2019
11
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0
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SizeDependent Analysis of Orthotropic Mindlin Nanoplate on Orthotropic ViscoPasternak Substrate with Consideration of Structural Damping
http://jsm.iauarak.ac.ir/article_665162.html
10.22034/jsm.2019.665162
1
This paper discusses static and dynamic response of nanoplate resting on an orthotropic viscoPasternak foundation based on Eringen’s nonlocal theory. Graphene sheet modeled as nanoplate which is assumed to be orthotropic and viscoelastic. By considering the Mindlin plate theory and viscoelastic KelvinVoigt model, equations of motion are derived using Hamilton’s principle which are then solved analytically by means of Fourier series Laplace transform method. The parametric study is thoroughly accomplished, concentrating on the influences of size effect, elastic foundation type, structural damping, orthotropy directions and damping coefficient of the foundation, modulus ratio, length to thickness ratio and aspect ratio. Results depict that the structural and foundation damping coefficients are effective parameters on the dynamic response, particularly for large damping coefficients, where response of nanoplate is damped rapidly.
0

236
253


A
Ghorbanpour Arani
Faculty of Mechanical Engineering, University of Kashan, Kashan, Iran
Institute of Nanoscience & Nanotechnology, University of Kashan, Kashan, Iran
Iran
aghorban@kashanu.ac.ir


M.H
Jalaei
Faculty of Mechanical Engineering, University of Kashan, Kashan, Iran
Iran


S
Niknejad
Faculty of Mechanical Engineering, University of Kashan, Kashan, Iran
Iran


