics Letters A 375(3): 601608.##[59] Danesh M., Farajpour A., Mohammadi M., 2012, Axial vibration analysis of a tapered nanorod based on nonlocal elasticity theory and differential quadrature method, Mechanics Research Communications 39(1): 2327.##[60] Filiz S., Aydogdu M., 2010, Axial vibration of carbon nanotube heterojunctions using nonlocal elasticity, Computational Materials Science 49(3): 619627.##[61] Mohammadian M., Abolbashari M.H., Hosseini S.M., 2019, Axial vibration of heterojunction CNTs mass nanosensors by considering the effects of small scale and connecting region: An analytical solution, Physica B: Condensed Matter 553: 137150.##[62] Liu K.C., Friend J., Yeo L., 2009, The axial–torsional vibration of pretwisted beams, Journal of Sound and Vibration 321(12): 115136.##[63] Aydogdu M., Filiz S., 2011, Modeling carbon nanotubebased mass sensors using axial vibration and nonlocal elasticity, Physica E: LowDimensional Systems and Nanostructures 43(6): 12291234.##[64] Bouadi A., 2018, A new nonlocal HSDT for analysis of stability of single layer graphene sheet, Advances in Nano Research 6(2): 147162.##[65] HamzaCherif R., 2018, Vibration analysis of nano beam using differential transform method including thermal effect, Journal of Nano Research 54: 114.##[66] Kadari B., 2018, Buckling analysis of orthotropic nanoscale plates resting on elastic foundations, Journal of Nano Research 55: 4256.##[67] Yazid M., 2018, A novel nonlocal refined plate theory for stability response of orthotropic singlelayer graphene sheet resting on elastic medium, Smart Structures and Systems 21(1): 1525.##[68] Youcef D.O., 2018, Dynamic analysis of nanoscale beams including surface stress effects, Smart Structures and Systems 21(1): 6574.##[69] Draoui A., 2019, Static and dynamic behavior of nanotubesreinforced sandwich plates using (FSDT), Journal of Nano Research 57: 117135.##[70] Mokhtar Y., 2018, A novel shear deformation theory for buckling analysis of single layer graphene sheet based on nonlocal elasticity theory, Smart Structures and Systems 21(4): 397405.##[71] Boutaleb S., 2019, Dynamic analysis of nanosize FG rectangular plates based on simple nonlocal quasi 3D HSDT, Advances in Nano Research 7(3): 189206.##[72] Karami B., 2018, A sizedependent quasi3D model for wave dispersion analysis of FG nanoplates, Steel and Composite Structures 28(1): 99110.##[73] Karami B., Janghorban M., Tounsi A.,2018, Nonlocal strain gradient 3D elasticity theory for anisotropic spherical nanoparticles, Steel and Composite Structures 27(2): 201216.##[74] Karami B., Janghorban M., Tounsi A., 2018, Variational approach for wave dispersion in anisotropic doublycurved nanoshells based on a new nonlocal strain gradient higher order shell theory, ThinWalled Structures 129: 251264.##[75] Bellifa H., 2017, A nonlocal zerothorder shear deformation theory for nonlinear postbuckling of nanobeams, Structural Engineering and Mechanics 62(6): 695702.##[76] Karami B., Janghorban M., Tounsi A., 2017, Effects of triaxial magnetic field on the anisotropic nanoplates, Steel and Composite Structures 25(3): 361374.##[77] Bouafia K., 2017, A nonlocal quasi3D theory for bending and free flexural vibration behaviors of functionally graded nanobeams, Smart Structures and Systems 19(2): 115126.##[78] Zemri A., 2015, A mechanical response of functionally graded nanoscale beam: an assessment of a refined nonlocal shear deformation theory beam theory, Structural Engineering and Mechanics 54(4): 693710.##[79] Şimşek M., 2011, Nonlocal effects in the forced vibration of an elastically connected doublecarbon nanotube system under a moving nanoparticle, Computational Materials Science 50(7): 21122123.##]
1

ReliabilityBased Robust MultiObjective Optimization of Friction Stir Welding Lap Joint AA1100 Plates
http://jsm.iauarak.ac.ir/article_677464.html
10.22034/jsm.2019.1877986.1493
1
The current paper presents a robust optimum design of friction stir welding (FSW) lap joint AA1100 aluminum alloy sheets using Monte Carlo simulation, NSGAII and neural network. First, to find the relation between the inputs and outputs a perceptron neural network model was obtained. In this way, results of thirty friction stir welding tests are used for training and testing the neural network. Using such obtained neural network model, for the reliability robust design of the FSW, a multiobjective genetic algorithm is employed. In this way, the statistical moments of the forces, temperature, strength, elongation, microhardness of welded zone, grain size and welded zone thickness are considered as the conflicting objectives. The optimization process was followed by multi criteria decision making process, NIP and TOPSIS, to propose optimum points for each of the pin profiles. It is represented that some beneficial design principles are involved in FSW which were discovered by the proposed optimization process.
0

600
606


E
Sarikhani
Automotive Simulation and Optimal Design Research Laboratory, School of Automotive Engineering, Tehran, Iran
Iran


