2016
8
1
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231
Torsion of Poroelastic Shaft with Hollow Elliptical Section
2
2
In this paper torsion of hollow Poroelastic shaft with Elliptical section is developed. Using the boundary equation scheme. It looks for a stress function where satisfied Poisson equation and vanishes on boundary. It also analyzed stress function and warping displacement for the hollow elliptical section in Poroelastic shaft. At the end, the result of elastic and poroelastic shaft in warping displacement and stress function is compared.
1

1
11


M
Jabbari
Department of Mechanical Engineering, Islamic Azad University, South Tehran Branch, Iran
Department of Mechanical Engineering, Islamic
Iran
mohsen.jabbari@gmail.com


M.F
Khansanami
Department of Mechanical Engineering, Islamic Azad University, South Tehran Branch, Iran
Department of Mechanical Engineering, Islamic
Iran
Torsion
Stress function
Warping
Poroelastic
Inhomogeneous
[[1] Timoshenko S.P., Goodier J.N., 1970, Theory of Elasticity, New York:, McGrawHill.##[2] Timoshenko S.P., 1953, History of Strength of Materials, New York:, McGrawHill.##[3] Baron F. M ., 1942,Torsion of multiconnected thinwalled cylinders, Journal of Applied Mechanics 9:7274.##[4] Li Z.., Ko J. M., Ni Y. Q., 2000, Torsional rigidity of reinforced concrete bars with arbitrary sectional shape, Finite Elements in Analysis and Design 35:349361.##[5] Mejak G ., 2000, Optimization of crosssection of hollow prismatic bars in torsion, Communications in Numerical Methods in Engineering 16:687695.##[6] Jiang W. G ., Henshall J. L ., 2002 , A coupling crosssection finite element model for torsion analysis of prismatic bars, European Journal of Mechanics Asolids 21: 513522.##[7] Louis Angelo M ., Ryan M ., 2007 , Torsion of a rectangular prismatic bar: Solution using a power fit model, Philippine Engineering Journal 28(1) : 7798.##[8] Doostfatemeh A., Hematiyan M.. R ., Arghavan S., 2009 , Closedform approximate formulations for torsional analyses of hollow tube with straight and circular edges, Journal of Mechanics 25:401409.##[9] Courant R., 1943 , Variational methods for the solution of problems of equilibrium and vibration, Bulletin of the American Mathematical Society 49(1):123.##[10] Timoshenko S.P., 1956, Strength of Materials, Berkshire (England) ,Van Nostrand.##[11] Quinlan P.M., 1964, The torsion of an irregular polygon, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Science 282 :208227.##[12] Muskhelishvilli N.I., 1953, Some Basic Problems of the Mathematical Theory of Elasticity, Groningen ,Holland.##[13] Booker J.R., Kitipornchai S., 1971, Torsion of multilayered rectangular section, Journal of the Engineering Mechanics Division ASCE 97:14511468.##[14] Kuo Y.M., Conway H.D., 1973 ,The torsion of composite tubes and cylinders, International Journal of Solids and Structures 9(12):15531565.##[15] Kuo Y.M., Conway H..D., 1974, Torsion of cylinders with multiple reinforcement, Journal of the Engineering Mechanics Division ASCE 100:221234.##[16] Kuo Y.M., Conway H.D., 1974, Torsion of composite rhombus cylinder, Journal of Applied Mechanics 41(1):302303.##[17] Kuo Y.M., Conway H.D., 1980, Torsion of reinforced square cylinder, Journal of the Engineering Mechanics Division 106 :13411347.##[18] Packham B.A., Shail R.., 1978 , St. venant torsion of composite cylinders, Journal of Elasticity 8(4):393407.##[19] Ripton R.,1998 , Optimal fiber configurations for maximum torsional rigidity, Archive for Rational Mechanics and Analysis 144(1):79106.##[20] Chen T., Benveniste Y., Chuang P.C , 2002 , Exact solutions in torsion of composite bars: thickly coated neutral inhomogeneities and composite cylinder assemblages, Proceedings of the Royal Society A : Mathematical, Physical and Engineering Science 458(2023):17191759.##[21] Ely J.F., Zienkiewicz O.C., 1960, Torsion of compound bars a relaxation solution, International Journal of Mechanical Sciences 1(4):356365.##[22] Herrmann L.R., 1965 , Elastic torsional analysis of irregular shapes, Journal of the Engineering Mechanics Division 91(6): 1120.##[23] Jaswon M.A., Ponter A.R., 1963, An integral equation solution of the torsion problem, Proceedings of the Royal Society A: Mathematical Physical and Engineering Science 273:237246.##[24] Kasikadelis J.T., Sapountzakis E.J, 1986 , Torsion of composite bars by boundary element method, Journal of Engineering Mechanics 111(9):11971210.##[25] Sapountzakis E.J., 2000 , Solution of nonuniform torsion of bars by an integral equation method, Computer and Structures 77(6):659667.##[26] Sapountzakis E.J., 2001 , Nonuniform torsion of multimaterial composite bars by the boundary element method, Computer and Structures 79(32):28052816.##[27] Koizumi M., 1993 ,The concept of FGM, Ceram Trans Function Grad Mater 34(1):310.##[28] Plunkett R., 1965 , Torsion of inhomogeneous elastic prismatic bars, Journal of Engineering for Industry 87:391392.##[29] Rooney F.J., Ferrari M., 1995, Torsion and flexure of inhomogeneous elements, Engineering of Composite 5(7):901911.##[30] Rooney F.J., Ferrari M., 1999, On the St. venant problems for inhomogeneous circular bars, Journal of Applied Mechanics 66(2):3244.##[31] Horgan C.O., Chan A..M., 1999, Torsion of functionally graded isotropic linearly elastic bars, Journal of Elasticity 52(2):181199.##[32] Tarn J.G., 2008, Chang HH. Torsion of cylindrically orthotropic elastic circular bars with radial inhomogeneity: some exact solutions and end effects, International Journal of Solids and Structures 45(1):303319.##[33] Rooney F.J ., Ferrari M.,1995,Torsion and flexure of inhomogeneous elements, Composites Engineering 5: 901911.##[34] Biot M..A., 1962 , Generalized theory of acoustic propagation in porous dissipative media, Journal of the Acoustical Society of America 34: 12541264.##[35] Biot M.A., 1972, Theory of finite deformation of porous solid, Indiana University Mathematics Journal 21:597620.##[36] Biot M..A., 1982, Generalized Lagrangian equations of nonlinear reaction diffusion, Chemical Physics 66:1126.##[37] Arghavan S., Hematiyan, M..R., 2009, Torsion of functionally graded hollow tubes, European Journal Mechanics A/Solids 28(3): 551559.##[38] Batra R..C, 2006, Torsion of a functionally graded cylinder, The American Institute of Aeronautics and Astronautics 44 (6):13631365.##[39] Horgan C.O, 2007, On the torsion of functionally graded anisotropic linearly elastic bars, Journal of Applied Mathematics 72 (5): 556562.##[40] Rooney F.J, Ferrari M., 1995, Torsion and flexure of inhomogeneous elements, Composites Engineering 5 (7):901911.##[41] Udea M., Nishimura T., Sakate T, 2002, Torsional analysis of functionally graded materials., Advances in Mechanics of Structures and Materials, Proceedings of 17th Australian Conference (ACMS17), Tayor and Francis, Queensland, Australia.##[42] Yaususi T., Shigeyasu A., 2000, Torsional characteristics of hemp palm branch with triangular crosssection (2composite bar), The Japan Society of Mechanical Engineers 66 (649): 18061811.##[43] Sofiyev A..H, 2005, The torsional buckling analysis of cylindrical shells with material nonhomogeneity in thickness direction under impulsive loading, Structural Engineering and Mechanics an International Journal 19(2):231236.##[44] Sofiyev A.H., 2003, Torsional buckling of crossply laminated orthotropic composite cylindrical shells subject to dynamic loading, European Journal of Mechanics A/Solids 22:943951.##[45] Sadd M. H.,. 2009, Elasticity Theory, Application, and Numerics, Department of Mechanical Engineering and Applied Mechanics University of Rhode Island.##]
Free Vibration of Sandwich Panels with Smart MagnetoRheological Layers and Flexible Cores
2
2
This is the first study on the free vibrational behavior of sandwich panels with flexible core in the presence of smart sheets of oil which is capable of the excitation of magnetic field. In order to model the core, the improved high order theory of sandwich sheets was used by a polynomial with unknown coefficients first degree shear theory was used for the sheets. The derived equations based on Hamilton principle with simple support boundary condition for upper and lower sheets were solved using Navier technique. Accuracy and precision of the theory were investigated by comparing the results of this study with those of analytical and numerical works. In the conclusion section, effect of the intensity of magnetic field and other physical parameters including ratio of sheet's length to width, ratio of sheet's length to thickness, ratio of core thickness to sheet's overall thickness, and ratio of oil layer thickness to sheet's overall thickness on natural frequency was investigated.
1

12
30


G
Payganeh
School of Mechanical Engineering, Shahid Rajaee Teacher Training University (SRTTU), Tehran, Iran
School of Mechanical Engineering, Shahid
Iran
g.payganeh@srttu.edu


K
Malekzadeh
Structural Analysis and Simulation Department,Space Research Institute, Malek Ashtar University of Technology
Structural Analysis and Simulation Department,Spac
Iran