A.A
Ghorbanpour Arani
School of Mechanical Engineering, College of Engineering, University of Tehran, Tehran, Iran
Iran
Nonlocal static and dynamic response
Orthotropic nanoplate and foundation
Fourier seriesLaplace transform
Structural and external damping
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Bose S., Khanra P., Mishra A.K., Kim N.H., Lee J.H., 2011, Recent advances in graphenebased biosensors, Biosensors and Bioelectronics 26: 46374648.##[8] Sun X., Liu Z., Welsher K., Robinson J.T., Goodwin A., Zaric S., Dai H., 2008, Nanographene oxide for cellular imaging and drug delivery, Nano Research 1: 203212.##[9] 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: 14771508.##[10] Akgöz, B., Civalek Ö., 2012, Free vibration analysis for singlelayered graphene sheets in an elastic matrix via modified couple stress theory, Materials and Design 42: 164171.##[11] Ghorbanpour Arani A., Abdollahian M., Jalaei M.H., 2015, Vibration of bioliquidfilled microtubules embedded in cytoplasm including surface effects using modified couple stress theory, Journal of Theoretical Biology 367: 2938.##[12] Eringen A.C., 2002, Nonlocal Continuum Field Theories, New York, Springer.##[13] Pradhan S.C., Murmu T., 2009, Small scale effect on the buckling of singlelayered graphene sheets under biaxial compression via nonlocal continuum mechanics, Computational Materials Science 47: 268274.##[14] Hosseini Hashemi Sh., Tourki Samaei A., 2011, Buckling analysis of micro/nanoscale plates via nonlocal elasticity theory, Physica E 43: 14001404.##[15] Shen H.S., 2011, Nonlocal plate model for nonlinear analysis of thin films on elastic foundations in thermal environments, Composite Structures 93: 11431152.##[16] Ansari R., Rouhi H., 2012, Explicit analytical expressions for the critical buckling stresses in a monolayer graphene based on nonlocal elasticity, Solid State Communications 152: 5659.##[17] Mohammadi M., Ghayour M., Farajpour A., 2013, Free transverse vibration analysis of circular and annular graphene sheets with various boundary conditions using the nonlocal continuum plate model, Composites: Part B 45: 3242.##[18] Zenkour A.M., Sobhy M., 2013, Nonlocal elasticity theory for thermal buckling of nanoplates lying on Winkler–Pasternak elastic substrate medium, Physica E 53: 251259.##[19] Ghorbanpour Arani A., Maboudi M.J., Kolahchi R., 2014, Nonlinear vibration analysis of viscoelastically coupled DLAGSsystem, European Journal of Mechanics A/Solids 45: 185197.##[20] Kananipour H., 2014, Static analysis of nanoplates based on the nonlocal Kirchhoff and Mindlin plate theories using DQM, Latin American Journal of Solids and Structures 11: 17091720.##[21] Mohammadi M., Farajpour A., Goodarzi M., Shehni nezhad pour H., 2014, Numerical study of the effect of shear inplane load on the vibration analysis of graphene sheet embedded in an elastic medium, Computational Materials Science 82: 510520.##[22] Golmakani M.E., Rezatalab J., 2014, Nonlinear bending analysis of orthotropic nanoscale plates in an elastic matrix based on nonlocal continuum mechanics, Composite Structures 111: 8597.##[23] Liu C.C., Chen Z.B., 2014, Dynamic analysis of finite periodic nanoplate structures with various boundaries, Physica E 60: 139146.##[24] Ghorbanpour Arani A., Jalaei M.H., 2015, Nonlocal dynamic response of embedded singlelayered graphene sheet via analytical approach, Journal of Engineering Mathematics 92: 129144.##[25] Pouresmaeeli S., Ghavanloo E., Fazelzadeh S.A., 2013, Vibration analysis of viscoelastic orthotropic nanoplates resting on viscoelastic medium, Composite Structures 96: 405410.##[26] Karličić D., Kozić P., Pavlović R., 2014, Free transverse vibration of nonlocal viscoelastic orthotropic multinanoplate system (MNPS) embedded in a viscoelastic medium, Composite Structures 115: 8999.##[27] Wang Y., Li F.M., Wang Y.Z., 2015, Nonlinear vibration of double layered viscoelastic nanoplates based on the nonlocal theory, Physica E 67: 6576.##[28] Hosseini Hashemi Sh., Mehrabani H., AhmadiSavadkoohi A., 2015, Exact solution for free vibration of coupled double viscoelastic graphene sheets by viscoPasternak medium, Composites Part B 78: 377383.##[29] Reddy J.N., 2004, Mechanics of Laminated Composite Plates and Shells: Theory and Analysis, CRC Press, Boca Raton.##[30] Ghorbanpour Arani A., Shiravand A., Rahi M., Kolahchi R., 2012, Nonlocal vibration of coupled DLGS systems embedded on viscoPasternak foundation, Physica B 407: 41234131.##[31] Kutlu A., Uğurlu B., Omurtag M.H., Ergin A., 2012, Dynamic response on Mindlin plates resting on arbitrarily orthotropic Pasternak foundation and partially in contact with fluid, Ocean Engineering 42: 112125.##[32] Kiani Y., Sadighi M., Eslami M.R., 2013, Dynamic analysis and active control of smart doubly curved FGM panels, Composite Structures 102: 205216.##[33] Krylov V.I., Skoblya N.S., 1977, A Handbook of Methods of Approximate Fourier Transformation and Inversion of the Laplace Transformation, Moscow, Mir Publishers.##[34] Mohammadi M., Farajpour A., Goodarzi M., Heydarshenas., 2013, Levy type solution for nonlocal thermomechanical vibration of orthotropic monolayer graphene sheet embedded in an elastic medium, Journal of Solid Mechanics 5: 116132.##[35] Thai HT., Kim SE., 2012, Analytical solution of a two variable refined plate theory for bending analysis of orthotropic Levytype plates, International Journal of Mechanical Sciences 54: 269276.##[36] Reddy J.N., 2000, Analysis of functionally graded plates, International Journal for Numerical Methods in Engineering 47: 663684.##]
1