A
Khalkhali
University of Science and Technology, Tehran, Iran
Iran
ab.khalkhali1@gmail.com
Robust design optimization
Friction Stir Welding
MultiObjective Optimization
Perceptron Neural Network
[[1] Thomas W.M., Nicholas E.D., Needham J.C., Murch M.G., TempleSmith P., Dawes C.J.,1995, Friction Welding, In Google Patents.##[2] Dawes C., Thomas W., 1995, Friction stir joining of aluminium alloys, TWI Bulletin 6(1): 1.##[3] Vijayan S., Raju R., Rao S.R.K., 2010, Multiobjective optimization of friction stir welding process parameters on aluminum alloy AA 5083 using taguchibased grey relation analysis, Materials and Manufacturing Processes 25(11): 12061212.##[4] Suresha C., Rajaprakash B., Upadhya S., 2011, A study of the effect of tool pin profiles on tensile strength of welded joints produced using friction stir welding process, Materials and Manufacturing Processes 26(9): 11111116.##[5] Cox C.D., Gibson B.T., Strauss A.M., Cook G.E., 2012, Effect of pin length and rotation rate on the tensile strength of a friction stir spotwelded al alloy: a contribution to automated production, Materials and Manufacturing Processes 27(4): 472478.##[6] Ganesh P., Kumar V.S., 2015, Superplastic forming of friction stir welded AA6061T6 alloy sheet with various tool rotation speed, Materials and Manufacturing Processes 30(9): 10801089.##[7] Montazerolghaem H., Badrossamay M., Tehrani A.F., Rad S.Z., Esfahani M.S., 2015, Dualrotation speed friction stir welding: Experimentation and modeling, Materials and Manufacturing Processes 30(9): 11091114.##[8] Shojaeefard M.H., Behnagh R.A., Akbari M., Givi M.K.B., Farhani F., 2013, Modelling and Pareto optimization of mechanical properties of friction stir welded AA7075/AA5083 butt joints using neural network and particle swarm algorithm, Materials & Design 44: 190198.##[9] Buffa G., Fratini L., Micari F., 2012, Mechanical and microstructural properties prediction by artificial neural networks in FSW processes of dual phase titanium alloys, Journal of Manufacturing Processes 14(3): 289296.##[10] Okuyucu H., Kurt A., Arcaklioglu E., 2007, Artificial neural network application to the friction stir welding of aluminum plates, Materials & Design 28(1): 7884.##[11] Shojaeefard M.H., Akbari M., Tahani M., Farhani F., 2013, Sensitivity analysis of the artificial neural network outputs in friction stir lap joining of aluminum to brass, Advances in Materials Science and Engineering 2013: 574914.##[12] Asadi P., Besharati Givi M. K., Rastgoo A., Akbari M., Zakeri V., Rasouli S., 2012, Predicting the grain size and hardness of AZ91/SiC nanocomposite by artificial neural networks, International Journal of Advanced Manufacturing Technology 63:10951107.##[13] Collette Y., Siarry P., 2003, Multiobjective Optimization: Principles and Case Studies, Decision Engineering Series, Springer, Berlin.##[14] Srinivas N., Deb K., 1994, Multiobjective optimization using nondominated sorting in genetic algorithms, Evolutionary Computation 2(3): 221248.##[15] NarimanZadeh N., Darvizeh A., Jamali A., 2006, Pareto optimization of energy absorption of square aluminum columns using multiobjective genetic algorithms, Journal of Engineering Manufacture, Proceedings of the Institution of Mechanical Engineers, Part B 220(2): 213224.##[16] Atashkari K., NarimanZadeh N., Go¨lcu M., Khalkhali A., Jamali A., 2007, Modelling and multiobjective optimization of a variable valvetiming sparkignition engine using polynomial neural networks and evolutionary algorithms, Journal of Energy Conversion and Management 48: 10291041.##[17] Amanifard N., NarimanZadeh N., Borji M., Khalkhali A., Habibdoust A., 2008, Modelling and Pareto optimization of heat transfer and ﬂow coefficients in micro channels using GMDH type neural networks and genetic algorithms, Journal of Energy Conversion and Management 49: 311325.##[18] Khalkhali A., Safikhani H., 2012, Applying evolutionary optimization on the airfoil design, Journal of Computational and Applied Research in Mechanical Engineering 2(1): 5162.##[19] Shojaeefard M.H., Khalkhali A., Faghihian H., Dahmardeh M., 2018, Optimal platform design using nondominated sorting genetic algorithm II and technique for order of preference by similarity to ideal solution; application to automotive suspension system, Engineering Optimization 50(3): 471482.##[20] Khalkhali A., Khakshournia S., Narimanzadeh N., 2014, A hybrid method of FEM, modified NSGAII and TOPSIS for structural optimization of sandwich panels with corrugated core, Journal of Sandwich Structures & Materials 16(4): 398417.##[21] Khalkhali A., 2015, Best compromising crashworthiness design of automotive Srail using TOPSIS and modified NSGAII, Journal of Central South University 22(1):121133.##[22] Jamali A., Hajiloo A., Narimanzadeh N., 2010, Reliability based robust Pareto design of linear state feedback controllers using a multiobjective uniformdiversity genetic algorithm (MUGA), Expert Systems With Applications 37: 401413.##[23] LÖnn D., Öman M., Nilsson L., Simonsson K., Finite element based robustness study of a truck cab subjected to impact loading, International Journal of Crashworthiness 14(2): 111124.##[24] Ditlevsen O., Madsen O.H.,1996, Structural Reliability Methods, John Wiley and Sons, New York.##[25] Papadrakakis M., Lagaros N.D., Plevris V., 2004, Structural optimization considering the probabilistic system response, International Journal of Theoretical and Applied Mechanics 31(34): 361393.##[26] Khakhali A., Narimanzadeh N., Darvizeh A., Masoumi A., Notghi B., 2010, Reliabilitybased robust multiobjective crashworthiness optimisation of Sshaped box beams with parametric uncertainties, International Journal of Crashworthiness 15(4): 443456.##[27] Khakhali A., Darvizeh A., Masoumi A., Narimanzadeh N., Shiri A., 2010, Robust design of sshaped box beams subjected to compressive load, Mathematical Problems in Engineering 2010: 627501.##[28] Fonseca C.M., Fleming P.J., 1996, Nonlinear system identification with multiobjective genetic algorithms, Proceedings of the 13th World Congress, International Federation of Automatic Control, Pergamon Press, San Francisco.##[29] Iba H., Kuita T., deGaris H., Sator T., 1993, System identification using structured genetic algorithms, Proceedings of 5th International Conference on Genetic Algorithms, Urbana.##[30] Khalkhali A., EbrahimiNejad S., Malek N.G., 2018, Comprehensive optimization of friction stir weld parameters of lap joint AA1100 plates using artificial neural networks and modified NSGAII, Materials Research Express 5(6): 066508.##]
1

Vibration of Timoshenko BeamSoil Foundation Interaction by Using the Spectral Element Method
http://jsm.iauarak.ac.ir/article_677316.html
10.22034/jsm.2020.1879476.1503
1
This article presents an analysis of free vibration of elastically supported Timoshenko beams by using the spectral element method. The governing partial differential equation is elaborated to formulate the spectral stiffness matrix. Effectively, the non classical end boundary conditions of the beam are the primordial task to calibrate the phenomenon of the Timoshenko beamsoil foundation interaction. Nondimensional natural frequencies and shape modes are obtained by solving the partial differential equations, numerically. Upon solving the eigenvalue problem, nondimensional frequencies are computed for the first three modes of vibration. Obtained results of this study are intended to describe multiple objects, such as: (1) the establishment of the modal analysis with and without elastic springs, (2) the quantification of the influence of the beam soil foundation interaction, (3) the influence of soil foundation stiffness’ on free vibration characteristics of Timoshenko beam. For this propose, the first three eigenvalues of Timoshenko beam are calculated and plotted for various stiffness of translational and rotational springs.
0

607
619


S
Hamioud
Department of Civil Engineering, University of Jijel, Jijel, Algeria
Algeria


S
Khalfallah
Department of Mechanical Engineering, National Polytechnic School, Constantine, Algeria
Algeria
khalfallah_s25@yahoo.com


S
Boudaa
Civil Engineering Department, University of Constantine, Constantine, Algeria
Algeria
Freevibration
Non classical boundary conditions
Timoshenko beam
Spectral element method
Finite Element Method
Beamsoil foundation interaction
Mechanical properties of soil
[[1] Tabatabaiefar H.R., Clifton T., 2016, Significance of considering soilstructure interaction effects on seismic design of unbraced building frames resting on soft soils, Australian Geomechanics 5(1): 5566.##[2] Mohod M.V., Dhadse G.D., 2014, Importance of soil structure interaction for framed structure, International Conference on Advances in Civil and Mechanical Engineering Systems, Surat, India.##[3] Lee U., 2009, Spectral element analysis method, In Spectral Element Method in Structural Dynamics, Chichester, UK.##[4] Hamioud S., Khalfallah S., 2016, Freevibration of BernoulliEuler Beam by the spectral element method, Technical Journal 10(34): 106112.##[5] Hamioud S., Khalfallah S., 2018, Freevibration of Timoshenko Beam using the spectral element method, International Journal for Engineering Modelling 31(12): 6176.##[6] Kocaturk T., Şimşek M., 2005, Free vibration analysis of Timoshenko beams under various boundary conditions, Sigma Journal of Engineering and Natural Sciences 3: 7993.##[7] Lee U., Cho J., 2008, FFTbased spectral element analysis for the linear continuum dynamic systems subjected to arbitrary initial conditions by using the pseudoforce method, International Journal for Numerical Methods in Engineering 74: 159174.##[8] Gopalakrishnan S., Chakraborty A., Roy Mahapatra D., 2008, Spectral Finite Element Method: Wave Propagation, Diagnostics and Control in Anisotropic and Inhomogenous Structures, Springer, London.##[9] Abbas B.A.H., 1984, Vibrations of beams with elastically restrained end, Journal of Sound and Vibration 97: 541548.##[10] Hernandez E., Otrola E., Rodriguez R., Sahueza F., 2008, Finite element approximation of the vibration problem for a Timoshenko curved rod, Revista de La Union Matemtica 49: 1528.##[11] Azevedo A.S.D.C, Vasconcelos A.C.A., Hoefel S.D.S., 2016, Dynamic analysis of elastically supported Timoshenko beam, XXXVII Iberian Latin American Congress on Computational Methods in Engineering, Brazilia, Brazil.##[12] Lee J., Schultz W.W., 2004, Eigenvalue analysis of Timoshenko beams and axisymmetric Mindlin plates by the pseudospectral method, Journal of Sound and Vibration 269: 609621.##[13] Zhou D., 2001, Free vibration of multispan Timoshenko beams using static Timoshenko beam functions, Journal of Sound and Vibration 241: 725734.##[14] Farghaly S.H., 1994, Vibration and stability analysis Timoshenko beams with discontinuities in crosssection, Journal of Sound and Vibration 174: 591605.##[15] Banerjee J.R., 1998, Free vibration of axially loaded composite Timoshenko beams using the dynamic stiffness matrix method, Computers & Structures 69: 197208.##[16] Lee Y.Y., Wang C.M., Kitipornchai S., 2003, Vibration of Timoshenko beams with internal hinge, Journal of Engineering Mechanics 129(3): 293301.##[17] Auciello N.M., Ercolano A., 2004, A general solution for dynamic response of axially loaded nonuniform Timoshenko beams, Journal of Solids and Structures 41(1819): 48614874.##[18] Thom T.T., Kien N.D., 2018, Free vibration of twodirectional FGM beams using a higherorder Timoshenko beam element, Vietnam Journal of Science and Technology 56(3): 380396.##[19] Shali S., Jafarali P., Nagaraja S.R., 2018, Identification of second spectrum of a Timoshenko beam using differential transform method, Journal of Engineering Science and Technology 13(4): 893908.##[20] Magdalena P., 2018, Spectral methods for modeling of wave propagation in structure in terms of damage detection A review, Applied Sciences Journal 8(7): 125.##[21] Sarigul M., 2018, Effect of elastically supports on nonlinear vibrations of a slightly curved beam, Uludag University Journal of the Faculty of Engineering 23(2): 255274.##[22] Hamioud S., Khalfallah S., 2017, Dynamic analysis of rods using the spectral element method, Algerian & Equipment Journal 57: 4955.##[23] Boudaa S., Khalfallah S., Hamioud S., 2019, Dynamic analysis of soilstructure interaction by the spectral element method, Innovative Infrastructure Solutions 4(1): 40.##[24] Ruta P., 1999, Application of Chebyshev series to solution of nonprismatic beam vibration problems, Journal of Sound and Vibration 227(2): 449467.##[25] Chen G., Qian L., Yin Q., 2014, Dynamic analysis of a Timoshenko beam subjected to an accelerating mass using spectral element method, Shock and Vibration 2014: 12.##]
1