H
MalekMohammadi
School of Mechanical Engineering, Shahid Rajaee Teacher Training University (SRTTU), Tehran, Iran
School of Mechanical Engineering, Shahid
Iran
Sandwich plates
Flexible cores
Free Vibration
Improved high order theory
[[1] Rabinow J., 1948, The magnetic fluid clutch, American Institute of Electrical Engineers, Transactions 67: 13081315.##[2] Carlson J.D., Jolly M.R., 2000, MR fluid, foam and elastomer devices, Mechatronics 10: 555569.##[3] Yao G.Z., Yap F.F., Chen G., Li W.H., Yeo S.H., 2002, MR damper and its application for semiactive control of vehicle suspension system, Mechatronics 12(7): 963973.##[4] Oh H.U., Onoda J., 2002, An experimental study of a semiactive magnetorheological fluid variable damper for vibration suppression of truss structures, Smart Materials and Structures 11(1): 156162.##[5] Sun Q., Zhou J.X., Zhang L., 2003, An adaptive beam model and dynamic characteristics of magnetorheological materials, Journal of Sound and Vibration 261(3): 465481.##[6] Yalcintas M ., Dai H., 2004, Vibration suppression capabilities of magnetorheological materials based adaptive structures, Smart Materials and Structures 13(1): 111.##[7] Rajamohan V., Sedaghati R., Rakheja S., 2010, Vibration analysis of a multilayer beam containing magnetorheological fluid, Smart Materials and Structures 19(1): 015013.##[8] Choi Y., Sprecher A.F., Conrad H., 1990, Vibration characteristics of a composite beam containing an electrorheological fluid, Journal of Intelligent Material Systems 1(1): 91104.##[9] Nayak B., Dwivedy K.S., Murthy R.K., 2011, Dynamic analysis of magnetorheological elastomerbased sandwich beam with conductive skins under various boundary conditions, Journal of Sound and Vibration 330(9): 18371859.##[10] Yeh J.Y, 2013, Vibration analysis of sandwich rectangular plates with magnetorheological elastomer damping treatment, Smart Materials and Structures 22(3): 035010.##[11] Manoharan R., Vasudevan R., Jeevanantham A.K., 2014, Dynamic characterization of a laminated composite magnetorheological fluid sandwich plate, Smart Materials and Structures 23(2): 025022.##[12] Kameswara Rao M., Desai,Y.M., ChitnisM.R., 2001, Free vibrations of laminated beams using mixed theory, Composite Structures 52(2): 149160.##[13] Kant T., Swaminathan K., 2001, Analytical solutions for free vibration of laminated composite and sandwich plates based on a higherorder refined theory, Composite Structures 53(1): 7385.##[14] Meunier M., Shenoi R.A., 2001, Dynamic analysis of composite sandwich plates with damping modelled using highorder shear deformation theory, Composite Structures 54(23): 243254.##[15] Nayak A.K., Moy S.S.J., Shenoi R.A., 2002, Free vibration analysis of composite sandwich plates based on Reddy's higherorder theory, Composites Part B: Engineering 33(7):505519.##[16] Frostig Y., Thomsen O.H., 2004, Highorder free vibration of sandwich panels with a flexible core, International Journal of Solids and Structures 41(56): 16971724.##[17] Malekzadeh K., Khalili M.R., Mittal R.K., 2005, Local and global damped vibrations of plates with a viscoelastic soft flexible core: an improved highorder approach, Journal of Sandwich Structures and Materials 7(5): 431456.##[18] Ćetković M., Vuksanović D.J., 2009, Bending, free vibrations and buckling of laminated composite and sandwich plates using a layer wise displacement model, Composite Structures 88(2): 219227.##[19] Yao Kuo Sh., LeChung Sh., 2009, Buckling and vibration of composite laminated plates with variable fiber spacing, Composite Structures 90(2): 196200.##[20] Vasudevan R., Sedaghati R., Rakheja S., 2010, Vibration analysis of a multilayer beam containing magnetorheological fluid, Smart Materials and Structures 19(1): 015013.##[21] Rahmani O., Khalili M.R ., Malekzadeh K., 2010, Free vibration response of composite sandwich cylindrical shell with flexible core, Composite Structures 92(5): 12691281.##[22] Meunier M., Shenoi R.A., 1999, Free vibration analysis of composite sandwich plates, Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science 213(7): 715727.##]
Closed Form Solution for ElectroMagnetoThermoElastic Behaviour of DoubleLayered Composite Cylinder
2
2
Electromagnetothermoelastic response of a thick doublelayered cylinder made from a homogeneous interlayer and a functionally graded piezoelectric material (FGPM) outer layer is investigated. Material properties of the FGPM layer vary along radius based on the power law distribution. The vessel is subjected to an internal pressure, an induced electric potential, a uniform magnetic field and a temperature gradient. Stresses and radial displacement are studied for different material inhomogeneity parameters in the FGPM layer. It has been shown that the material inhomogeneity parameters significantly affect the stress distribution in both layers. Therefore by selecting a suitable material parameter one can control stress distribution in both homogeneous and FGPM layers. It has been found that under electromagnetothermomechanical loading minimum effective stress can be achieved by selecting in the FGPM layer.
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31
44


A
Loghman
Department of Solid Mechanics, Faculty of Mechanical Engineering, University of Kashan, Islamic Republic of Iran
Department of Solid Mechanics, Faculty of
Iran
aloghman@kashanu.ac.ir


H
Parsa
Department of Solid Mechanics, Faculty of Mechanical Engineering, University of Kashan, Islamic Republic of Iran
Department of Solid Mechanics, Faculty of
Iran
Closed form solution
Electromagnetothermoelastic
Doublewalled cylinder
Homogeneous interlayer
FGPM outer layer
[[1] Nie G.J., Batra R.C., 2010, Material tailoring and analysis of functionally graded isotropic and incompressible linear elastic hollow cylinders, Composite Structures 92: 265274.##[2] Babaei M.H., Chen Z.T., 2008, Analytical solution for the electromechanical behaviour of a rotating functionally graded piezoelectric hollow cylinder, Archive of Applied Mechanics 78: 489500.##[3] Saadatfar M., Razavi A.S., 2009, Piezoelectric hollow cylinder with thermal gradient, Journal of Mechanical Science and Technology 23: 4553.##[4] Ghorbanpour Arani A., Kolahchi R., Mosallaie Barzoki A.A., 2010, Effect of material inhomogeneity on electrothermomechanical behaviors of functionally graded piezoelectric rotating shaft, Applied Mathematical Modelling 36: 27712789.##[5] Ghorbanpour Arani A., Loghman A., Abdollahitaheri A., Atabakhshian V., 2010, Electrothermomechanical behavior of a radially polarized rotating functionally graded piezoelectric cylinder, Journal of Mechanics of Materials and Structures 6(6): 869884.##[6] Haghpanah Jahromi B., Ajdari A., NayebHashemi H., Vaziri A., 2010, Autofrettage of layered and functionally graded metal–ceramic composite vessels, Composite Structures 92( 8): 18131822.##[7] Mithchell J.A., Reddy J.N., 1995, A study of embedded piezoelectric layers in composite cylinders, Journal of Applied Mechanics 62:166173.##[8] Wang H.M., Ding H.J., Chen Y.M., 2005, Dynamic solution of a multilayered orthotropic piezoelectric hollow cylinder for axisymmetric plane strain problems, International Journal of Solids and Structures 42:85102.##[9] Yin X.C., Yue Z.Q., 2002, Transient planestrain response of multilayered elastic cylinders to axisymmetric impulse, Journal of Applied Mechanics 69: 825835.##[10] Dai H.L., Fu Y.M., 2007, Magnetothermoelastic interactions in hollow structures of functionally graded material subjected to mechanical loads, International Journal of Pressure Vessels and Piping 84(3): 132138.##[11] Dai H.L., Rao Y.N., 2013, Dynamic thermoelastic behavior of a doublelayered hollow cylinder with an FGM layer, Journal of Thermal Stresses 36( 9): 962984.##[12] Loghman A., Parsa H., 2014, Exact solution for magnetothermoelastic behaviour of doublewalled cylinder made of an inner FGM and an outer homogeneous layer, International Journal of Mechanical Sciences 88: 9399.##[13] Hosseini S.M., Akhlaghi M., Shakeri M., 2007, Transient heat conduction in functionally graded thick hollow cylinders by analytical method, International Journal of Heat and Mass Transfer 43: 669675.##[14] Loghman A., Ghorbanpour Arani A., Amir S., Vajedi S., 2010, Magnetothermoelastic creep analysis of functionally graded cylinders, International Journal of Pressure Vessel and Piping 87: 389395.##[15] Dai H.L., Hong L., Fu Y.M., Xiao X., 2010, Analytical solution for electromagnetothermoelastic behaviors of a functionally graded piezoelectric hollow cylinder, Applied Mathematical Modelling 34(2): 343357.##]
Dynamic Stability of Laminated Composite Plates with an External Smart Damper
2
2
The dynamic stability of a composite plate with external electrorheological (ER) damper subjected to an axial periodic load is investigated. Electrorheological fluids are a class of smart materials, which exhibit reversible changes in mechanical properties when subjected to an electric field. As a result, the dynamic behavior of the structure is changed. The ER damper is used for suppressing the vibrations and improving the stability of the system. The Bingham plastic model is employed to express the behavior of the ER fluid. The finite element model of the structure is developed and constant acceleration average method is used to obtain the response of the system. Effect of different parameters such as the electric field, the orientation of the ER damper, the initial gap between the two electrodes of the ER damper and the stacking sequences of the plate on the first instability boundaries of the composite plate are investigated.
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45
57


M
Hoseinzadeh
Department of Mechanical Engineering , Ferdowsi University of Mashhad , Mashhad, Iran
Department of Mechanical Engineering , Ferdowsi
Iran


J
Rezaeepazhand
Department of Mechanical Engineering , Ferdowsi University of Mashhad , Mashhad, Iran
Department of Mechanical Engineering , Ferdowsi
Iran
jrezaeep@um.ac.ir
Laminated composite
Dynamic buckling
FEA
Smart structures
[[1] Simitses G.J., 1987, Stability of dynamically loaded structures, Applied Mechanics Reviews 40(10): 14031408.##[2] Moorthy J., Reddy J.N., 1990, Parametric instability of laminated composite plates with transverse shear deformation, International Journal of Solids Structures 26(7): 801811.##[3] Shivamoggi B. K., 1977, Dynamic buckling of thin elastic plate: nonlinear theory, Journal of Sound and Vibration 54 (l) : 7582.##[4] Chen L.W., Yang J.Y., 1990, Dynamic stability of laminated composite plates by the finite element method, Computers and Structures 36(5): 845851.##[5] Kwon Y.W., 1991, Finite element analysis of dynamic instability of layered composite plates using a highorder bending theory, Computers and Structures 38(1): 5762.##[6] Sahu S.K., Datta P.K., 2000, Dynamic instability of laminated composite rectangular plates subjected to nonuniform harmonic inplane edge loading, in: Proceedings of the IMECH E Part G, Journal of Aerospace Engineering 214(5): 295312.##[7] Hoseinzadeh M., Rezaeepazhand J., 2011, Dynamic buckling of perforated metallic cylindrical panels reinforced with composite patches, Journal of Reinforced Plastics and Composites 30(18): 15191528.##[8] Park W.C., Choi S.B., Suh M.S., 1999, Material characteristics of an ER fluid and its influence on damping forces of an ER damper Part II: damping forces, Materials and Design 20: 325330.##[9] Lee H.G., Choi S.B., 2002, Dynamic properties of an ER fluid under shear and flow modes, Materials and Design 23: 6976.##[10] El Wahed A.K., Sproston J.L., Stanway R., Williams E.W., 2003, An improved model of ERfluids in squeezeflow through model updating of the estimated yield stress, Journal of Sound and Vibration 268: 581599.##[11] Nakamura T., Saga N., Nakazawa M., 2004, Variable viscous control of a homogeneous ER fluid device considering its dynamic characteristics, Mechatronics 14: 5568.##[12] Patil S.S., Gawade S.S., Patil S.R., 2011, Electrorheological Fluid Damper for Vibration Reduction in Rotary System, International Journal of Fluids Engineering 3(3): 325333.##[13] Sung K.G., Han Y.M., Cho J.W., Choi S.B., 2008, Vibration control of vehicle ER suspension system using fuzzy moving sliding mode controller, Journal of Sound and Vibration 311: 10041019.##[14] Hong S. R., Choi S. B., Lee D. Y., 2006, Comparison of vibration control performance between flow and squeeze mode ER mounts: Experimental work, Journal of Sound and Vibration 291 :740748.##[15] Kim J., Kim J.Y., Choi S.B.,2003, Material characterization of ER fluids at high frequency, Journal of Sound and Vibration 267 : 5765.##[16] Yeh J. Y., Chen L. W., 2004, Vibration of a sandwich plate with a constrained layer and electrorheological fluid core, Composite Structures 65: 251258.##[17] Yeh J.Y., Chen L.W., 2005, Dynamic stability of a sandwich plate with a constraining layer and electrorheological fluid core, Journal of Sound and Vibration 285: 637652.##[18] Mohammadi F., Sedaghati R., 2012, Vibration analysis and design optimization of sandwich cylindrical panels fully and partially treated with electrorheological fluid materials, Journal of Intelligent Material Systems and Structures 23: 16791697.##[19] Pahlavan L., Rezaeepazhand J., 2007, Dynamic response analysis and vibration control of a cantilever beam with a squeezemode electrorheological damper, Smart Materials and Structures 16: 21832189.##[20] Rezaeepazhand J., Pahlavan L., 2009, Transient response of sandwich beams with electrorheological core, Journal of Intelligent Material Systems and Structures 20: 171179.##[21] Tabassian R., Rezaeepazhand J., 2012, Stability of smart sandwich beams with crossply faces and electrorheological core subjected to axial load, Journal of Reinforced Plastics and Composites 31: 5564.##[22] Jung W.J., Jeong W.B., Hong S.R., Choi S.B., 2004, Vibration control of a flexible beam structure using squeezemode ER mounts, Journal of Sound and Vibration 273: 185199.##[23] Owen D.R.J., Hinton E., 1980, Finite Elements in Plasticity: Theory and Practice, Pineridge Press, Swansea. ##]
Reflection and Transmission at the Boundary of Two Couple Stress Generalized Thermoelastic Solids
2
2
In this paper the reflection and transmission at a plane interface between two different couple stress generalized thermoelastic solid half spaces in context of LoardShulman(LS)[1967] and GreenLindsay(GL)[1972] theories in welded contact has been investigated. Amplitude ratios of various reflected and transmitted waves are obtained due to incidence of a set of coupled longitudinal waves and coupled transverse waves. It is found that the amplitude ratios of various reflected and transmitted waves are functions of angle of incidence, frequency and are affected by the couple stress properties of the media. Some special cases are deduced from the present formulation.
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58
77