Influence of Rotation on Vibration Behavior of a Functionally Graded Moderately Thick Cylindrical Nanoshell Considering Initial Hoop Tension
http://jsm.iauarak.ac.ir/article_665254.html
10.22034/jsm.2019.665254
1
In this research, the effect of rotation on the free vibration is investigated for the sizedependent cylindrical functionally graded (FG) nanoshell by means of the modified couple stress theory (MCST). MCST is applied to make the design and the analysis of nano actuators and nano sensors more reliable. Here the equations of motion and boundary conditions are derived using minimum potential energy principle and firstorder shear deformation theory (FSDT). The formulation consists of the Coriolis, centrifugal and initial hoop tension effects due to the rotation. The accuracy of the presented model is verified with literatures. The novelty of this study is the consideration of the rotation effects along with the satisfaction of various boundary conditions. Generalized differential quadrature method (GDQM) is employed to discretize the equations of motion. Then the investigation has been made into the influence of some factors such as the material length scale parameter, angular velocity, length to radius ratio, FG power index and boundary conditions on the critical speed and natural frequency of the rotating cylindrical FG nanoshell.
0

254
271


H
Safarpour
Faculty of Engineering, Department of Mechanics, Imam Khomeini International University, Qazvin, Iran
Iran


M.M
Barooti
Faculty of Engineering, Department of Mechanics, Imam Khomeini International University, Qazvin, Iran
Iran