Numerical Analysis of the Effect of External Circumferential Cracks in Transition Thickness Zone of Pressurized Pipes Using XFEM – ElasticPlastic Behavior
http://jsm.iauarak.ac.ir/article_677283.html
10.22034/jsm.2019.1882104.1511
1
The elasticplastic behavior of the material is considered to analyze the effect of an external circumferential crack on a pipe with thickness transition and double slopes. Using the extended finite element method (XFEM), the Jintegral of 3D cracks were investigated and compared between straight pipes and pipes with thickness transition and different slopes. Considering internal pressure, this work highlighted the investigation of a 3D crack problem in a thickness transition pipe with a double slope, In the extended finite element method (XFEM), the level sets and the enrichment zone were defined. A crack is easily modeled by enrichment functions. The comparison between the values of the Jintegral showed that the pipe containing thickness transition with double slopes is more sensitive to the considered cracks, more precisely, the parameters of the first thickness transition have more influence on the variation of Jintegral than the parameters of the second thickness transition. The decreasing of the angle of the slopes and the increase of the ratio of the thicknesses is one effective method of reducing the Jintegral.
0

620
631


H
Salmi
Department of National Higher School of Mechanics, ENSEM, Laboratory of Control and Mechanical Characterization of Materials and Structures, Morocco
Morocco
houda.salmi111@gmail.com


Kh
EL Had
Institute of Maritims Studies, Laboratory of Materials and Structures Casablanca, Morocco
Morocco


H
EL Bhilat
Department of National Higher School of Mechanics, ENSEM, Laboratory of Control and Mechanical Characterization of Materials and Structures, Morocco
Morocco


A
Hachim
Institute of Maritims Studies, Laboratory of Materials and Structures Casablanca, Morocco
Morocco
Elasticplastic
Pipe with thickness transition and double slope
Threedimensional crack
XFEM
Jintegral
[[1] Rahman S., Ghadiali N., Wilcowski G.M., Moberg F., Brickstad B., 1998, Crackopeningarea analysis for circumferential troughwall cracks restrain of bending thickness transition and weld residual stresses, International Journal of Pressure Vessels and Piping 75: 397415.##[2] Électricité de F., 1997, RSEM: Règles de Surveillance en Exploitation des Matériels Mécaniques des Ilots Nucléaires REP, Edition AFCEN.##[3] Abdelkader S., Saıd H., 2006, Numerical study of elliptical cracks in cylinders with a thickness transition, International Journal of Pressure Vessels and Piping 83: 3541.##[4] Abdelkader S., Saıd H., 2006, Comparison of semielliptical cracks in cylinders with a thickness transition and in a straight cylinder – Elasticplastic behavior, Engineering Fracture Mechanics 73: 26852697.##[5] Wessel E.T., Murrysville P.A., Server W.L., Kennedy E.L., 1991, Primer: Fracture Mechanics in the Nuclear Power Industry, EPRI Report, NP5792SR.##[6] CEA: The French Alternative Energies and Atomic Energy Commission, Commissariat à L’Energie Atomique (France)’, http://www.cea.fr/.##[7] CASTEM, http://wwwcast3m.cea.fr/##[8] Chapuliot S., Lacire M.H., 1999, Stress intensity factors for external circumferential cracks in tubes over a wide range of radius over thickness ratios, American Society of Mechanical Engineers, Pressure Vessels and Piping Division 1999 :395106.##[9] Le Delliou P., Porte P., Code RSEM: calcul simplifié du paramètre J pour un défaut axisymétrique débouchant en surface externe d’une transition d’épaisseur, RAPPORT EDF HT2C/99/025/A.##[10] Idapalapati S., Xiao Z.M., Yi D., Kumar S.B., 2012, Fracture analysis of girth welded pipelines with 3D embedded cracks subjected to biaxial loading conditions, Engineering Fracture Mechanics 96: 570587.##[11] Xiao Z., Zhang Y., Luo J., 2018, Fatigue crack growth investigation on offshore pipelines with threedimensional interacting cracks, Geoscience Frontiers 9(6): 16891698.##[12] Salmi H., El Had Kh., El Bhilat H., Hachim A., 2019, Numerical analysis of the effect of external circumferential elliptical cracks in transition thickness zone of pressurized pipes using XFEM, Journal of Applied and Computational Mechanics 5(5): 861874.##[13] Salmi H., El Had Kh., El Bhilat H., Hachim A., 2019, Numerical modeling and comparison study of elliptical cracks effect on the pipes straight and with thickness transition exposed to internal pressure, using XFEM in elastic behavior, Journal of Computational and Applied Research in Mechanical Engineering 5(5):861874.##[14] SzuYing W., BorJiun T., JienJong Ch., 2015, Elasticplastic finite element analyses for reducers with constantdepth internal circumferential surface cracks, International Journal of Pressure Vessels and Piping 131: 1014.##[15] Zhibo M., Zhao Y., 2018,Verification and validation of common derivative terms approximation in meshfree numerical scheme, Journal of Computational and Applied Research in Mechanical Engineering 4(3): 231244.##[16] Yazdani M., 2018, A novel modification of decouple scaled boundary finite element method in fracture mechanics problems, JCARME 7(2): 243260.##[17] Surendran M., Pramod A.L.N., Nataraj S., 2019, Evaluation of fracture parameters by coupling the edgebased smoothed finite element method and the scaled boundary finite element method, Journal of Computational and Applied Research in Mechanical Engineering 5(3): 540551.##[18] Moës N., Gravouil A., Belytschko T., 2002, Nonplanar 3D crack growth by the extended finite element and level sets, Part I: Mechanical model, International Journal for Numerical Methods in Engineering 53: 25492568.##[19] Belytschko T., Black T., 1999, Elastic crack growth in finite elements with minimal remeshing, International Journal for Numerical Methods in Engineering 45: 601620.##[20] Stolarska M., Chopp D., Moes N., Belytschko T., 2001, Modelling crack growth by level sets in the extended finite element method, International Journal for Numerical Methods in Engineering 51: 943960.##[21] Kumar S., Singh I.V., Mishra B.K., 2013, Numerical investigation of stable crack growth in ductile materials using XFEM, Procedia Engineering 64: 652660.##[22] Malekan M., Khosravi A., Cimini Jr C.A.,2019, Deformation and fracture of cylindrical tubes under detonation loading: A review of numerical and experimental analyses, International Journal of Pressure Vessels and Piping 173: 114132.##[23] Sharma K., Singh I.V., Mishra B.K., Bhasin V., 2014, Numerical modeling of partthrough cracks in pipe and pipe bend using XFEM, Procedia Materials Science 6: 7279.##[24] Kwang S.W., Prodyot B., 2004, Jintegral and fatigue life computations in the incremental plasticity analysis of large scale yielding by pversion of F.E.M., Structural Engineering & Mechanics 17(1): 5168.##[25] Guangzhong L., Guangzhong L., Dai Z., Jin M., Zhaolong H., 2016, Numerical investigation of mixedmode crack growth in ductile material using elasticplastic XFEM, Journal of the Brazilian Society of Mechanical Sciences and Engineering 38: 16891699.##[26] Liu X., Lu Z.X., Chen Y., Sui Y. L., Dai L.H., 2018, Failure assessment for the highstrength pipelines with constantdepth circumferential surface cracks, Hindawi Advances in Materials Science and Engineering 36835: 111.##[27] Irwin G.R., 1961, Plastic zone near a crack and fracture toughness, Sagamore Research Conference Proceedings 4: 6378.##[28] French construction code, construction des appareils à pression non soumis à l’action de la flamme, The Code for construction of unfired pressure vessels, Division 1, part C – design and calculation, section C2 – rules for calculating cylindrical, spherical and conical shell subjected to internal pressure.##[29] Kumar V., German M., 1988, ElasticPlastic Fracture Analysis of ThroughWall and Surface Flaws in Cylinders, EPRI Topical Report, NP5596, Electric Power Research Institute, Palo Alto, CA.##[30] Van V., Krystyn J., 2006, Mechanical Behavior of Materials.##[31] Sukumar N., Chopp D.L., Moran B., 2003, Extended finite element method and fast marching method for threedimensional fatigue crack propagation, Engineering Fracture Mechanics 70: 2948.##[32] Eshelby J.D., 1956, The continuum theory of lattice defects, Solid State Physics 3: 79144.##[33] Mahaffey R.M., Van Vuuren S.J., 2014, Review of pump suction reducer selection: Eccentric or concentric reducers, Journal of the South African Instituti Engineering 56(3): 6576.##[34] ELGharib J., 2009, Macro commande MACR_ASCOUF_MAIL, Code Aster Clé: U4.CF.10, Révision: 1122, Document diffusé sous licence Gnufdl.##]
1