R
Kumar
Department of Mathematics, Kurukshetra University, Kurukshetra, Haryana, 136119, India
Department of Mathematics, Kurukshetra University,
India
rajneesh_kuk@rediffmail.com


K
Kumar
Department of Mathematics, DeenBandhu Chhotu Ram University of Science and Technology, Sonipat, Haryana, 131001, India
Department of Mathematics, DeenBandhu Chhotu
India


R.C
Nautiyal
Department of Mathematics, DeenBandhu Chhotu Ram University of Science and Technology, Sonipat, Haryana, 131001, India
Department of Mathematics, DeenBandhu Chhotu
India
Couple stress thermoelastic solid
Longitudinal wave
Transverse wave
Reflection
Transmission
Amplitude ratios
[[1] Voigt W., 1887, Theoretische studien uber die elastizitastsverhaltnisse der kristalle, Abhandlungen der Königlichen Gesellschaft der Wissenschaften zu Göttingen 34:351.##[2] Cosserat E., Cosserat F., 1909, Theorie des Corps Deformables, Hermann et Fils, Paris.##[3] Toupin R.A., 1962, Elastic materials with couplestresses, Archive for Rational Mechanics and Analysis 11(1): 385414.##[4] Mindlin R.D., Tiersten H.F., 1962, Effects of couplestresses in linear elasticity, Archive for Rational Mechanics and Analysis 11: 415448.##[5] Mindlin R.D., 1963, Influence of couplestresses on stressconcentrations, Experimental Mechanics 3: 17.##[6] Koiter W.T., 1964, Couplestresses in the theory of elasticity, Proceedings of the Koninklijke Nederlandse Academie van Wetenschappen, Amsterdam.##[7] Yang J.F.C., Lakes R.S., 1982, Experimental study of micropolar and couple stress elasticity in compact bone in bending, Journal of Biomechanics 15: 9198.##[8] Yang F., Chong A.C.M., Lam D.C.C., Tong P., 2002, Couple stress based strain gradient theory of elasticity, International Journal of Solids and Structures 39: 27312743.##[9] Sengupta P.R., Ghosh B., 1974, Effects of couple stresses on the surface waves in elastic media, Gerlands Beitr Geophys 83:118.##[10] Sengupta P.R., Ghosh B., 1974, Effects of couple stresses on the propagation of waves in an elastic layer, Pure and Applied Geophysics 112:331338.##[11] Sengupta P.R., Benerji D.K., 1978, Effects of couplestresses on propagation of waves in an elastic layer immersed in an infinite liquid, International Journal of Pure and Applied Mathematics 9:1728.##[12] Georgiadis H.G., Velgaki E.G., 2003, Highfrequency rayleigh waves in materials with microstructure and couplestress effects, International Journal of Solids and Structures 40:25012520.##[13] Lubarda V.A., Markenscoff X., 2000, Conservation integrals in couple stress elasticity, Journal of the Mechanics and Physics of Solids 48:553564.##[14] Bardet J.P., Vardoulakis I., 2001, The asymmetry of stress in granular media, International Journal of Solids and Structures 38:353367.##[15] Lubarda V.A., 2003, Circular inclusions in antiplane strain couple stress elasticity, International Journal of Solids and Structures 40:38273851.##[16] Jasiuk I., OstojaStarzewski M., 1995, Planar cosserat elasticity of materials with holes and intrusions, Applied Mechanics Reviews 48(11):S11S18.##[17] Akgoz B., Civalek O., 2013, Modeling and analysis of microsized plates resting on elastic medium using the modified couple stress theory, Meccanica 48(4):863873.##[18] Sharma V., Kumar S., 2014, Velocity dispersion in an elastic plate with microstructure: effects of characteristic length in a couple stress model, Meccanica 49:10831090.##[19] Biot M., 1956, Thermoelasticity and irreversible thermodynamics, Journal of Applied Physics 27: 240253.##[20] Lord H., Shulman Y., 1967, A generalized dynamical theory of elasticity, Journal of the Mechanics and Physics 15: 299309.##[21] Green A.E., Lindsay K.A., 1972, Thermoelasticity, Journal of Elasticity 2: 17.##[22] Ram P., Sharma N., 2008, Reflection and transmission of micropolar thermoelastic waves with an imperfect bonding, International Journal of Applied Mathematics and Mechanics 4(3): 123.##[23] Xue B.B., Xu H.Y., Fu Z.M., Sun Q.Y., 2010, Reflection and refraction of longitudinal displacement wave at interface between two micropolar elastic solid, Advanced Materials Research 139141: 214217.##[24] Kumar R., Kaur M., Rajvanshi S.C., 2014, Reflection and transmission between two micropolar thermoelastic halfspaces with threephaselag model, Journal of Engineering Physics and Thermophysics 87(2): 295307.##]
Dynamic Response of an Axially Moving Viscoelastic Timoshenko Beam
2
2
In this paper, the dynamic response of an axially moving viscoelastic beam with simple supports is calculated analytically based on Timoshenko theory. The beam material property is separated to shear and bulk effects. It is assumed that the beam is incompressible in bulk and viscoelastic in shear, which obeys the standard linear model with the material time derivative. The axial speed is characterized by a simple harmonic variation about a constant mean speed. The method of multiple scales with the solvability condition is applied to dimensionless form of governing equations in modal analysis and principal parametric resonance. By a parametric study, the effects of velocity, geometry and viscoelastic parameters are investigated on the response.
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78
92


H
Seddighi
School of Mechanical Engineering, University of Shahrood , Shahrood , Islamic Republic of Iran
School of Mechanical Engineering, University
Iran


H.R
Eipakchi
School of Mechanical Engineering, University of Shahrood , Shahrood , Islamic Republic of Iran
School of Mechanical Engineering, University
Iran
hamidre_2000@vatanmail.ir
Viscoelastic
Axially moving beam
Perturbation
Dynamic Response
Timoshenko theory
[[1] Chen L.Q., Yang X.D., Cheng C.J., 2004, Dynamic stability of an axially accelerating viscoelastic beam, European Journal of Mechanics  A/Solids 23: 659666.##[2] Mockensturm E.M., Guo J., 2005, Nonlinear vibration of parametrically excited viscoelastic axially moving strings, Journal of Applied Mechanics 72: 374380.##[3] Tang Y.Q., Chen L.Q. , Yang X.D., 2009,Nonlinear vibrations of axially moving Timoshenko beams under weak and strong external excitations, Journal of Sound and Vibration 320: 10781099.##[4] Chen L.Q., Tang Y.Q., Lim C.W., 2010, Dynamic stability in parametric resonance of axially accelerating viscoelastic Timoshenko beams, Journal of Sound and Vibration 329: 547565.##[5] Ding H. , Chen L.Q., 2011, Approximate and numerical analysis of nonlinear forced vibration of axially moving viscoelastic beams, Acta Mechanica Sinica 27(3): 426437.##[6] Chen L.Q., Tang Y.Q., 2011, Combination and principal parametric resonances of axially accelerating viscoelastic beams: Recognition of longitudinally varying tensions. Journal of Sound and Vibration 330 (23): 55985614.##[7] Ghayesh M., 2011, Nonlinear forced dynamics of an axially moving viscoelastic beam with an internal resonance, International Journal of Mechanical Sciences 53(11): 10221037.##[8] Wang B., Chen L.Q., 2012, Asymptotic analysis on weakly forced vibration of axially moving viscoelastic beam constituted by standard linear solid model , Applied Mathematics and Mechanics 33(6): 817828.##[9] Ghayesh M., Amabili M. , Païdoussis M.P., 2012, Nonlinear vibrations and stability of an axially moving beam with an intermediate spring support: twodimensional analysis, Nonlinear Dynamics 70: 335354.##[10] Ghayesh M., Amabili M., Farokhi H., 2013, Coupled global dynamics of an axially moving viscoelastic beam, International Journal of Nonlinear Mechanics 51: 5474.##[11] Youqi T., 2013, Nonlinear vibrations of axially accelerated viscoelastic Timoshenko beam, Chinese Journal of Theoretical and Applied Mechanics 45 (6): 965973.##[12] Riandeh E., Calleja R.D., Prolongo M.G. , 2000, Polymer Viscoelasticity: stress and Strain in Practice, Marcel Dekker Inc., New York.##[13] Brinson H.F., Brinson L.C., 2008, Polymer Engineering Science and Viscoelasticity: an Introduction, Springer Science Business Media, LLC, New York.##[14] Rao S.S., 2007, Vibration of Continues Systems, John Wiley, New Jersey.##[15] Roylance D., 2001, Engineering Viscoelasticity, Massachusetts Institute of Technology, Cambridge, Department of Material Science and Engineering.##[16] Nayfeh A.H., 1993, Introduction to Perturbation Techniques, John Wiley, New York.##[17] Seddighi H., Eipakchi H.R., 2013, Natural Frequency and Critical Speed Determination of an Axially Moving Viscoelastic Beam, Mechanics of TimeDependent Materials 17:529541.##]
A Simple Finite Element Procedure for Free Vibration and Buckling Analysis of Cracked BeamLike Structures
2
2
In this study, a novel and very simple finite element procedure is presented for free vibration and buckling analysis of slim beamlike structures damaged by edge cracks. A cracked region of a beam is modeled using a very short element with reduced second moment of area (I). For computing reduced I in a cracked region, the elementary theory of bending of beams and local flexibility approach are used. The method is able to model cracked beamcolumns by using ordinary beam elements. Therefore, it is possible to solve these problems with much less computational costs compared to 2D and 3D standard FE models. Numerical examples are offered to demonstrate the efficiency and effectiveness of the presented method.
1