M
Ghadiri
Faculty of Engineering, Department of Mechanics, Imam Khomeini International University, Qazvin, Iran
Iran
ghadiri@eng.ikiu.ac.ir
Critical speed
Initial hoop tension
Functionally graded material
GDQM
Moderately thick cylindrical nanoshell
Modified couple stress theory
[[1] Ghadiri M., Safarpour H., 2016, Free vibration analysis of embedded magnetoelectrothermoelastic cylindrical nanoshell based on the modified couple stress theory, Applied Physics A 122: 833.##[2] Bryan G. H., 1890, On the beats in the vibrations of a revolving cylinder or bell, Proceedings of the Cambridge Philosophical Society.##[3] DiTaranto R., Lessen M., 1964, Coriolis acceleration effect on the vibration of a rotating thinwalled circular cylinder, Journal of Applied Mechanics 31: 700701.##[4] Srinivasan A., Lauterbach G. F., 1971, Traveling waves in rotating cylindrical shells, Journal of Engineering for Industry 93: 12291232.##[5] Zohar A., Aboudi J., 1973, The free vibrations of a thin circular finite rotating cylinder, International Journal of Mechanical Sciences 15: 269278.##[6] Padovan J., 1973, Natural frequencies of rotating prestressed cylinders, Journal of Sound and Vibration 31: 469482.##[7] Padovan J., 1975, Traveling waves vibrations and buckling of rotating anisotropic shells of revolution by finite elements, International Journal of Solids and Structures 11: 13671380.##[8] Padovan J., 1975, Numerical analysis of asymmetric frequency and buckling eigenvalues of prestressed rotating anisotropic shells of revolution, Computers & Structures 5: 145154.##[9] Endo M., Hatamura K., Sakata M., Taniguchi O., 1984, Flexural vibration of a thin rotating ring, Journal of Sound and Vibration 92: 261272.##[10] Saito T., Endo M., 1986, Vibration of finite length, rotating cylindrical shells, Journal of Sound and Vibration 107: 1728.##[11] Huang S., Soedel W., 1988, Effects of coriolis acceleration on the forced vibration of rotating cylindrical shells, Journal of Applied Mechanics 55: 231233.##[12] Huang S., Hsu B., 1990, Resonant phenomena of a rotating cylindrical shell subjected to a harmonic moving load, Journal of Sound and Vibration 136: 215228.##[13] Yang Z., Nakajima M., Shen Y., Fukuda T., 2011, Nanogyroscope assembly using carbon nanotube based on nanorobotic manipulation, MicroNano Mechatronics and Human Science (MHS), International Symposium.##[14] Malekzadeh P., Heydarpour Y., 2012, Free vibration analysis of rotating functionally graded cylindrical shells in thermal environment, Composite Structures 94: 29712981.##[15] FirouzAbadi R., TorkamanAsadi M., Rahmanian M., 2013, Whirling frequencies of thin spinning cylindrical shells surrounded by an elastic foundation, Acta Mechanica 224: 881892.##[16] HosseiniHashemi S., Ilkhani M., Fadaee M., 2013, Accurate natural frequencies and critical speeds of a rotating functionally graded moderately thick cylindrical shell, International Journal of Mechanical Sciences 76: 920.##[17] Toupin R. A., 1962, Elastic materials with couplestresses, Archive for Rational Mechanics and Analysis 11: 385414.##[18] Koiter W., 1964, Couple stresses in the theory of elasticity, Proceedings van de Koninklijke Nederlandse Akademie van Wetenschappen.##[19] Mindlin R. D., 1964, Microstructure in linear elasticity, Archive for Rational Mechanics and Analysis 16: 5178.##[20] Asghari M., Kahrobaiyan M., Rahaeifard M., Ahmadian M., 2011, Investigation of the size effects in Timoshenko beams based on the couple stress theory, Archive of Applied Mechanics 81: 863874.##[21] Yang F., Chong A., Lam D., Tong P., 2002, Couple stress based strain gradient theory for elasticity, International Journal of Solids and Structures 39: 27312743.##[22] Park S., Gao X., 2006, Bernoulli–Euler beam model based on a modified couple stress theory, Journal of Micromechanics and Microengineering 16: 2355.##[23] Reddy J., 2011, Microstructuredependent couple stress theories of functionally graded beams, Journal of the Mechanics and Physics of Solids 59: 23822399.##[24] Shaat M., Mahmoud F., Gao X.L., Faheem A. F., 2014, Sizedependent bending analysis of Kirchhoff nanoplates based on a modified couplestress theory including surface effects, International Journal of Mechanical Sciences 79: 3137.##[25] Ghadiri M., Safarpour H., 2017, Free vibration analysis of sizedependent functionally graded porous cylindrical microshells in thermal environment, Journal of Thermal Stresses 40: 5571.##[26] Miandoab E. M., Pishkenari H. N., YousefiKoma A., Hoorzad H., 2014, Polysilicon nanobeam model based on modified couple stress and Eringen’s nonlocal elasticity theories, Physica E: Lowdimensional Systems and Nanostructures 63: 223228.##[27] Love A. E. H., 2013, A Treatise on the Mathematical Theory of Elasticity , Cambridge University Press.##[28] Donnell L. H., 1934, A new theory for the buckling of thin cylinders under axial compression and bending, Transactions of the American Society of Mechanical Engineers 56: 795806.##[29] Sanders Jr J. L., 1959, An Improved FirstApproximation Theory for Thin Shells, Nasa TR R24.##[30] Leissa A. W., 1973, Vibration of Shells, Scientific and Technical Information Office, Nasa Report No. SP288.##[31] Reissner E., 1945, The effect of transverse shear deformation on the bending of elastic plates, Journal of Applied Mechanics 12: 6877.##[32] Mindlin R. D., 1951, Influence of rotary inertia and shear on flexural motions of isotropic elastic plates, Journal of Applied Mechanics 18: 3138.##[33] Arani A. G., Zarei M. S., Amir S., Maraghi Z. K., 2013, Nonlinear nonlocal vibration of embedded DWCNT conveying fluid using shell model, Physica B: Condensed Matter 410: 188196.##[34] Arani A. G., Kolahchi R., Maraghi Z. K., 2013, Nonlinear vibration and instability of embedded doublewalled boron nitride nanotubes based on nonlocal cylindrical shell theory, Applied Mathematical Modelling 37: 76857707.##[35] HosseiniHashemi S., Ilkhani M., 2016, Exact solution for free vibrations of spinning nanotube based on nonlocal first order shear deformation shell theory, Composite Structures 157: 111.##[36] Tu Q., Yang Q., Wang H., Li S., 2016, Rotating carbon nanotube membrane filter for water desalination, Scientific Reports 6: 26183.##[37] Wattanasakulpong N., Ungbhakorn V., 2014, Linear and nonlinear vibration analysis of elastically restrained ends FGM beams with porosities, Aerospace Science and Technology 32: 111120.##[38] Safarpour H., Hosseini M., Ghadiri M., 2017, Influence of threeparameter viscoelastic medium on vibration behavior of a cylindrical nonhomogeneous microshell in thermal environment: An exact solution, Journal of Thermal Stresses 40: 13531367.##[39] Barber J. R., 2010, Intermediate Mechanics of Materials , Springer Science & Business Media.##[40] Tauchert T. R., 1974, Energy Principles in Structural Mechanics, McGrawHill Companies.##[41] Bellman R., Casti J., 1971, Differential quadrature and longterm integration, Journal of Mathematical Analysis and Applications 34: 235238.##[42] Bellman R., Kashef B., Casti J., 1972, Differential quadrature: a technique for the rapid solution of nonlinear partial differential equations, Journal of Computational Physics 10: 4052.##[43] Shu C., 2012, Differential Quadrature and its Application in Engineering, Springer Science & Business Media.##[44] Shu C., Richards B. E., 1992, Application of generalized differential quadrature to solve two‐dimensional incompressible Navier‐Stokes equations, International Journal for Numerical Methods in Fluids 15: 791798.##[45] Ghadiri M., Shafiei N., Akbarshahi A., 2016, Influence of thermal and surface effects on vibration behavior of nonlocal rotating Timoshenko nanobeam, Applied Physics A 122: 119.##[46] Beni Y. T., Mehralian F., Razavi H., 2015, Free vibration analysis of sizedependent shear deformable functionally graded cylindrical shell on the basis of modified couple stress theory, Composite Structures 120: 6578.##[47] Alibeigloo A., Shaban M., 2013, Free vibration analysis of carbon nanotubes by using threedimensional theory of elasticity, Acta Mechanica 224: 14151427.##[48] Tadi Beni Y., Mehralian F., Zeighampour H., 2016, The modified couple stress functionally graded cylindrical thin shell formulation, Mechanics of Advanced Materials and Structures 23: 791801.##]
1