Investigation of Strain Gradient Theory for the Analysis of Free Linear Vibration of Nano Truncated Conical Shell
http://jsm.iauarak.ac.ir/article_677402.html
10.22034/jsm.2019.1882391.1513
1
In this paper the nano conical shell model is developed based on modified strain gradient theory. The governing equations of the nano truncated conical shell are derived using the FSDT, and the size parameters through modified strain gradient theory have been taken into account. Hamilton’s principle is used to obtain the governing equations, and the shell’s equations of motion are derived with partial differentials along with the classical and nonclassical boundary conditions. Galerkin’s method and the Generalized Differential Quadrature (GDQ) approach are applied to obtain the linear free vibrations of the carbon nano cone (CNC). The CNC is studied with simply supported boundary condition. The results of the new model are compared with those of the classical and couple stress theories, which point to the conclusion that the classical and couple stress models are special cases of modified strain gradient theory. Results also reveal that rigidity of the nano truncated conical shell in the strain gradient theory is greater than that in the modified couple stress and classical theories respectively, which leads to an increase in dimensionless natural frequency ratio. Moreover, the study investigates the effect of the size parameters on nano shell vibration for different lengths and vertex angles.
0

632
648


A.R
Sheykhi
Department of Mechanical Engineering , Science and Research Branch, Islamic Azad University, Tehran, Iran
Iran


Sh
Hosseini Hashemi
School of Mechanical Engineering, Iran University of Science and Technology, Tehran, Iran
Iran


A
Maghsoudpour
Department of Mechanical Engineering , Science and Research Branch, Islamic Azad University, Tehran, Iran
Iran
a.maghsoudpour@srbiau.ac.ir


Sh
Etemadi Haghighi
Department of Mechanical Engineering , Science and Research Branch, Islamic Azad University, Tehran, Iran
Iran
GDQ Method
Galerkin’s method
Strain gradient theory
Carbon nano cone (CNC
[[1] FirouzAbadi R.D., Fotouhi M.M., Haddadpour H., 2011, Free vibration analysis of nano cones using a nonlocal continuum model, Physics Letters A 375(41): 35933598.##[2] Firouz Abadi R.D., Fotouhi M.M., Haddadpour H., 2012, Stability analysis of nano cones under external pressure and axial compression using nonlocal shell model, Physica E: LowDimensional Systems and Nanostructures 44(9): 18321837.##[3] Fotouhi M.M., FirouzAbadi R.D., Haddadpour H., 2013, Free vibration analysis of nano cones embedded in an elastic medium using a nonlocal continuum shell model, International Journal of Engineering Science 64(1): 1422.##[4] Tadi Beni Y., Soleimani I., 2015, Free torsional vibration and static analysis of the conical nanoshell based on modified couple stress theory, 3rd International Conference on Nanotechnology of Science and Research Pioneers Institute, Istanbul, Turkey.##[5] Zeighampour H., Tadi Beni Y., Mehralian F., 2015, A shear deformable conical shell formulation in the frame work of couple stress theory, Acta Mechanica 226(8): 26072629.##[6] Zeighampour H., Tadi Beni Y., 2014, Analysis of conical shells in the framework of coupled stresses, International Journal of Engineering Science 81: 107122.##[7] Sofiyev A.H., 2013, The nonlinear dynamics of FGM truncated conical shells surrounded by an elastic medium, International Journal of Mechanical Sciences 66: 3344.##[8] Sofiyev A.H., Kuruoglu N., 2011, Natural frequency of laminated orthotropic shells with different boundary conditions and resting on the Pasternak type elastic foundation, Composites: Part B 42(6): 15621570.##[9] Sofiyev A.H., Kuruoglu N., 2014, Nonlinear buckling of an FGM truncated conical shell surrounded by an elastic medium, ThinWalled Structures 80: 178191.##[10] Sofiyev A.H., 2014, Largeamplitude vibration of nonhomogenous orthotropic composite truncated conical shells, Composites Part B: Engineering 61: 365374.##[11] Mehri M., Asadi H., Wang Q., 2016, Buckling and vibration analysis of a pressurized CNT reinforced functionally graded truncated conical shell under an axial compression using HDQ method , Computer Methods in Applied Mechanics and Engineering 303: 75100.##[12] Ansari R., Rouhi H., Rad A.N., 2014, Vibrational analysis of carbon nanocones under different boundary conditions:an analytical approach, Mechanics Research Communications 56: 130135.##[13] Kamarian S., Salim M., Dimitri R., Tornabene F., 2016, Free vibration analysis of conical shells reinforced with agglomerated carbon nanotubes, International Journal of Mechanical Sciences 108109: 157165.##[14] Sofiyev A.H., 2012, Largeamplitude vibration of nonhomogenous orthotropic composite truncated conical shells, Composites Part B: Engineering 94(7): 22372245.##[15] Tohidi H. , HosseiniHashemi S.H., Maghsoudpour A., Etemadi S., 2017, Strain gradient theory for vibration analysis of embedded CNTreinforced micro Mindlin cylindrical shells considering agglomeration effects, Structural Engineering and Mechanics 62(5):551565.##[16] Zeighampour H., Tadi Beni Y., 2014, Cylindrical thinshell model based on modified strain gradient theory, International Journal of Engineering Science 78: 2747.##[17] Tadi Beni Y., Mehralian F., Razavi H., 2014, Free vibration analysis of sizedependent shear deformable functionally graded cylindrical shell on the basis of modified couple stress theory, Composite Structures 111: 349353.##[18] Gholami R., Darvizeh A., Ansari R., Sadeghi F., 2016, Vibration and buckling of firstorder shear deformable circular cylindrical micro/nanoshells based on Mindlinʼs strain gradient elasticity theory, European Journal of Mechanics A/Solids 58: 7688.##[19] Zhang B., He Y., Liu D., Shen L., Lei J., 2015, Free vibration analysis of fourunknown shear deformable functionally graded cylindrical micro shells based on the strain gradient elasticity theory, Composite Structures 119: 578597.##[20] Bakhtiari M., Lakis A., Kerboua Y., 2018, Nonlinear vibration of truncated conical shells: Donnell, sanders and nemeth theories, Rapport Technique n°EPMRT 01.##[21] Tohidi H., HosseiniHashemi Sh., Maghsoudpour A., Etemadi Haghighi Sh., 2017, Dynamic stability of FGCNTreinforced viscoelastic micro cylindrical shells resting on nonhomogeneous orthotropic viscoelastic medium subjected to harmonic temperature distribution and 2D magnetic field, Wind and Structures 25(2): 131156.##[22] Ghadiri M., Shafiei N., 2015, Nonlinear bending vibration of a rotating nanobeam based on nonlocal Eringen’s theory using differential quadrature method, Microsystem Technologies 22(12): 28532867.##[23] Malekzadeh P., Golbahar Haghighi M.R., Shojaee M., 2014, Nonlinear free vibration of skew nano plates with surface and small scale effects, ThinWalled Structures 78: 4856.##[24] Lam D.C.C., Yang F., Chong A.C.M., Wang J., Tong P., 2003, Experiments and theory in strain gradient elasticity, Journal of the Mechanics and Physics of Solids 51(8): 14771508.##[25] Reddy J.N., 2002, Mechanics of Laminated Composite Plates and Shells: Theory and Analysis, CRC Press, Boca Raton, USA.##]
1