93
103


M.R
Shirazizadeh
Department of Mechanical and Aerospace Engineering, Science and Research Branch, Islamic Azad University, Tehran, Iran
Department of Mechanical and Aerospace Engineering
Iran
mshirazizadeh@yahoo.com


H
Shahverdi
Department of Aerospace Engineering and Center of Excellence in Computational Aerospace, Amirkabir University of Technology, 424 Hafez Avenue, Tehran 158754413, Iran
Department of Aerospace Engineering and Center
Iran


A
Imam
Department of Mechanical and Aerospace Engineering, Science and Research Branch, Islamic Azad University, Tehran, Iran
Department of Mechanical and Aerospace Engineering
Iran
Cracked beam
Modal Analysis
Buckling load
F.E.M
[[1] Kirmsher P.G., 1944, The effect of discontinuity on natural frequency of beams, Proceedings of the American Society of Testing and Materials 44: 897904.##[2] Thomson W.J., 1943, Vibration of slender bars with discontinuities in stiffness, Journal of Applied Mechanics 17: 203207.##[3] Zheng T., Ji T., 2012, An approximate method for determining the static deflection and Natural frequency of a##cracked beam, Journal of Sound and Vibration 331: 26542670.##[4] Okamura H., Liu H.W., ChornShin C., Liebowitz H., 1969, A cracked column under compression, Engineering Fracture Mechanics 1: 547564.##[5] Rizos P.F., Aspragathos N., Dimarogonas A.D., 1990, Identification of crack location and magnitude in a cantilever beam from the vibration modes, Journal of Sound and Vibration 138: 381388.##[6] Ostachowicz W.M., Krawczuk M., 1991, Analysis of the effect of cracks on the Natural frequencies of a cantilever##beam, Journal of Sound and Vibration 150: 191201.##[7] Zheng D.Y., Fan S.C., 2003, Vibration and stability of cracked hollowsectional beams, Journal of Sound and Vibration 267: 933954.##[8] Yazdchi K., Gowhari Anaraki A.R., 2008, Carrying capacity of edgecracked columns under concentric vertical loads, Acta Mechanica 198: 119.##[9] Liu H.W., Chu C.S., Liebowitz H., 1973, Cracked columns under compression fixed ends, Engineering Fracture##Mechanics 3: 219230.##[10] Shirfin E.I., Ruotolo R., 1999, Natural frequencies of a beam with an arbitrary number of cracks, Journal of Sound##and Vibration 222: 409423.##[11] Li Q.S., 2001, Buckling of multistep cracked columns with shear deformation, Engineering Structures 23: 356364.##[12] Douka E., Bamnios G., Trochidis A., 2004, A method for determining the location and depth of cracks in double##cracked beams, Applied Acoustics 65: 9971008.##[13] Fernandez Saez J., Rubio L., Navarro C., 1999, Approximate calculations of the fundamental frequency for bending##vibrations of cracked beams, Journal of Sound and Vibration 225: 345352.##[14] Attar M.A., 2012, Transfer matrix method for free vibration analysis and crack identification of stepped beams with##multiple edge cracks and different boundary conditions, International Journal of Mechanical Sciences 57: 1933.##[15] Shen M.H.H., Pierre C., 1990, Natural modes of bernoullieuler beams with symmetric cracks, Journal of Sound and Vibration 138: 115134.##[16] Tharp T.M., 1987, A finite element for edgecracked beam columns, International Journal of Numerical Methods in Engineering 24: 19411950.##[17] Gounaris G., Dimarogonas A., 1998, A finite element of a cracked prismatic beam for structural analysis, Computers##& Structures 28: 309313.##[18] Ostachowicz W.M., Krawczuk M., 1990, Vibration analysis of a cracked beam, Computers & Structures 36: 245250.##[19] Skrinar M., Plibersek T., 2007, New finite element for transversely cracked slender beams subjected to transverse##loads, Computational Materials Science 39: 250260.##[20] Bouboulas A.S., Anifantis N.K., 2008, Formulation of cracked beam element for analysis of fractured skeletal structures, Engineering Structures 30: 894901.##[21] Ansys Level 6.1, 1973, Data Preparation Manual, ANSYS, Canonsburg, Pennsylvania.##]
A New Numerical Procedure for Determination of Effective Elastic Constants in Unidirectional Composite Plates
2
2
In this paper a composite plate with similar unidirectional fibers is considered. Assuming orthotropic structure, theory of elasticity is used for investigating the stress concentration. Also, complex variable functions are utilized for solving the plane stress problems. Then the effective characteristics of this plate are studied numerically by using ANSYS software. In this research a volume element of fibers in square array is considered. In order to investigate the numerical finite element modeling, the modeling of a quarter unit cell is considered. For determining the elasticity coefficients, stress analysis is performed for considered volume with noting to boundary conditions. Effective elasticity and mechanical properties of composite which polymer epoxy is considered as its matrix, are determined theoretically and also by the proposed method in this paper with finite element method. Finally, the variations of mechanical properties with respect to fibervolume fraction are studied.
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104
115


S
Daryazadeh
National Technical University , Kharkov Polytechnic Institute, Ukraine, Kharkov
National Technical University , Kharkov Polytechni
Ukraine


L
Lvov Gennadiy
National Technical University , Kharkov Polytechnic Institute, Ukraine, Kharkov
National Technical University , Kharkov Polytechni
Ukraine


M
Tajdari
Department of Mechanical Engineering, Islamic Azad University, Arak Branch, Arak, Iran
Department of Mechanical Engineering, Islamic
Iran
m.tajdari@srbiau.ac.ir
Composite plate
Unidirectional fibers
Effective elastic constants
Orthotropic plate
[[1] Voigt W., 1889, Uber die beziehung zwischen den beiden elastizitatskonstanten isotroper korper, Wiedemann's Annalen 38 : 573587.##[2] Reuss A., 1929, Berechnung der fliessgrense von mischkristallen auf grund der plastizitatsbedingun fur einkristalle, Zeitschrift Angewandte Mathematik und Mechanik 9 : 4958.##[3] Halpin J.C., Kardos J.L., 1976, The halpintsai equations: a review, Polymer Engineering and Science 16(5): 344352.##[4] Chamis C.C., 1989, Mechanics of composite materials: past, present and future, The Journal of Composites Technology and Research 11: 314.##[5] Hashin Z., Rosen B.W., 1964, The elastic moduli of fiber reinforced materials, Journal of Applied Mechanics 31: 223232.##[6] Christensen R.M., 1990, A critical evaluation for a class of micromechanical models, Journal of Mechanics and Physics of Solids 38(3): 379 404.##[7] Mori T., Tanaka K., 1973, Average stress in matrix and average elastic energy of materials with misfitting inclusions, Acta Metallurgica 21: 571574.##[8] Hill R., 1965, Theory of mechanical properties of fiberstrengthen materials3 selfconsistent model, Journal of Mechanics and Physics of Solids 13 :189198.##[9] Bubiansky B., 1965, On the elastic modulli of some heterogeneous materials, Journal of Mechanics and Physics of Solids 13: 223227.##[10] Chou T.w., Nomura S., Taya M., 1980, A self consistent approach to the elastic stiffness of shortfiber composites, Journal of Composite Materials 14: 178188.##[11] Huang Z.M., 2001, Simulation of the mechanical properties of fibrous composites by the bridging micromechanics model, Composites: Part A 32: 143172.##[12] Huang Z.M., 2001, Micromechanical prediction of ultimate strength of transversely isotropic fibrous composites, International Journal of Solids and Structures 38: 41474172.##[13] Vanin G. A., 1985, MicroMechanics of Composite Materials, Nauka Dumka, Kiev.##[14] Carpeenosa D. M., 1985, Composite Materials, Nauka Dumka, Kiev.##]
Numerical and Experimental Study of Buckling of Rectangular Steel Plates with a Cutout
2
2
Steel plates are used in various structures, such as the structures of the deck and body of ships, bridges, and aerospace industry. In this study, we investigate the buckling and postbuckling behavior of rectangular steel plates having circular cutouts with two boundary conditions: first, clamped supports at upper and lower ends and free supports at other edges; second, clamped supports at upper and lower ends and simply supports at other edges, using finite element method (by ABAQUS software) and experimental tests(by an INSTRON servo hydraulic machine). In this research, in addition to the aspect ratio, the effect of changing the location of the cutout on the buckling analysis is investigated. The results of both numerical and experimental analyses are compared and showing a very good agreement between them.
1

116
129


M
Shariati
Department of Mechanical Engineering, Ferdowsi University of Mashhad, Mashhad, Iran
Department of Mechanical Engineering, Ferdowsi
Iran
mshariati44@um.ac.ir


Y
Faradjian
Department of Mechanical Engineering, Shahrood University of Technology, Shahrood, Iran
Department of Mechanical Engineering, Shahrood
Iran