Axially Symmetric Vibrations of a LiquidFilled Poroelastic Thin Cylinder Saturated with Two Immiscible Liquids Surrounded by a Liquid
http://jsm.iauarak.ac.ir/article_665907.html
10.22034/jsm.2019.665907
1
This paper studies axially symmetric vibrations of a liquidfilled poroelastic thin cylinder saturated with two immiscible liquids of infinite extent that is surrounded by an inviscid elastic liquid. By considering the stress free boundaries, the frequency equation is obtained. Particular case, namely, liquidfilled poroelastic cylinder saturated with single liquid is discussed. When the wavenumber is large, the frequency equation is reduced to that of Rayleightype surface wave at the plane boundary of a poroelastic halfspace. In this case, the asymptotic expressions of Bessel functions and modified Bessel functions are used. In both general and particular cases, the case of the propagation of Rayleigh waves in a poroelastic halfspace is obtained. The parameter values of Columbia fine sandy loam saturated with airwater mixture are used for the numerical evaluation. In all the cases, phase velocity as a function of wavenumber is computed and presented graphically. From the numerical results, some inferences are drawn.
0

272
280


B
Sandhyarani
Department of Mathematics, Osmania University, Hyderabad, India
India
sandhyarani.bandari@gmail.com


J
Anand Rao
Department of Mathematics, Osmania University, Hyderabad, India
India