Study of Torsional Vibrations of Composite Poroelastic Spherical ShellBiot’s Extension Theory
http://jsm.iauarak.ac.ir/article_677455.html
10.22034/jsm.2020.1885789.1529
1
Torsional vibrations of composite poroelastic dissipative spherical shell are investigated in the framework of Biot’s extension theory.Here composite poroelastic spherical shell consists of two spherical shells, one is placed on other, and both are made of different poroelastic materials. Consideration of the stressfree boundaries of outer surface and the perfect bonding between two shells leads to complex valued frequency equation. Limiting case when the ratio of thickness to inner radius is very small is investigated numerically. In this case, thick walled composite spherical shell reduces to thin composite spherical shell. For illustration purpose, four composite materials, namely, Berea sandstone saturated with water and kerosene, Shale rock saturated with water and kerosene are employed. The particular cases of a poroelastic solid spherical shell and poroelastic thick walled hollow spherical shell are discussed. If the shear viscosity of fluid is neglected, then the problem reduces to that of classical Biot’s theory. Phase velocity and attenuation are computed and the results are presented graphically. Comparison is made between the results of Biot’s extension theory and that of classical Biot’s theory. It is conclude that shear viscosity of fluid is causing the discrepancy of the numerical results.
0

649
662


R
Gurijala
Department of Mathematics, Kakatiya University, Warangal, Telangana, India
India
rajitha.akshu@gmail.com


M
Reddy Perati
Department of Mathematics, Kakatiya University, Warangal, Telangana, India
India
Torsional vibrations
Composite spherical shell
Frequency equation
Phase velocity
Attenuation
[[1] Richard Rand H., 1968, Torsional vibrations of elastic prolate spheroids, Journal of the Acoustical Society of America 44 (3): 749751.##[2] Heyliger P.R., Pan E., 2016, Free vibrations of layered magneto electro elastic spheres, Journal of the Acoustical Society of America 140(2): 988999.##[3] Biot M.A., 1956, The theory of propagation of elastic waves in fluidsaturated porous solid, Journal of the Acoustical Society of America 28: 168178.##[4] Shah S.A., Tajuddin M., 2011, Torsional vibrations of poroelastic prolate spheroids, International Journal of Applied Mechanics and Engineering 16: 521529.##[5] Shanker B., Nageswara Nath C., Ahmed Shah S., Manoj Kumar J., 2013, Vibration analysis of a poroelastic composite hollow sphere, Acta Mechanica 224: 327341.##[6] Rajitha G., Sandhya Rani B., Malla Reddy P., 2012, Vibrations in a plane angular sector of poroelastic elliptic cone, Special Topics and Reviews in Porous Media 3(2): 157168.##[7] Rajitha G., Malla Reddy P., 2014, Investigation of flexural vibrations in poroelastic elliptic cone, Proceedings of International Conference on Mathematical Sciences.##[8] Rajitha G., Malla Reddy P., 2014, Axially symmetric vibrations of composite poroelastic spherical shell, International Journal of Engineering Mathematics 2014: 416406.##[9] Shah A., Nageswaranath Ch., Ramesh M., Ramanamurthy M.V., 2017, Torsional vibrations of coated hollow poroelastic spheres, Open Journal of Acoustics 7: 1826.##[10] Sahay P.N., 1996, Elasto dynamics of deformable porous media, Proceedings of the Royal Society of London A 452: 15171529.##[11] Solorza S., Sahay P.N., 2009, On extensional waves in a poroelastic cylinder within the framework of viscosityextended Biot theory: The case of tractionfree openpore cylindrical surface, Geophysics Journal International 179: 16791702.##[12] Malla Reddy P., Rajitha G., 2015, Investigation of torsional vibrations of thickwalled hollow poroelastic cylinder using Biot's extension theory, Indian Academy of Sciences 40(6): 19251935.##[13] Rajitha G., Malla Reddy P., 2018, Analysis of radial vibrations in thick walled hollow poroelastic cylinder in the framework of Biot’s extension theory, Multidiscipline Modeling in Materials and Structures 14(5): 970983.##[14] Milton A., Irene A.S., 1964, Handbook of Mathematical Functions, Dover Publications, National Bureau of Standard Applied Mathematics Series 55.##[15] Sandhya Rani B., Anand Rao J., Malla Reddy P., 2018, Study of radial vibrations in an infinitely long fluidfilled transversely isotropic thickwalled hollow composite poroelastic cylinders, Journal of Theoretical and Applied Mechanics 48(3): 3144.##]
1

Three Dimensional Thermal Shock Problem in MagnetoThermoelastic Orthotropic Medium
http://jsm.iauarak.ac.ir/article_677284.html
10.22034/jsm.2020.1885944.1530
1
The paper is concerned with the study of magnetothermoelastic interactions in three dimensional thermoelastic medium under the purview of threephaselag model of generalized thermoelasticity. The medium under consideration is assumed to be homogeneous orthotropic medium. The fundamental equations of the threedimensional problem of generalized thermoelasticity are obtained as a vectormatrix differential equation form by employing normal mode analysis which is then solved by eigenvalue approach. Stresses and displacements are presented graphically for different thermoelastic models.
0

663
680


S
Biswas
Department of Mathematics, University of North Bengal, Darjeeling, India
India
siddharthabsws957@gmail.com