H
Mehrabi
Department of Mechanical Engineering, Shahrood University of Technology, Shahrood, Iran
Department of Mechanical Engineering, Shahrood
Iran
Buckling
Steel plates
Cutout
Experimental analysis
FEM
[[1] Timoshenko S.P., Gere J.M., 1961, Theory of Elastic Stability, McGrawHill Book Company, New York.##[2] ElSawy Khaled M., Nazmy Aly S., 2001, Effect of aspect ratio on the elastic buckling of uniaxially loaded plates with eccentric holes , ThinWalled Structures 39: 983998.##[3] ElSawy Khaled M., Nazmy Aly S., Ikbal Martini M., 2004, Elastoplastic buckling of perforated plates under uniaxial compression , ThinWalled Structures 42: 10831101.##[4] Narayanan R., Chow F.Y., 1984, Ultimate capacity of uniaxially compressed perforated plates, ThinWalled Structures 2: 241264.##[5] Shanmugam N.E., Thevendran V., Tan Y.H., 1999, Design formula for axially compressed perforated plates, ThinWalled Structures 34: 120.##[6] Roberts T.M., Azizian Z.G.,1984, Strength of perforated plates subjected to inplane loading, ThinWalled Structures 2: 153164.##[7] Mignot F., Puel JP., Suquet PM., 1980, Homogenization and bifurcation of perforated plates, Engineering science 18: 409414.##[8] Yetterman A.L., Brown C.J., 1985, The elastic stability of square perforated plates, Computer & Structures 21(6): 12671272.##[9] Maan F.S., Querin O.M., Barton D.C., 2007, Extension of the fixed grid finite element method to eigenvalue problems, Advances in Engineering Software 38(89): 607617.##[10] Singh Anand V., Tanveer M., 2006, Eigenvalue analysis of doubly connected plates with different configurations, Journal of Sound and Vibration 295: 7693.##[11] Aydin Komur M., Sonmez M., 2008, Elastic buckling of rectangular plates under linearly varying inplane normal load with a circular cutout, Mechanics Research Communications 35(6): 361371.##[12] Rahai A.R., Alinia M.M., Kazemi S., 2008, Buckling analysis of stepped plates using modified buckling mode shapes, ThinWalled Structures 46: 484493.##[13] Eccher G., Rasmussen K.J.R., Zandonini R., 2008, Elastic buckling analysis of perforated thinwalled structures by the isoparametric spline finite strip method, ThinWalled Structures 46: 165191.##[14] Maiorana E., Pellegrino C.. Modena C., 2009, Elastic stability of plates with circular and rectangular holes subjected to axial compression and bending moment, Thin Walled Structure 47(3): 241255.##[15] Eccher G., Rasmussen K.J.R., Zandoninib R., 2009, Geometric nonlinear isoparametric spline finite strip analysis of perforated, Thinwalled structures 47(2): 219232.##[16] Paik J.K., 2008, Ultimate strength of perforated steel plates under combined biaxial compression and edge shear loads, ThinWalled Structures 46: 207213.##]
Dynamic Analysis of Offshore Wind Turbine Towers with Fixed Monopile Platform Using the Transfer Matrix Method
2
2
In this paper, an analytical method for vibrations analysis of offshore wind turbine towers with fixed monopile platform is presented. For this purpose, various and the most general models including CS, DS and AF models are used for modeling of wind turbine foundation and axial force is modeled as a variable force as well. The required equations for determination of wind turbine tower response excited by the Morrison force are derived based on Airy wave theory. The transfer matrix is derived for each element of the tower using EulerBernoulli’s beam differential equation and the global transfer matrix is obtained considering boundary conditions of the tower and constructing the point matrix. The effective wave force is intended in several case studies and Persian Gulf Environmental conditions are examined for the installation of wind farms. Finally, the obtained results by the transfer matrix method are compared with the results of the finite elements method and experimental data which show good agreement in spite of low computational cost.
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130
151


M
Feyzollahzadeh
Faculty of Mechanical and Energy Engineering, Shahid Beheshti University, Tehran, Iran
Faculty of Mechanical and Energy Engineering,
Iran


M.J
Mahmoodi
Faculty of Mechanical and Energy Engineering, Shahid Beheshti University, Tehran, Iran
Faculty of Mechanical and Energy Engineering,
Iran
mj_mahmoudi@sbu.ac.ir
Offshore wind turbine tower
Transfer matrix method
Natural Frequencies
Foundation models
Morrison wave force
[[1] Herbert G.M., Iniyan S., Sreevalsan E., Rajapandian S., 2007, A review of wind energy technologies, Renewable and Sustainable Energy 11: 11171145.##[2] Manwell J.F., McGowan J.G., Rogers J.G., 2002, Wind Energy Explained (Theory, Design and Application), John Wiley & Sons.##[3] Data sheet offshore wind energy, 2010, European Wind Energy Association, Publishing Physics Web, www.ewea.com.##[4] Mostafaeipour A., 2010, Feasibility study of offshore wind turbine installation in Iran compared with the world, Renewable and Sustainable Energy 14: 122.##[5] Samani M., Zadegan H., Saibani M., 2011, Feasibility study of offshore wind turbine installation in the Persian Gulf, Proceedings of the 13th Marine Industries Conference .##[6] Kaljahi A., Lotfollahi M., 2013, Performance analysis of tension leg platform offshore wind turbine in The Caspian Sea, Proceedings of the First New Energy Conference.##[7] Kaljahi A., Lotfollahi M., 2013, Technical feasibility study of using offshore wind turbine in the Iran, Proceedings of the First New Energy Conference.##[8] Breton S.P., Moe G., 2009, Status, plans and technologies for offshore wind turbines in Europe and North America, Renewable Energy 34: 646654.##[9] Van Bussel G.J.W., Zaaijer M.B., 2001, Reliability, availability and maintenance aspects of large scale offshore wind farms, Proceedings of the MAREC.##[10] Bhattacharya S., Lombardi D., Wood D.M., 2010, Similitude relationships for physical modeling of monopilesupported offshore wind turbines, International Journal of Physical Modeling in Geotechnics 11: 5868.##[11] Kim K.T., Lee C.W., 2011, Structural vibration analysis of largescale wind turbines considering periodically timevarying parameters, Proceedings of the 13th World Congress in Mechanism and Machine Science.##[12] Chaoyang F., Nan W., Bol Z., Changzheng C., Dynamic performance investigation for largescale wind turbine tower, Proceedings of the IEEE.##[13] Bazeos N., Hatzigeorgiou G. D., HondrosI D., Karamaneas H., Karabalis D. L., Beskos D. E., 2002, Static, seismic and stability analyses of a prototype wind turbine steel tower, Engineering Structures 24: 10151025.##[14] Salehi S., Pirooz M., Daghigh M., 2009, Aerodynamic and structural analysis of offshore wind turbine tower in The Persian Gulf, Proceedings of the Marine industries conference.##[15] Lavassas G., Nikolaidis G., Zervas P., Efthimiou E., Doudoumis I.N., Baniotopoulos C.C., 2003, Analysis and design of the prototype of a steel 1MW wind turbine tower, Engineering Structures 25: 10971106.##[16] He Z., Jianyuan X., Xiaoyu W., 2009, The dynamic characteristics numerical simulation of the wind turbine generators tower based on the turbulence model, Proceedings of the International Conference on Industrial Electronics and Applications.##[17] Bush E., Manuel L., 2009, Foundation models for offshore wind turbines, Proceedings of the Aerospace Sciences Meeting Including the New Horizons Forum and Aerospace Exposition.##[18] Passon P., Kühn1M., Butterfield S., Jonkman J., Camp T., Larsen T.J., 2007, OC3 benchmark exercise of aeroelastic offshore wind turbine codes, Journal of Physics, Conference Series 75: 112.##[19] Chen J., Jiang D., 2010, Modal analysis of wind turbine tower, Proceedings of the IEEE.##[20] Murtagh P.J., Basu B., Broderick B.M., 2004, Simple models for natural frequencies and mode shapes of towers supporting utilities, Computers and Structures 84: 17451750.##[21] Maalawi Y., 2007, A Model for yawing dynamic optimization of a wind turbine structure, International Journal of Mechanical Sciences 49: 11301138.##[22] Wang J., Qin D., Lim T., 2010, Dynamic analysis of horizontal axis wind turbine by thinwalled beam theory, Journal of Sound and Vibration 325: 35653586.##[23] Kort D.A., 2003, The transfer matrix method applied to steel sheet pile walls, International Journal for Numerical and Analytical Methods in Geomechanics 27: 453472.##[24] Dawson B., Davies M., 1974, An improved transfer matrix procedure, International Journal for Numerical Methods in Engineering 8: 111117.##[25] Tso W.K., Chan P.C.K., 1973, Static analysis of stepped coupled walls by transfer matrix method, Building science 8: 167177.##[26] Holzer H., 1921, Die Berechnung der Drehschwingungen, Springer.##[27] Myklestad N.O., 1944, New method of calculating natural modes of uncoupled bending vibrations of airplane wings and other types of beams, Aeronaut Science 6: 153166.##[28] Pestel C., Leckie A., 1963, Matrix Methods in Elastomechanics, McGraw Hill, New York.##[29] Dai H.L., Wang L., Qian Q., Gan J., 2012, Vibration analysis of threedimensional pipes conveying fluid with consideration of steady combined force by transfer matrix method, Applied Mathematics and Computation 219: 24532464.##[30] Orasanu N., Craifaleanu A., 2011, Theoretical and experimental analysis of the vibrations of an elastic beam with four concentrated masses, Proceedings of the SISOM 2011 and Session of the Commission of Acoustics.##[31] Li Q.S., Fang J.Q., Jeary A.P., 2000, Free vibration analysis of cantilevered tall structures under various axial loads, Engineering Structures 22: 525534.##[32] Rohani A., 2002, Vibration analysis of rotor, bearing and membrane system in a Gas turbine, Msc Thesis, Sharif University of Technology,Tehran.##[33] Uhrig R., 1966, The transfer matrix method seen as one method of structural analysis among others, Journal of Sound and Vibration 4: 136148.##[34] Fallah A., 1999, Lateral vibration analysis of ship’s rotor, Msc Thesis, Sharif University of Technology, Tehran.##[35] Farshidianfar A., Hoseinzadeh M., Raghebi M., 2008, A novel way for crack detection in rotors using mode shape changes, Journal of Mechanic and Aerospace 8: 2337.##[36] Bababake M., 2004, Vibration analysis of rotorbearing system by transfer matrix method, Msc Thesis, Sharif University of Technology, Tehran.##[37] Meng W., Zhangqi W., Huaibi Z., 2009, Analysis of wind turbine steel tower by transfer matrix method, Proceedings of the International Conference on Electrical Engineering.##[38] Meng W., Zhangqi W., 2011, The vibration frequencies of wind turbine steel tower by transfer matrix method, Proceedings of the Third International Conference on Measuring Technology and Mechatronics Automation.##[39] Guidelines for Design of Wind Turbines, 2002, Second Edition, Printed by Jydsk Centraltrykkeri, Denmark.##[40] Andersen L.V., Vahdatirad M.J., Sichani M.T., Sorensen J.D.,2012, Natural frequencies of wind turbines on mono pile foundations in clayey soilsA probabilistic approach, Computers and Geotechnics 43: 111.##[41] Petersen B., Pollack M., Connell B., Greeley D., Daivis D., Slavik C., 2010, Evaluate the effect of turbine period of vibration requirements on structural design parameters, Applied Physical Sciences Corp 1012.##[42] Schaumann P., Boker C., 2011, Support Structures of Wind Energy Converters, Springer, Wien New York.##[43] Sadeghi K., 2002, Coasts, Ports and Offshore Structures Engineering, Press of Water and Power University, First Edition.##[44] Taghipoor M., Qureshi Tayebi A., Lotfollahi yaghin A., 2005, Investigation of hydrodynamic forces on the roughness of the pile and compare it with candles, smooth and rough, Proceedings of the First Congress on Civil Engineering.##[45] Feyzollahzadeh M., Vibration analysis of offshore wind turbine on a monopile support structure, Msc Thesis, Shahid Beheshti University,Tehran.##[46] Bir G., Jonkman J., 2008, Modal dynamics of large wind turbines with different support structures, Proceedings of the International Conference on Offshore Mechanics and Arctic Engineering.##[47] Recommended Practice for Planning, Designing and Constructing Fixed Offshore Platforms Working Stress Design, 2000, API Recommended Practice, 2AWSD.##[48] Jonkman J., Butterfield S., Passon P., Larsen T., Camp T., Nichols J., Azcona J., Martinez A., 2008, Offshore code comparison collaboration within IEA wind annex XXIII: phase II results regarding monopile foundation modeling, NREL/CP50042471, National Renewable Energy Laboratory.##[49] Han M., Benaroya H., Wei T., 1999, Dynamics of transversely vibrating beams using four engineering theories, Journal of Sound and vibration 5: 935988.##[50] Wu J., Chen C., 2007, Forced vibration analysis of an offshore tower carrying an eccentric tip mass with rotary Inertia due to support excitation, Ocean Engineering 34: 12351244.##[51] Zhang Y., , Liu Y., , Chen P., Murphy K.D., 2011, Buckling loads and eigen frequencies of a branced beam resting on elastic foundation, Acta Mechanica Solida Sinica 24: 510518.##[52] Parvanova S., 2011, Beams on Elastic Foundation, University of Architecture, Civil Engineering and Geodesy Sofia, 111125.##[53] Feyzollahzadeh M., Yadavar Nikravesh M., Rahi A., 2013, Dynamic analysis of offshore wind turbine tower using the transfer matrix method, Proceedings of the 9th International Energy Conference.##[54] Jonkman J., Musial W., 2010, Offshore code comparison collaboration (OC3), Final Technical Report, NREL/TP500048191, National Renewable Energy Laboratory.##[55] Passon P., 2006, Memorandum: Derivation and Description of the SoilPileInteraction Models, IOP Publishing Physics, IEAAnnex XXIIII Subtask 2, Stuttgart, Germany.##[56] Devriendt C., Jordaens P., Ingelgem Y. V., Sitter G. D., Guillaume P., 2012, Monitoring of Resonant Frequencies and Damping Values of an Offshore Wind Turbine on a Monopile Foundation, Offshore Wind Infrastructure, IOP Publishing Physics.##[57] General Specification V90 – 3.0 MW Variable Speed Turbine, 2004, Item no. 950010.R1, IOP Publishing Physics.##]
An Exact Solution for KelvinVoigt Model Classic Coupled Thermo Viscoelasticity in Spherical Coordinates
2
2
In this paper, the classic KelvinVoigt model coupled thermoviscoelasticity model of hollow and solid spheres under radial symmetric loading condition is considered. A full analytical method is used and an exact unique solution of the classic coupled equations is presented. The thermal and mechanical boundary conditions, the body force, and the heat source are considered in the most general forms and where no limiting assumption is used. This generality allows simulate varieties of applicable problems. At the end, numerical results are presented and compared with classic theory of thermoelasticity.
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152
167