P
Malla Reddy
Department of Mathematics, Kakatiya University, Warangal, India
India
Axially symmetric vibrations
Thin cylinder
Liquid
Wavenumber
Phase velocity
[[1] Biot M.A., 1956, The theory of propagation of elastic waves in a fluidsaturated porous solid, Journal of Acoustical Society of America 28: 158191.##[2] Tuncay K., Corapcioglu M.Y., 1997, Wave propagation in porous media saturated by two fluids, Journal of Applied Mechanics 64: 313319.##[3] Tuncay K., Corapcioglu M.Y., 1996, Body waves in poroelastic media saturated by two immiscible fluids, Journal of Geophysical Physical Research 101: 149159.##[4] Santos J. E., Corbero J., Douglas Jr. J., 1990, Static and dynamic behavior of a porous solid saturated by a two phase fluid, Journal of Acoustical Society of America 87: 14281438.##[5] Sahay P.N., Spanos T. J. T., De la C., 2001, Seismic wave propagation in inhomogeneous and anisotropic porous media, Geophysical Research International 145: 209222.##[6] Hanyga A., 2004, Two fluid porous flow in a single temparature approximation, International Journal of Engineering Science 42: 15211545.##[7] Lo W.Ch., Sposito G., Majer E., 2007, Wave propagation through elastic porous media containing two immiscible fluids, Water Resources Research 41: 120.##[8] Lin T.C., 1956, Wave propagation through fluid contained in a cylindrical elastic shell, Journal of Acoustical Society of America 28: 11651176.##[9] Ram K., 1971, Flexural vibrations of fluidfilled circular cylindrical shells, Acta Acustica United with Acustica 24: 137146.##[10] Sharma M. D., Gogna M. L., 1990, Propagation of elastic waves in a cylindrical bore in a liquid saturated porous solid, Geophysical Journal International 103: 4754.##[11] Thomas J. P., Bikash S., Serio K., ShuKong Ch., 1992, Axially symmetric wave propagation in fluidloaded cylindrical shells: I Theory, Journal of Acoustical Society of America 92: 11441155.##[12] Vinay D., 1993, Longitudinal waves in a homogeneous anisotropic cylindrical bars immersed in fluid, Journal of Acoustical Society of America 93: 12491255.##[13] Grinchenko V.T., Komissarova G. L., 1994, Axisymmetric waves in a fluidfilled, hollow, elastic cylinder surrounded by a fluid, International Applied Mathematics 30: 657664.##[14] Vashishth A. K., Khurana P., 2005, Wave propagation along a cylindrical borehole in an anisotropic poroelastic solid, Geophysical Journal International 161: 295302.##[15] Seyyed M.H., Hosseeini H., 2008, Non axisymmetric interaction of a spherical radiator in a fluidfilled permeable borehole, International Journal of Solids and Structures 45: 2447.##[16] Ashish A., Tomar S. K., 2007, Elastic waves along a cylindrical borehole in a poroelastic medium saturated by two immiscible fluids, The Journal of Earth System Science 116: 225234.##[17] Tajudddin M., Buchilingam P., 1990, Propagation of surface waves in a poroelastic solid layer lying over an elastic solid, Acta Geophysica 38: 279287.##[18] Tajuddin M., 1984, Rayleigh waves in porous elastic saturated solids, Journal of Acoustical Society of America 33: 682684.##[19] Malla Reddy P., Sandhya Rani B., Tajuddin, M., 2011, Dispersion study of axially symmetric waves in cylindrical bone filled with marrow, International Journal Biomathematics 4: 109118.##[20] Ahmed Shah S., 2008, Axially symmetric vibrations of fluidfilled poroelastic circular cylindrical shells, Journal of Sound and Vibration 318: 389405.##[21] Ahmed Shah S., Tajuddin, M., 2010, On flexural vibrations of poroelastic circular cylindrical shells immersed in an acoustic medium, Special Topics and Reviews in Porous media 1: 6778.##[22] Shanker B., Nath C. N., Shah S. A., Malla Reddy P., 2013, Vibrations in a fluidloaded poroelastic hollow cylinder surrounded by a fluid in planestrain form, International Journal of Applied Mechanics and Engineering 18: 189216.##[23] Shanker B., Nageswara Nath C., Ahmed Shah S., Manoj Kumar J., 2013, Vibration analysis of poroelastic composite hollow sphere, Acta Mechanica 224: 327341.##[24] Shanker B., Nageswara Nath C., Ahmed Shah S., Manoj Kumar J., 2013, Free vibrations of fluidloaded poroelastic hollow sphere surrounded by a fluid, International Journal of Applied Mathematics and Mechanics 9: 1434.##[25] Ramesh M., Ahmed Shah S., Ramana Murthy M.V., 2014, Analysis of radial vibrations of poroelastic circular cylindrical shells immersed in an acoustic medium, International Journal of Engineering Science and Technology 6: 2635.##[26] Abramowitz M., Stegun I. A., 1965, Hand book of Mathematical Functions, Dover publication, New York.##]
1