S. M
AboDahab
Department of Mathematics, Faculty of Science, Taif University, Saudi Arabia
Department of Mathematics, Faculty of Science, South Valley University, Egypt
Saudi Arabia
sdahb@yahoo.com
Eigenvalue approach
Orthotropic medium
Threephaselag model
Magnetic effect
[[1] Lord H.W., Shulman Y., 1967, A generalized dynamical theory of thermoelasticity, Journal of the Mechanics and Physics of Solids 15: 299309.##[2] Green A.E., Lindsay K.A., Thermoelasticity, Journal of Elasticity 2: 17.##[3] Green A.E., Naghdi P.M., 1991, A reexamination of the basic properties of thermomechanics, Proceedings of Royal Society London Series A 432: 171194.##[4] Green A.E., Naghdi P.M., 1992, On damped heat waves in an elastic solid, Journal of Thermal Stresses 15: 252264.##[5] Green A.E., Naghdi P.M., 1993, Thermoelasticity without energy dissipation, Journal of Elasticity 31: 189208.##[6] Chandrasekharaih D.S., 1986, Thermoelasticity with second sound: A review, Applied Mechanics Reviews 39(3): 355376.##[7] Chandrasekharaih D.S., 1998, Hyperbolic thermoelasticity: A review of recent literature, Applied Mechanics Reviews 51(12): 705729.##[8] Ignaczak J., Hetnarski R.B., 2014, Generalized Thermoelasticity: Mathematical Formulation, Encyclopedia of Thermal Stresses 2014: 19741986.##[9] Tzou D.Y., 1995, A unique field approach for heat conduction from macro to micro scales, Journal of Heat Transfer 117: 816.##[10] Roy Choudhuri S.K., 2007, On a thermoelastic three phase lag model, Journal of Thermal Stresses 30: 231238.##[11] Biswas S., Mukhopadhyay B., Shaw S., 2017, Thermal shock response in magnetothermoelastic orthotropic medium with threephaselag model, Journal of Electromagnetic waves and Applications 31(9): 879897.##[12] Othman M.I.A., Hasona W.M., Mansour N.T., 2015, The effect of magnetic field on generalized thermoelastic medium with two temperature under three phase lag model, Multidiscipline Modeling in Materials and Structures 11(4): 544557.##[13] Said S.M., 2016, Influence of gravity on generalized magnetothermoelastic medium for threephase lag model, Journal of Computational and Applied Mathematics 291:142157.##[14] Othman M.I.A., Said S.M., 2014, 2D problem of magnetothermoelasticity fiber reinforced medium under temperaturedependent properties with threephaselag theory, Meccanica 49(5): 12251243.##[15] ElKaramany A.S., Ezzat M.A., 2004, Thermal shock problem in generalized thermoelasticity under four theories, International Journal of Engineering Science 42: 649671.##[16] Sherief H.H., ElMaghraby N.M., Allam A.A., 2013, Stochastic thermal shock in generalized thermoelasticity, Applied Mathematical Modelling 37: 762775.##[17] Ezzat M.A., Youssef H.M., 2010, Three dimensional thermal shock problem of generalized thermoelastic halfspace, Applied Mathematical Modelling 34: 36083622.##[18] Kalkal K.K., Deswal S., 2014, Effects of phase lags on three dimensional wave propagation with temperature dependent properties, International Journal of Thermophysics 35(5): 952969.##[19] ElKaramany A.S., Ezzat M.A., 2013, On the threephaselag linear micropolar thermoelasticity theory, European Journal of Mechanics A/ Solids 40: 198208.##[20] Ezzat M. A., ElKaramany A.S., Fayik M.A., 2012, Fractional order theory in thermoelastic solid with threephaselag heat transfer, Archive of Applied Mechanics 82(4): 557572.##[21] Said S.M., Othman M.I.A., 2016, Effects of gravitational and hydrostatic initial stress on a twotemperature fiberreinforced thermoelastic medium for threephaselag, Journal of Solid Mechanics 8(4): 806822.##[22] Lofty K.h., 2014, Two temperature generalized magnetothermoelastic interactions in an elastic medium under three theories, Applied Mathematics and Computation 227: 871888.##[23] Sarkar N., Lahiri A., 2012, Electromagnetothermoelastic interactions in an orthotropic slab with two thermal relaxation times, Computational Mathematics and Modelling 23(4): 461477.##[24] Das N.C., Bhakta P.C., 1985, Eigen function expansion method to the solution of simultaneous equations and its application in mechanics, Mechanics Research Communications 12: 1929.##[25] Ezzat M.A., 2006, The relaxation effects of the volume properties of electrically conducting viscoelastic material, Materials Science and Engineering B: SolidState Materials for Advanced Technology 130: 1123.##[26] Ezzat M.A., 2004, Fundamental solution in generalized magnetothermoelasticity with two relaxation times for perfect conductor cylindrical region, International Journal of Engineering Science 42: 15031519.##[27] Ezzat M.A., ElKaramany A.S., ElBary A.A., 2016, Electrothermoelasticity theory with memorydependent heat transfer, International Journal of Engineering Science 99: 2238.##]
1

Moving Three Collinear Griffith Cracks at Orthotropic Interface
http://jsm.iauarak.ac.ir/article_677311.html
10.22034/jsm.2020.1894276.1554
1
This work deals with the interaction of Pwaves between a moving central crack and a pair of outer cracks situated at the interface of an orthotropic layer and an elastic halfspace. Initially, we considered a twodimensional elastic wave equation in orthotropic medium. The Fourier transform has been applied to convert the basic problem to solve the set of four integral equations. These set of integral equations have been solved to to get the analytical expressions for the stress intensity factor (SIF) and crack opening displacements (COD) by using the finite Hilbert transform technique and Cooke’s result. The main objective of this work is to investigate the dynamic stress intensity factors and crack opening displacement at the tips of the cracks. The aims of the study of these physical quantities (SIF, COD) is the prediction of possible arrest of the cracks within a certain range of crack velocity by monitoring applied load. SIF and COD have been depicted graphically for various types of orthotropic materials. We presented a parametric study to explore the influence of crack growing and propagation. This result is very much applicable in bridges, roads, and buildings fractures.
0

681
699


P
Mandal
Department of Civil Engineering, Indian Institute of Technology, Hyderabad, India
India
palas.mandal89@gmail.com


S.C
Mandal
Department of Mathematics, Jadavpur University, India
India
Moving Griffith crack
Orthotropic media
PWave
Stress intensity factor
Crack opening displacement
[[1] Lowengrub M., Srivastava K.N., 1968, On two coplanar Griffith cracks in an infinite elastic medium, International Journal of Engineering Science 6: 359363.##[2] Lowengrub M., 1975, A pair of coplanar cracks at the interface of two bonded dissimilar elastic halfplanes, International Journal of Engineering Science 13: 731741.##[3] Atkinson C., List R.D., 1978, Steadystate crack propagation into media with spatially varying elastic properties, International Journal of Engineering Science 16: 717.##[4] Chen E.P., 1978, Sudden appearance of a crack in a stretched finite strip, Journal of Applied Mechanics 45: 277280.##[5] Itou S., 1978, Dynamic stress concentration around two coplanar Griffith cracks in an infinite elastic medium, Journal of Applied Mechanics 45: 803806.##[6] Itou S., 1980, Diffraction of an antiplane shear wave by two coplanar Griffith cracks in an infinite elastic medium, International Journal of Solids and Structure 16: 11471153.##[7] Srivastava K.N., Palaiya R.M., Karaulia D.S., 1980, Interaction of antiplane shear waves by a Griffith crack at the interface of two bonded dissimilar elastic halfspaces, International Journal of Fracture 16: 349358.##[8] Rose L.R., 1986, Microcrack interaction with the main crack, International Journal of Fracture 31: 233242.##[9] Kundu T., 1987, The transient response of two cracks at the interface of a layered half space, International Journal of Engineering Science 25(1112): 14271439.##[10] Georgiadis H.G., Papadopoulos G.A., 1988, Cracked orthotropic strip with clamped boundaries, Journal of Applied Mathematics and Physics 39: 573578.##[11] Das A.N., Ghosh M.L., 1992, Two coplanar Griffith cracks moving along the interface of two dissimilar elastic medium, Engineering Fracture Mechanic 41: 5969.##[12] Erdogan F., Wu B.,1993, Interface Crack problems in layered orthotropic materials, Journal of Mechanics Physics and Solids 41(5): 889917.##[13] Mandal S.C., Ghosh M.L., 1994, Interaction of elastic waves with a periodic array of coplanar Griffith cracks in an orthotropic medium, International Journal of Engineering Science 32(1): 167178.##[14] Das S., Patra B.,1996, Interaction between threeline cracks in a sandwiched orthotropic layer, Applied Mechanics and Engineering 3: 249269.##[15] Brencich A., Carpinteri A., 1996, Interaction of the main crack with the ordered distribution of microcracks: a numerical technique by displacement discontinuity boundary elements, International Journal of Fracture 76: 373389.##[16] Shabeeb N.I., Binienda W.K., Kreider K. L., 1999, Analysis of driving force for multiple cracks in a nonhomogeneous plate, Journal of Applied Mechanics 66: 501506.##[17] Wang C.Y., RubioGonzale C., Masson J. J., 2001,The dynamics stress intensity factor for a semiinfinite crack in orthotropic materials with concentrated shear impact loads, International Journal of Solids and Structure 38: 12651280.##[18] Li X.F., 2001, Closedform solution for a modeIII interface crack between two bonded dissimilar elastic layers, International Journal of Fracture 109: L3L8.##[19] LiraVergara E., RubioGonzalez C., 2005, Dynamic stress intensity factor of interfacial finite cracks in orthotropic materials subjected to concentrated loads, International Journal of Fracture 135: 285309.##[20] Matbuly M.S., 2006, Analytical solution for an interfacial crack subjected to dynamic antiplane shear loading, Acta Mechanics 163: 7785.##[21] Das S., 2006, Interface Crack problems in layered orthotropic materials, International Journal of Solids and Structure 43: 78807890.##[22] Itou S., 2016, Dynamic stress intensity factors of three collinear cracks in an orthotropic plate subjected to timeharmonic disturbance, Journal of Mechanics 32(5): 491499.##[23] Mandal P., Mandal S.C., 2017, Interface crack at orthotropic media, International Journal of Applied and Computational Mathematics 3(4): 32533262.##[24] Basak P., Mandal S.C., 2017, Semiinfinite moving crack in an orthotropic strip, International Journal of Solids and Structure 128: 221230.##[25] Karan S., Basu S., Mandal S.C., 2018, Impact of a torsional load on a pennyshaped crack sandwiched between two elastic layers embedded in an elastic medium, Acta Mechanica 229: 17591772.##[26] Das S., Debnath L., 2003, Interaction between Griffith Cracks in a sandwiched orthotropic layer, Applied Mathematics Letters 16: 609617.##[27] Bagheri R., Ayatollahi M., Mousavi M., 2015, Analytical solution of multiple moving cracks in functionally graded piezoelectric strip, Applied Mathematics and Mechanics 36(6): 777792.##[28] Monfared M.M., Bagheri R., 2016, Multiple interacting arbitrary shaped cracks in an FGM plane, Theoretical and Applied Fracture Mechanics 86: 161170.##[29] Monfared M.M., Ayatollahi M., Bagheri R., 2016, Inplane stress analysis of dissimilar materials with multiple interface cracks, Applied Mathematical Modelling 40(1920): 8464 8474.##[30] Habib A., Rasul B., 2018, Several embedded cracks in a functionally graded piezoelectric strip under dynamic loading, Computers & Mathematics with Applications 76(3): 534550.##[31] Monfared M.M., Bagheri R., Yaghoubi R., 2017, The mixed mode analysis of arbitrary configuration of cracks in an orthotropic FGM strip using the distributed edge dislocations, International Journal of Solids and Structures 130: 2135.##[32] Hejazi A.A., Ayatollahi M., Bagheri R., Monfared M.M., 2013, Dislocation technique to obtain the dynamic stress intensity factors for multiple cracks in a halfplane under impact load, Archive of Applied Mechanics 84(1): 95107.##[33] Ershad H., Bagheri R., Noroozi M., 2018, Transient response of cracked nonhomogeneous substrate with piezoelectric coating by dislocation method, Mathematics and Mechanics of Solids 23(12): 15251536.##[34] Bagheri R., Mirzaei A.M., 2017, Fracture analysis in an imperfect FGM orthotropic strip bonded between two magnetoelectroelastic layers, Iranian Journal of Science and Technology, Transactions of Mechanical Engineering 43(2): 253271.##[35] Mandal P., Mandal S.C., 2020, Sh waves interaction with crack at orthotropic interface, Waves in Random and Complex Media, DOI:10.1080/17455030.2020.1720043.##]
1