S
Bagheri
Mechanical Engineering Department, Islamic Azad University, South Tehran Branch, Tehran, Iran
Mechanical Engineering Department, Islamic
Iran


M
Jabbari
Mechanical Engineering Department, Islamic Azad University, South Tehran Branch, Tehran, Iran
Mechanical Engineering Department, Islamic
Iran
mohsen.jabbari@gmail.com
Coupled thermo viscoelasticity
Hollow sphere
Exact solution
KelvinVoigt method
[[1] Lahiri A., Kar T. K., 2007, Eigenvalue approach to generalized thermoviscoelasticity with one relaxation time parameter, Tamsui Oxford Journal of Mathematical Sciences 23(2): 185218.##[2] Hetnarski R. B., 1964, Solution of the coupled problem of thermoelasticity in the form of series of functions, Archiwum Mechaniki Stosowanej 16: 919941.##[3] Hetnarski R. B., Ignaczak J., 1993, Generalized thermoelasticity closedform solutions, Journal of Thermal Stresses 16: 473498.##[4] Hetnarski R. B., Ignaczak J., 1994, Generalized thermoelasticity: response of semispace to a short laser Pulse, Journal of Thermal Stresses 17: 377396.##[5] Georgiadis H. G., Lykotrafitis G., 2005, Rayleigh waves generated by a thermal source: a threedimensional transient thermoelasticity solution, Journal of Applied Mechanics 72: 129138.##[6] Wagner P., 1994, Fundamental matrix of the system of dynamic linear thermoelasticity, Journal of Thermal Stresses 17: 549565.##[7] Bahtui A., Eslami M. R., 2007, Coupled thermoelasticity of functionally graded cylindrical shells, Mechanics Research Communications 34: 118.##[8] Bagri A., Eslami M. R., 2004, Generalized coupled thermoelasticity of disks based on the lordshulman model, Journal of Thermal Stresses 27: 691704.##[9] AbdAlla A.M., Hammad H. A. H., AboDahab S.M., 2004, Magnetothermoviscoelastic interactions in an unbounded body with a spherical cavity subjected to a periodic loading, Applied Mathematics and Computation 155: 235248.##[10] Knopoff L., 1955, The interaction between elastic wave motions and a magnetic field in electrical conductors, Journal of Geophysical Research 60: 441456.##[11] Chadwick P., 1957, Elastic waves propagation in a magnetic field, Proceeding of the International Congress of Applied Mechanics, Brusseles, Belgium.##[12] Nowacki W., Francis P.H., Hetnarski R.B., 1975, Dynamic Problems of Thermoelasticity, Noordhoff, Leyden.##[13] Misra J. C., Samanta S. C., Chakrabarti A. K., 1991, Magnetothermomechanical interaction in an aeolotropic viscoelastic cylinder permeated by a magnetic field subjected to a periodic loading, International Journal of Engineering Science 29 (10): 12091216.##[14] Misra J. C., Chatopadhyay N. C. , Samanta S. C., 1994, Thermoviscoelastic waves in an infinite aeolotropic body with a cylindrical cavitya study under the review of generalized theory of thermoelasticity, Composite Structures 52 (4): 705717.##[15] Abdalla A. N. , Yahia A.A., AboDahab S. M., 2003, On the reflection of the generalized magnetothermoviscoelastic plane waves, Chaos, Solitons & Fractal 16: 211231.##[16] Kaleski S., 1963, Aborpation of magnetoviscoelastic surface waves in a real conductor in a magnetic field, Proceedings of Vibration Problems 4 : 319329.##[17] AbdAlla A. M., Mahmoud S. R., 2011, Magnetothermoviscoelastic interactions in an unbounded nonhomogeneous body with a spherical cavity subjected to a periodic loading, Applied Mathematical Sciences 5(29):1431 1447.##[18] Song Y. C., Zhang Y. Q., Xu H. Y., Lu B. H., 2006, Magnetothermoviscoelastic wave propagation at the interface between two micropolar viscoelastic media, Applied Mathematics and Computation 176: 785802.##[19] AboDahab S.M., 2012, Effect of magnetothermoviscoelasticity in an unbounded body with a spherical cavity subjected to a harmonically varying temperature without energy dissipation, Meccanica 47:613620.##[20] Sharma J. N., 2005, Some considerations on the rayleighlamb wave propagation in viscothermoelastic plate, Journal of Vibration and Control 11: 1311 1335.##[21] Sharma J. N., Singh D., Kumar R., 2004, Propagation of generalized viscothermoelastic RayleighLamb waves in homogeneous isotropic plates, Journal of Thermal Stresses 27: 645 669.##[22] RoyChudhuri S. K., Mukhopdhyay S., 2000, Effect of rotation and relaxation on plane waves in generalized thermoviscoelasticity, International Journal of Mathematics and Mathematical Sciences 23: 497505.##[23] Othman M. I. A., Abbas I. A., 2012, Fundamental solution of generalized thermoviscoelasticity using the finite element method, Computational Mathematics and Modeling 23 (2):158167.##[24] Kar A., Kanoria M., 2009, Generalized thermoviscoelastic problem of a spherical shell with threephaselag effect,. Applied Mathematical Modelling 33: 32873298.##[25] Ezzat M. A., Othman M. I., El Karamany A.S., 2002, State space approach to generalized thermoviscoelasticity with two relaxation times, International Journal of Engineering Science 40: 283302.##[26] Ezzat M. A., El Karamany A. S., Smaan A. A., 2001, State space formulation to generalized thermoviscoelasticity with thermal relaxation, Journal of Thermal Stresses 24: 823 846.##[27] Jabbari M., Dehbani H., Eslami M. R., 2010, An exact solution for classic coupled thermoelasticity in spherical coordinates, Journal of Pressure Vessel Technology 132 (3): 031201.##]
Frequency Aanalysis of Annular Plates Having a Small Core and Guided Edges at Both Inner and Outer Boundaries
2
2
This paper deals with frequency analysis of annular plates having a small core and guided edges at both inner and outer boundaries. Using classical plate theory the governing differential equation of motion for the annular plate having a small core is derived and solved for the case of plate being guided at inner and outer edge boundaries. The fundamental frequencies for the first six modes of annular plate vibrations are computed for different materials and varying values of the radius parameter. The fundamental frequencies thus obtained may be classified into to axisymmetric and/or nonaxisymmetric modes of vibration. The exact values of fundamental frequencies presented in this paper clearly show that no mode switching takes place for the case of annular plates with guided edges. The results presented in this paper will be of use in design and also serve as benchmark values to enable the researchers to validate their results obtained using numerical methods such as differential quadrature or finite element methods.
1

168
174


L.B
Rao
School of Mechanical and Building Sciences, VIT University, Chennai Campus, VandalurKelambakkam Road, Chennai600127, Tamil Nadu, India
School of Mechanical and Building Sciences,
India
bhaskarbabu_20@yahoo.com


C.K
Rao
Nalla Narsimha Reddy Engineering College, Korremula 'X' Road, Chowdariguda (V), Ghatkesar (M), Ranga Reddy (dt)  500088, Telangana State, India
Nalla Narsimha Reddy Engineering College,
India
Annular Plate
vibrations
Guided edge
Mode switching
[[1] Leissa A.W., 1969, Vibration of Plates, NASA SP160.##[2] Leissa A.W., 1977, Recent research in plate vibrations: classical theory, Shock and Vibration Digest 9(10): 1324.##[3] Leissa A.W., 1987, Recent research in plate vibrations, classical theory, Shock and Vibration Digest 19: 1118.##[4] Weisensel G.N., 1989, Natural frequency information for circular and annular plates, Journal of Sound and Vibration 133(1): 129134.##[5] Soedel W., 1993, Vibrations of Shells and Plates, Marcel Dekker, New York.##[6] Gabrielson T.B., 1999, Frequency constants for transverse vibration of annular disks, Journal of the Acoustical Society of America 105(6): 33113317.##[7] Irie T., Yamada G., Takagi K., 1982, Natural frequencies of thick annular plates, Journal of Applied Mechanics 49(3): 633638.##[8] Ramaiah G. K., 1980, Flexural vibrations of annular plates under uniform inplane compressive forces, Journal of Sound and Vibration 70(1): 117131.##[9] Vera S.A., Laura P.A.A., Vega D.A., 1999, Transverse vibrations of a freefree circular annular plate, Journal of Sound and Vibration 224(2): 379383.##[10] Amabili M., Garziera R., 1999, Comments and additions to transverse vibrations of circular, annular plates with several combinations of boundary conditions, Journal of Sound and Vibration 228: 443447.##[11] Southwell R.V., 1922, On the transverse vibrations of uniform circular disc clamped at its center and the effects of rotation, Proceedings of the Royal Society of London A 101(709): 133153.##[12] Kim C.S., Dickinson S.M., 1990, The flexural vibration of thin isotropic and polar orthotropic annular and circular plates with elastically restrained peripheries, Journal of Sound and Vibration 143(1): 171179.##[13] Bhaskara Rao L., Kameswara Rao C., 2011, Fundamental buckling of annular plates with elastically restrained guided edges against translation, Mechanics Based Design of Structures and Machines 39(4): 409419.##[14] Bhaskara Rao L., Kameswara Rao C., 2012, Vibrations of circular plates with guided edge and resting on elastic foundation, Journal of Solid Mechanic 4(3): 307312.##[15] Wang C.Y., Wang C.M., 2005, Examination of the fundamental frequencies of annular plates with small core, Journal of Sound and Vibration 280(35): 11161124.##]
Consolidation Around a Heat Source in an Isotropic Fully Saturated Rock with Porous Structure in QuasiStatic State
2
2
The titled problem of coupled thermoelasticity for porous structure has been solved with an instantaneous heat source acting on a plane area in an unbounded medium. The basic equations of thermoelasticity, after being converted into a onedimensional form, have been written in the form of a vectormatrix differential equation and solved by the eigenvalue approach for the field variables in the Laplace transform domain in closed form. The deformation, temperature and pore pressure have been determined for the space time domain by numerical inversion from the Laplace transform domain. Finally the results are analyzed by depicting several graphs for the field variables.
1

175
183


N
Das Gupta
Department of Mathematics, Jadavpur University, Kolkata, India
Department of Mathematics, Jadavpur University,
India
gangulynilanjana@rediffmail.com


N.C
Das
Department of Mathematics, Brainware Group of Institutions, Barasat, India
Department of Mathematics, Brainware Group
India
Consolidation
Porous
Isotropic
Thermoelasticity
QuasiStatic
[[1] Nunziato J.W., Cowin S.C., 1979, A nonlinear theory of elastic materials with voids, Archive for Rational Mechanics and Analysis 72: 175201.##[2] Iesan D., 2006, Nonlinear plane strain of elastic materials with voids, Mathematics and Mechanics of solids 11:361384.##[3] Cowin S.C., Nunziato J.W., 1983, Linear elastic materials with voids, Journal of Elasticity 13: 125147.##[4] Iesan D., 1986, A theory of thermoelastic materials with voids, Acta Mechanica 60: 6789.##[5] Dhaliwal R.S., Wang J., 1995, A heatflux dependent theory of thermoelasticity with voids, Acta Mechanica 110:3339.##[6] Puri P., Cowin S.C., 1985, Plane waves in linear elastic materials with voids, Journal of Elasticity 15:167183.##[7] Ciarletta M., Chirita S., 2006, On some growthdecay results in thermoelasticity of porous media, Journal of Thermal Stresses 29: 905924.##[8] Cicco S.D., Diaco M., 2002, A theory of thermoelastic materials with voids without energy dissipation, Journal of Thermal Stresses 25: 493503.##[9] Chirita S., Scalia A., 2001, On the spatial and temporal behaviour in linear thermoelasticity of potentials with voids, Journal of Thermal Stresses 24: 433 455.##[10] Scalia A., Pompei A., Chirita S., 2004, On the behaviour of steady time harmonic oscillations thermoelastic materials with voids, Journal of Thermal Stresses 27: 209226.##[11] Chirita S., Ciarletta M., 2008, On the structural stability of thermoelastic model of porous media, Mathematical Methods in the Applied Sciences 31:1934.##[12] Giraud A., Rousset G., 1995, Consolidation around a volumic spherical decaying heat source, Journal of Thermal Stresses 18:513527.##[13] Booker J.R., Savvidou C., 1984, Consolidation around a spherical heat source, International Journal of Solids and Structures 20:10791090.##[14] Sharma J.N., Grover D., 2012, Thermoelastic vibration analysis of Mems/Nems plate resonators with voids, Acta mechanica 223: 167187.##[15] Kumar R., Rani L., 2004, Response of generalized thermoelastic halfspace with voids to mechanical and thermal sources, Meccanica 39: 563584.##[16] Kumar R., Devi S., 2011, Deformation in porousthermoelastic material with temperature dependent properties, An International Journal Applied Mathematics and Information Sciences 5:132147.##[17] Lord H.W., Shulman Y., 1967, A generalized dynamic theory of thermoelasticity, Journal of the Mechanics and Physics of Solids 15:299309.##[18] Rice J.R., Cleary M.P., 1976, Some basic stress diffusion solutions for fluid saturated elastic porous media with compressible constituents, Reviews of Geophysics and Space Physics 14:227241.##[19] Coussy O., 1991, Mecanique des Milieux Preux, Technip Paris.##[20] Biot MA., 1955, Theory of elasticity and consolidation for a porous anisotropic solid, Journal of Applied Physics 26:182185.##[21] Lahiri A., Das N.C., Sarkar S., Das M., 2009, Matrix method of solution of coupled differential equations and its applications in generalized thermoelasticity, Bulletin of Calcutta Mathematical Society 101: 571590.##[22] Zakian V., 1969, Numerical inversion of Laplace transforms, Electronic Letters 5: 120121.##]
Generalized Differential Quadrature Method for Vibration Analysis of Cantilever Trapezoidal FG Thick Plate
2
2
This paper presents a numerical solution for vibration analysis of a cantilever trapezoidal thick plate. The material of the plate is considered to be graded through the thickness from a metal surface to a ceramic one according to a power law function. Kinetic and strain energies are derived based on the ReissnerMindlin theory for thick plates and using Hamilton's principle, the governing equations and boundary conditions are derived in the Cartesian coordinates. A transformation of coordinates is used to convert the equations and boundary conditions from the original coordinate into a new computational coordinates. Generalized differential quadrature method (GDQM) is selected as a strong method and natural frequencies and corresponding modes are derived. The accuracy and convergence of the proposed solution are confirmed using results presented by other authors. Finally, the effect of the power law index, angles and thickness of the plate on the natural frequencies are investigated.
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184
203


K
Torabi
Department of Solid Mechanics, Faculty of Mechanical Engineering, University of Kashan, Kashan, Iran
Department of Solid Mechanics, Faculty of
Iran
kvntrb@kashanu.ac.ir


H
Afshari
Department of Solid Mechanics, Faculty of Mechanical Engineering, University of Kashan, Kashan, Iran
Department of Solid Mechanics, Faculty of
Iran
Generalized differential quadrature method (GDQM)
Vibration analysis
Trapezoidal plate
Functionally graded materials (FGM)
[[1] Chopra I., Durvasula S., 1971, Vibration of simply supported trapezoidal plates I. symmetric trapezoids, Journal of Sound and Vibration 19: 379392.##[2] Chopra I., Durvasula S., 1972, Vibration of simply supported trapezoidal plates II. unsymmetric trapezoids, Journal of Sound and Vibration 20: 125134.##[3] Orris R.M., Petyt M., 1973, A finite element study of the vibration of trapezoidal plates, Journal of Sound and Vibration 27: 325344.##[4] Srinivasan R.S., Babu B.J.C., 1983, Free vibration of cantilever quadrilal plates, Journal of the Acoustical Society of America 73: 851855.##[5] Maruyama K., Ichinomiya O., Narita Y., 1983, Experimental study of the free vibration of clamped trapezoidal plates, Journal of Sound and Vibration 88: 523534.##[6] Bert C.W., Malik M., 1996, Differential quadrature method for irregular domains and application to plate vibration, International Journal of Mechanical Sciences 38: 589606.##[7] Xing Y., Liu B., 2009, Highaccuracy differential quadrature finite element method and its application to free vibrations of thin plate with curvilinear domain, International Journal for Numerical Methods in Engineering 80: 17181742.##[8] Shufrin I., Rabinovitch O., Eisenberger M., 2010, A semianalytical approach for the geometrically nonlinear analysis of trapezoidal plates, International Journal of Mechanical Sciences 52: 15881596.##[9] Zhou L., Zheng W.X., 2008, Vibration of skew plates by the MLSRitz method, International Journal of Mechanical Sciences 50: 11331141.##[10] Zamani M., Fallah A., Aghdam M.M., 2012, Free vibration analysis of moderately thick trapezoidal symmetrically laminated plates with various combinations of boundary conditions, European Journal of Mechanics  A/Solids 36: 204212.##[11] HosseiniHashemi Sh., Fadaee M., Atashipour S.R., 2011, A new exact analytical approach for free vibration of Reissner–Mindlin functionally graded rectangular plates, International Journal of Mechanical Sciences 53: 1122.##[12] Shaban M., Alipour M.M., 2011, Semianalytical solution for free vibration of thick functionally graded plates rested on elastic foundation with elastically restrained edge, Acta Mechanica Solida Sinica 24: 340354.##[13] Hasani Baferani A., Saidi A.R., Ehteshami H., 2011, Accurate solution for free vibration analysis of functionally graded thick rectangular plates resting on elastic foundation, Composite Structure 93: 18421853.##[14] Zhu P., Liew K.M., 2011, Free vibration analysis of moderately thick functionally graded plates by local Kriging meshless method, Composite Structure 93: 29252944.##[15] HosseiniHashemi Sh., Salehipour H., Atashipour S.R, Sburlati R., 2013, On the exact inplane and outofplane free vibration analysis of thick functionally graded rectangular plates: Explicit 3D elasticity solutions, Composites Part B 46: 108115.##[16] Jin G., Su Z., Shi Sh., Ye T., Gao S., 2014, Threedimensional exact solution for the free vibration of arbitrarily thick functionally graded rectangular plates with general boundary conditions, Composite Structure 108: 565577.##[17] Xia P., Long S.Y., Cui H.X., Li G.Y., 2009, The static and free vibration analysis of a nonhomogeneous moderately thick plate using the meshless local radial point interpolation method, Engineering Analysis with Boundary Elements 33: 770777.##[18] Huang M., Ma X.O., Sakiyama T., Matuda M., Morita C., 2005, Free vibration analysis of plates using leastsquarebased on finite difference method, Journal of Sound and Vibration 288: 931955.##[19] NguyenXuan H., Liu G.R., ThaiHoang C., 2010, An edgebased smoothed finite element method (ESFEM) with stabilized discrete shear gap technique for analysis of ReissnerMinslin, Computer Methods in Applied Mechanics and Engineering 199: 471489.##[20] Leung A.Y.T., Zhu B., 2005, Transverse vibration of Mindlin Plates on twoparameter foundations by analytical trapezoidal pelements, Journal of Engineering Mechanics 131: 11401145.##[21] Huang C.S., Leissa A.W., Chang M.J., 2005, Vibrations of skewed cantilevered triangular, trapezoidal and parallelogram Mindlin plates with considering corner stress singularities, International Journal for Numerical Methods in Engineering 62: 17891806.##[22] Abrate S., 2006, Free vibration, buckling, and static deflections of functionally graded plates, Composites Science and Technology 66: 23832394.##[23] Zhao X., Lee Y.Y., Liew K.M., 2009, Free vibration analysis of functionally graded plates using the elementfree kpRitz method, Journal of Sound and Vibration 319: 918 939.##[24] Eftekhari S.A., Jafari A.A., 2013, Modified mixed RitzDQ formulation for free vibration of thick rectangular and skew plates with general boundary conditions, Applied Mathematical Modelling 37: 73987426.##[25] Petrolito J., 2014, Vibration and stability analysis of thick orthotropic plates using hybridTrefftz elements, Applied Mathematical Modelling 38:58585869.##[26] Mindlin R.D., 1951, Influence of rotary inertia and shear on flexural motions of isotropic elastic plates, Journal of Applied Mechanics 18: 3138.##[27] Liew K.M., Wang C.M., Xiang Y., Kitipornchai S., 1998, Vibration of Mindlin Plates, Elsevier.##[28] Kaneko T., 1975, On Timoshenko’s correction for shear in vibrating beams, Journal of Physics D: Applied Physics 8: 19281937.##[29] Bert C.W., Malik M., 1996, Differential quadrature method in computational mechanics: A review, Applied Mechanics Reviews 49: 128.##]
Steady Thermal Stresses in a Thin Rotating Disc of Finitesimal Deformation with Mechanical Load
2
2
Seth’s transition theory is applied to the problems of thickness variation parameter in a thin rotating disc by finite deformation. Neither the yield criterion nor the associated flow rule is assumed here. The results obtained here are applicable to compressible materials. If the additional condition of incompressibility is imposed, then the expression for stresses corresponds to those arising from Tresca yield condition. It has observed that for rotating disc made of compressible material required higher angular speed to yield at the internal surface as compare to disc made of incompressible material and a much higher angular speed is required to yield with the increase in radii ratio. With the introduction of thermal effects, lesser angular speed is required to yield at the internal surface. Thermal effect in the disc increase the value of circumferential stress at the internal surface and radial stresses at the external surface for compressible as compare to incompressible material.
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204
211