Thermoelastic Damping and Frequency Shift in Kirchhoff Plate Resonators Based on Modified Couple Stress Theory With DualPhaseLag Model
http://jsm.iauarak.ac.ir/article_677555.html
10.22034/jsm.2020.1896290.1569
1
The present investigation deals with study of thermoelastic damping and frequency shift of Kirchhoff plate resonators by using generalized thermoelasticity theory of dualphaselag model. The basic equations of motion and heat conduction equation are written with the help of KirchhoffLove plate theory and dual phase lag model. The analytical expressions for thermoelastic damping and frequency shift of modified couple stress dualphaselag thermoelastic plate have been obtained. A computer algorithm has been constructed to obtain the numerical results. Influences of modified couple stress dualphaselag thermoelastic plate, dual phaselag thermoelastic plate and LordShulman (LS, 1967) thermoelastic plate with few vibration modes on the thermoelastic damping and frequency shift are examined. The thermoelastic damping and frequency shift with varying values of length and thickness are shown graphically for clampedclamped and simplysupported boundary conditions. It is observed from the results that the damping factor and frequency shift have noticed larger value in the presence of couple stress for varying values of length but opposite effect are shown for varying values of thickness in case of both vibration modes and boundary conditions.
0

700
712


S
Devi
Department of Mathematics, Abhilashi University, Mandi, Himachal Pradesh, India
India
shaloosharma2673@gmail.com


R
Kumar
Department of Mathematics, Kurukshetra University, Kurukshetra, Haryana, India
India
rkumar@kuk.ac.in
Modified couple stress theory
KirchhoffLove plate theory
Dualphaselag model
Thermoelastic damping
Frequency shift
[[1] AbdElaziz E.M., Marin M., Othman M.I.A., 2019, On the effect of Thomson and initial stress in a thermo porous elastic solid under GN electromagnetic theory, Symmetry 11(3): 413.##[2] Alashti R.A., Abolghasemi A.H., 2014, A sizedependent BernoulliEuler beam formulation based on a new model of couple stress theory, Transactions C: Aspects 27(6): 951960.##[3] Chen W., Li X., 2014, A new modified couple stress theory for anisotropic elasticity and microscale laminated Kirchhoff plate model, Archive of Applied Mechanics 84: 323341.##[4] Cosserat E., Cosserat F., 1909, Theory of Deformable Bodies, Hermann et Fils, Paris.##[5] Daliwal R.S., Singh A., 1980, Dynamical Coupled Thermoelasticity, Hindustan Publishers, Delhi, India.##[6] Guo F.L., Wang G.Q., Rogerson G.A., 2012, Analysis of thermoelastic damping in microand nanomechanical resonators based on dualphaselagging generalized thermoelasticity theory, International Journal of Engineering Science 60: 5965.##[7] Guo F.L., Song J., Wang G.Q., Zhou Y.F., 2014, Analysis of thermoelastic dissipation in circular microplate resonators using the generalized thermoelasticity theory of dualphaselagging model, Journal of Sound and Vibration 333: 24652474.##[8] Kakhki E.K., Hosseini S.M., Tahani M., 2016, An analytical solution for thermoelastic damping in a microbeam based on generalized theory of thermoelasticity and modified couple stress theory, Applied Mathematical Modeling 40(4): 31643174.##[9] Kumar R., Devi S., Sharma V., 2017, A problem of thick circular plate in modified couple stress thermoelastic diffusion with phaselags, Multidiscipline Modeling in Materials and Structures 12(3): 478494.##[10] Kumar R., Devi S., 2017, Thermoelastic beam in modified couple stress thermoelasticity induced by laser pulse, Computers and Concrete 19(6): 707716.##[11] Koiter W.T., 1964, Couplestresses in the theory of elasticity, Proceedings of the Royal Netherlands Academy of Sciences 67: 1744.##[12] Kumar R., Devi S., 2017, Response of thermoelastic functionally graded beam due to ramp type heating in modified couple stress with dual phase lag model, Multidiscipline Modelling in Materials and Structures 13(3): 471488.##[13] Kumar R., Devi S., Sharma V., 2017, Damping in microscale modified couple stress thermoleastic circular plate resonators, AAM 12(2): 924945.##[14] Kumar R., Devi S., 2018, Damping and frequency shift in microscale modified couple stress thermoelastic plate resonators, Journal of Solid Mechanics 10(3): 621636.##[15] Marin M., 1997, An uniqueness result for body with voids in linear thermoelasticity, Rendiconti di Matematica 17(7): 103113.##[16] Marin M., Florea O., 2014, On temporal behavior of solutions in thermoelasticity of porous micropolar bodies, Analele Universitatii "Ovidius" Constanta 22(1): 169188.##[17] Ma H.M., Gao X.L., Reddy J.N., 2008, A microstructuredependent Timoshenko beam model based on a modified couple stress theory, Journal of Mechanics and Physics of Solids 56(12): 33793391.##[18] Mindlin R.D., Tiersten H.F., 1962, Effects of couplestresses in linear elasticity, Archive for Rational Mechanics and Analysis 11: 415448.##[19] Mindlin R.D., 1963, Influence of couple stresses on stressconcentrations, Experimental Mechanics 3: 17.##[20] Mindlin R.D., 1964, Microstructure in linear elasticity, Archives for Rational Mechanics and Analysis 15: 5178.##[21] Park S.K., Gao X.L., 2006, Bernoulli–Euler beam model based on a modified couple stress theory, Journal of Micromechanics and Microengineering 16: 2355.##[22] Rao S.S., 2007, Vibration of Continuous Systems, John Wiley & Sons, Inc. Hoboken, New Jersey.##[23] Rezazadeh G., Vahdat A.S., TayefehRezaei S., Cetinkaya C., 2012, Thermoelastic damping in a micro beam resonator using modified couple stress theory, Acta Mechanica 223: 11371152.##[24] Roychoudhuri S.K., 2007, On a thermoelastic threephaselag model, Journal of Thermal Stresses 30: 231238.##[25] Sharma J.N., 2011, Thermoelastic damping and frequency shift in micro/nanoscale anisotropic beams, Journal of Thermal Stresses 34(7): 650666.##[26] Sourki R., Hoseini S.A.H., 2016, Free vibration analysis of sizedependent cracked microbeam based on the modified couple stress theory, Applied Physics A 122: 413.##[27] Sun Y., Tohmyoh H., 2009, Thermoelasic damping of the axisymmetric vibration of circular plate resonators, Journal of Sound and Vibration 319: 392405.##[28] Toupin R.A., 1962, Elastic materials with couplestresses, Archive for Rational Mechanics and Analysis 11: 385414.##[29] Tsiatas G.C., 2009, A new Kirchhoff plate model based on a modified couple stress theory, Journal of Solids and Structures 46: 27572764.##[30] Tzou D.Y., 1995, A unified approach for heat conduction from macrotomicro scales, Journal of Heat Transfer 117: 816.##[31] Tzou D.Y., 1997, MacrotoMicroscale Heat Transfer: The Lagging Behaviour, Series in Chemical and Mechanical Engineering, Taylor and Francis, Washington.##[32] Voigt W., 1887, Theoretische Studienuber die Elasticitatsverhaltnisse der Krystalle,##Abhandlungen der Königlichen Gesellschaft der Wissenschaften in Göttingen, German.##[33] Yang F., Chong A.C.M., Lam D.C.C., Tong P., 2002, Couple stress based strain gradient theory for elasticity, International Journal of Solids and Structures 39: 27312743.##]
1