J
Kaur
Department of Mathematics, Punjabi University Patiala, Punjab 147002, India
Department of Mathematics, Punjabi University
India


P
Thakur
Department of Mathematics, IEC University Baddi, Solan, Himachal Pradesh 174103, India
Department of Mathematics, IEC University
India
dr_pankajthakur@yahoo.com


S.B
Singh
Department of Mathematics, Punjabi University Patiala, Punjab 147002, India
Department of Mathematics, Punjabi University
India
Plastic
Transitional
Finitesimal
Stresses
Disc
Load
temperature
[[1] Timoshenko S.P., Goodier J.N., 1951, Theory of Elasticity , 3rd Edition, New York, McGrawHill Book Coy, London.##[2] Chakrabarty J., 1987, Theory of Plasticity, New York, McGrawHill Book Coy.##[3] Heyman J., 1958, Plastic design of rotating discs, Proceedings of the Institution of Mechanical Engineers 172(1): 531546.##[4] Parmaksigoglu C., Guven U., 1998, Plastic stress distribution in a rotating disc with rigid inclusion under a radial tem perature gradient, Mechanics of Structures and Machines 26 : 920.##[5] Seth B.R., 1962, Transition theory of elasticplastic deformation, creep and relaxation, Nature 195:896897.##[6] Seth B.R., 1966, Measure concept in mechanics, International Journal of NonLinear Mechanics 1(1): 3540.##[7] Parkus H., 1976, ThermoElasticity, SpringerVerlag, Wien, New York, USA.##[8] Gupta S. K., Thakur P. , 2008, Creep transition in an isotropic disc having variable thickness subjected to internal pressure, Proceedings of the National Academy of Sciences Section A 78(1): 5766.##[9] Gupta S.K., Thakur P. ,2007, Thermo elastic  plastic transition in a thin rotating disc with inclusion, Thermal Science 11(1): 103118.##[10] Gupta S.K., Thakur P.,2007, Creep transition in a thin rotating disc with rigid inclusion, Defence Science Journal 57(2) : 185195.##[11] Thakur P. ,2009, Elastic  plastic transition in a thin rotating disc having variable density with Inclusion, Structural Integrity and Life 9(3):71179.##[12] Thakur P., 2010 , Elasticplastic transition stresses in a thin rotating disc with rigid inclusion by infinitesimal deformation under steady state Temperature, Thermal Science International Scientific Journal 14(1): 209219.##[13] Thakur P., 2010, Creep transition stresses in a thin rotating disc with shaft by finite deformation under steady state temperature, Thermal Science International Scientific Journal 14(2) : 425436.##[14] Thakur P., 2011, Effect of transition stresses in a disc having variable thickness and Poisson’s ratio subjected to internal pressure, Wseas Transactions on Applied and Theoretical Mechanics 6(4): 147159.##[15] Thakur P., 2012, Deformation in a thin rotating disc having variable thickness and edge load with inclusion at the elasticplastic transitional stress, Integritet i Vek Konstrukcija 12(1): 6570.##[16] Thakur P., 2013 , Stresses in a thin rotating disc of variable thickness with rigid shaft, International Journal for Technology of Plasticity 37(1): 114.##[17] Thakur P., Singh S. B., Kaur J., 2013, Steady thermal stresses in a rotating disk with shaft having density variation parameter subjected to thermal load , Structural Integrity and Life 13(2): 109116.##[18] Thakur P., 2013, Analysis of stresses in a thin rotating disc with inclusion and edge loading, Scientific Technical Review 63(3): 916.##[19] Thakur P., Singh S. B., Kaur J., 2013, Thickness variation parameter in thin rotating disc, FME Transaction 41(2) : 96102.##[20] Thakur P., Singh S. B., Kaur J., 2014, Elasticplastic transitional stress in a thin rotating disc with shaft having variable thickness under steady state temperature, Kragujevac Journal of Science 36: 517.##[21] Levitsky M., Shaffer B. W., 1975, Residual thermal stresses in a solid sphere form a thermosetting material, Journal of Applied Mechanics 42 (3): 651655.##]
Free Vibration Analysis of Continuously Graded Fiber Reinforced Truncated Conical Shell Via ThirdOrder Shear Deformation Theory
2
2
This paper deals with free vibration analysis of continuously graded fiber reinforced (CGFR) truncated conical shell based on thirdorder shear deformation theory (TSDT), by developing special powerlaw distributions. The orthotropic (CGFR) truncated conical shell are clamped and simply supported at the both ends. It is assumed to have a smooth variation of fibers volume fraction in the thickness direction. Symmetric and classic volume fraction profiles are examined. The appropriate displacement functions which identically satisfy the axisymmertic conditions are used to simplify the motion equations to a set of coupled ordinary differential equation with variable coefficients, which can be solved by generalized differential quadrature method (GDQM), to obtain the natural frequencies. The fast rate of convergence of the method is observed. To validate the results, comparisons are made with the available solutions for isotropic and CGM isotropic truncated conical shells. The effect of various geometrical parameters on the vibrational behavior of the CGFR truncated conical shell is investigated. This literature mainly contributes to illustrate the impact of the powerlaw distributions on the vibrarional behavior of orthotropic continuous grading truncated conical shell. This paper is also supposed to present useful results for continuouly graded fibers volume fraction in the thickness direction of a truncated conical shell and comparison with similar discrete laminated composite one.
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212
231


M.H
Yas
Mechanical Engineering Department, Razi University, Kermanshah, Iran
Mechanical Engineering Department, Razi University
Iran
yas@razi.ac.ir


M
Nejati
Mechanical Engineering Department, Razi University, Kermanshah, Iran
Mechanical Engineering Department, Razi University
Iran


A
Asanjarani
Department of Mechanical Engineering, Islamic Azad University, Arak Branch, Iran
Department of Mechanical Engineering, Islamic
Iran
Continuously graded fiber reinforced
Special powerlaw distributions
Truncated conical shell
Free Vibration
TSDT
[[1] Malekzadeh P., 2009, Threedimensional free vibration analysis of thick functionally graded plates on elastic foundations, Composite Structures 89: 367373.##[2] HosseiniHashemi Sh., Rokni H., Damavandi T., Akhavan H., Omidi M., 2010, Free vibration of functionally graded rectangular plates using firstorder shear deformation plate theory, Applied Mathematical Modelling 34: 12761291.##[3] Pan E., Han F., 2005, Exact solution for functionally graded and layered magnetoelectro elastic plates, International Journal of Engineering Science 43: 321339.##[4] Yas M.H., Sobhani Aragh B., 2010, Free vibration analysis of continuously graded fiber reinforced plates on elastic foundation, International Journal of Engineering Science 48: 18811895.##[5] Chen W.Q., 2000, Vibration theory of nonhomogeneous, spherically isotropic piezoelastic bodies, Journal of Sound and Vibration 229: 833860.##[6] Chiroiu V., Munteanu L., 2007, On the free vibrations of a piezoceramic hollow sphere, Mechanics Research Communications 34: 123129.##[7] Bahtui A., Eslami M.R., 2007, Coupled thermoelasticity of functionally graded cylindrical shells, Mechanics Research Communications 34: 118.##[8] Haddadpour H., Mahmoudkhani S., Navazi H.M., 2007, Free vibration analysis of functionally graded cylindrical shells including thermal effects, ThinWalled Structures 45: 591599.##[9] Sobhani Aragh B., Yas M.H., 2010, Static and free vibration analyses of continuously graded ﬁberreinforced cylindrical shells using generalized powerlaw distribution, Acta Mechanica 215: 155173.##[10] Sobhani Aragh B., Yas M.H., 2010, Threedimensional analysis of thermal stresses in fourparameter continuous grading ﬁber reinforced cylindrical panels, International Journal of Mechanical Sciences 52: 10471063.##[11] Sobhani Aragh B., Yas M.H., 2010, Threedimensional free vibration of functionally graded fiber orientation and volume fraction cylindrical panels, Materials & Design 31: 45434552.##[12] Yas M.H., Sobhani Aragh 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