Influence of Rigidity, Irregularity and Initial Stress on Shear Waves Propagation in Multilayered Media
http://jsm.iauarak.ac.ir/article_677312.html
10.22034/jsm.2020.1896884.1572
1
The propagation of shear waves in an anisotropic fluid saturated porous layer over a prestressed semiinfinite homogeneous elastic halfspace lying under an elastic homogeneous layer with irregularity present at the interface with rigid boundary has been studied. The rectangular irregularity has been taken in the halfspace. The dispersion equation for shear waves is derived by using the perturbation technique followed by Fourier transformations. The dimensionless phase velocity is plotted against dimensionless wave number for the different size of ratios of depth of rectangular irregularity with the height of the layer and anisotropy parameters with the help of MATLAB graphical routines in presence and absence of initial stress. From the graphical results, it has been seen that the phase velocity is significantly influenced by the wave number, the depth of the irregularity, rigid boundary and initial stress. The acquired outcomes can be valuable for the investigation of geophysical prospecting and understanding the cause and evaluating of damage due to earthquakes.
0

713
728


R.K
Poonia
Department of Mathematics, Chandigarh University, Mohali, Punjabp140413, India
India


N
Basatiya
Department of Mathematics, Chandigarh University, Mohali, Punjabp140413, India
India


V
Kaliraman
Department of Mathematics, Chaudhary Devi Lal University, SirsaHaryana125055, India
India
vsisaiya@gmail.com
Rigidity
Rectangular irregularity
Initial stress
Shear waves
Anisotropic layer
Dispersion equation
Perturbation technique
[[1] Biot M. A., 1940, The influence of initial stress on elastic wave, Journal of Applied Physics 11(8): 522530.##[2] Alam P., Kundu S., 2017, Influences of heterogeneities and initial stresses on the propagation of lovetype waves in a transversely isotropic layer over an inhomogeneous HalfSpace, Journal of Solid Mechanics 4(9): 783793.##[3] Kundu S., Gupta S., Manna S., 2014, SHtype waves dispersion in an isotropic medium sandwiched between an initially stressed orthotropic and heterogeneous semiinfinite media, Meccanica 49(3): 749758.##[4] Gupta S., Vishwakarma S.K., Majhi D.K., Kundu S., 2011, Influence of rigid boundary and initial stress on the propagation of Love wave, Applied Mathematics 2: 586594.##[5] Kundu S., Manna S., Gupta S., 2014, Love wave dispersion in prestressed homogeneous medium over a porous halfspace with irregular boundary surfaces, International Journal of Solids and Structures 51: 36893697.##[6] Chattopadhyay A., Gupta S., Sharma V.K., Kumari P., 2010, Effects of irregularity and anisotropy on the propagation of shear waves, International Journal of Engineering, Science and Technology 2(1): 116126.##[7] Chattopadhyay A., Gupta S., Singh A.K., Sahu S. A., 2010, Propagation of SH Waves in an Irregular Non Homogeneous Monoclinic Crustal Layer over a SemiInfinite Monoclinic Medium, Applied Mathematical Sciences 4(44): 21572170.##[8] Chattopadhyay A., Gupta S., Sharma V.K., Kumari P., 2010, Effects of irregularity and anisotropy on the propagation of shear waves, International Journal of Engineering Science and Technology 2(1): 116126.##[9] Rouze N. C., Wang M. H., Palmeri M. L., Nightingale K. R., 2013, Finite element modeling of impulsive excitation and shear wave propagation in an Incompressible, transversely isotropic medium, Journal of Biomechanics 46(16): 27612768.##[10] Vaishnav P.K., Kundu S., AboDahab S.M., Saha A., 2017, Torsional surface wave propagation in anisotropic layer sandwiched between heterogeneous halfspace, Journal of Solid Mechanics 9(1): 213224.##[11] Biot M.A., 1956, Theory of propagation of elastic waves in a fluid saturated porous solid, The Journal of the Acoustical Society of America 28: 335354.##[12] Biot M.A., Willis D.G., 1957, Elastic coefficients of the theory of consolidation, The Journal of the Acoustical society of America 24: 594601.##[13] Konczak Z., 1988, On propagation of shear waves in a multilayered medium including a fluid saturated porous stratum, Acta Mechnica 79: 169181.##[14] Kumar R., Madan D. K., Sikka J.S., 2014, Love wave propagation in an irregular fluid saturated porous anisotropic layer with rigid boundary, Journal of Applied Sciences Research 10(4): 281287.##[15] Kumar R., Madan D.K., Sikka J. S., 2015, Effect of irregularity and inhomogeneity on the propagation of love waves in fluid saturated porous isotropic layer, Journal of Applied Science and Technology (JAST) 20(12): 1621.##[16] Kaliraman V., Poonia R.K., 2018, Elastic wave propagation at imperfect boundary of micropolar elastic solid and fluid saturated porous solid halfspace, Journal of Solid Mechanics 10(3): 655671.##[17] Poonia R.K., Madan D.K., Kaliraman V., 2019, Rigidity and irregularity effect on surface wave propagation in a fluid saturated porous layer, Journal of Solid Mechanics 11(4): 886901.##[18] Gupta S., Chattopadhyay A., Majhi D.K., 2010, Effect of initial stress on propagation of love wave in an anisotropic porous layer, Journal of Solid Mechanics 2(1): 5062.##[19] Kumar R., Madan D.K., Sikka J.S., 2014, Shear wave propagation in multilayered medium including an irregular fluid saturated porous stratum with rigid boundary, Advances in Mathematical Physics 2014: 163505.##[20] Kumar R., Madan D.K., Sikka J.S., 2016, Effect of rigidity and inhomogeneity on the propagation of Love waves in an irregular fluid saturated porous isotropic layer, International Journal of Mathematics and Computation 27(2): 5570.##[21] Prasad R.M., Kundu S., 2019, Dispersion of torsional surface wave in a prestressed heterogeneous layer sandwiched between anisotropic porous halfspaces under gravity, Journal of Solid Mechanics 11(4): 707723.##[22] Poonia R.K., Sonu Kaliraman V., Kumar P., 2019, Surface wave propagation under initially stressed porous medium, International Journal on Emerging Technologies 10(2): 4853.##[23] Poonia R. K., Kharb K., Madan D. K., 2019, Rigidity effects on surface waves in multilayered media, International Journal on Emerging Technologies 10(2): 6972.##[24] Ewing W.M., Jardetzky W.S., Press F., 1957, Elastic Waves in Layered Media, McGrawHill, New York.##[25] Biot M.A., 1955, Theory of elasticity and consolidation for a porous anisotropic solid, Journal of Applied Physics 26(2): 182185.##[26] Willis H.F., 1948, A formula for expanding an integral as a series, Philosophical Magazine 39: 455459.##[27] Tranter C.J., 1966, Integral Transform in Mathematical Physics, Methuen.##[28] Ding H., Chen W., Zhang L., 2006, Elasticity of Transversely Isotropic Materials, Springer.##]