Fundamental Solution in the Theory of Thermoelastic Diffusion Materials with Double Porosity
http://jsm.iauarak.ac.ir/article_665384.html
10.22034/jsm.2019.665384
1
The main purpose of present article is to find the fundamental solution of partial differential equations in the generalized theory of thermoelastic diffusion materials with double porosity in case of steady oscillations in terms of elementary functions.
0

281
296


T
Kansal
Department of Mathematics, M.N.College, Shahabad, 136135, India
India
tarun1_kansal@yahoo.co.in
Thermoelastic
Diffusion
Double porosity
Steady oscillations
[[1] Lord H.W., Shulman Y., 1967, A generalized dynamical theory of thermoelasticity, Journal of the Mechanics and Physics of Solids 15: 299309.##[2] Nowacki W., 1974, Dynamical problems of thermodiffusion in solidsI, Bulletin of the Polish Academy of Sciences: Technical Sciences 22: 5564.##[3] Nowacki W., 1974, Dynamical problems of thermodiffusion in solidsII, Bulletin of the Polish Academy of Sciences: Technical Sciences 22: 205211.##[4] Nowacki W., 1974, Dynamical problems of thermodiffusion in solidsIII, Bulletin of the Polish Academy of Sciences: Technical Sciences 22: 257266.##[5] Nowacki W., 1976, Dynamical problems of diffusion in solids, Engineering Fracture Mechanics 8: 261266.##[6] Sherief H.H., Hamza F.A., Saleh H.A., 2004, The theory of generalized thermoelastic diffusion, International Journal of Engineering Science 42: 591608.##[7] Iesan D., 1986, A theory of thermoelastic materials with voids, Acta Mechanica 60: 6789.##[8] Aouadi M., 2010, A theory of thermoelastic diffusion materials with voids, Zeitschrift für Angewandte Mathematik und Physik 61: 357379.##[9] Barenblatt G.I., Zheltov I.P., Kochina I.N., 1960, Basic concept in the theory of seepage of homogeneous liquids in fissured rocks (strata), Journal of Applied Mathematics and Mechanics 24: 12861303.##[10] Warren J., Root P., 1963, The behavior of naturally fractured reservoirs, Society of Petroleum Engineers Journal 3: 245255.##[11] Wilson R.K., Aifantis E.C., 1982, On the theory of consolidation with double porosity I, International Journal of Engineering Science 20: 10091035.##[12] Iesan D., Quintanilla R., 2014, On a theory of thermoelastic materials with a double porosity structure, Journal of Thermal Stresses 37: 10171036.##[13] Kansal T., 2018, Generalized theory of thermoelastic diffusion with double porosity, Archives of Mechanics 70: 241268.##[14] Svanadze M., 2005, Fundamental solution in the theory of consolidation with double Porosity, Journal of the Mechanical Behavior of Biomedical Materials 16: 123130.##[15] Svanadze M., De Cicco S., 2013, Fundamental solutions in the full coupled linear theory of elasticity for solid with double porosity, Archives of Mechanics 65: 367390.##[16] Svanadze M., 2013, Fundamental Solution in the linear theory of consolidation for elastic solids with double porosity, Journal of Mathematical Sciences 195: 258268.##[17] Scarpetta E., Svanadze M., Zampoli V., 2014, Fundamental solutions in the theory of thermoelasticity for solids with double porosity, Journal of Thermal Stresses 37: 727748.##[18] Kumar R., Vohra R., Gorla M.G., 2016, Some considerations of fundamental solution in micropolar thermoelastic materials with double porosity, Archives of Mechanics 68: 263284.##[19] Kumar R., Kansal T., 2012, Plane waves and fundamental solution in the generalized theories of thermoelastic diffusion, International Journal of Applied Mathematics and Mechanics 8: 120.##[20] Kupradze V.D., Gegelia T.G., Basheleishvili M.O., Burchuladze T.V., 1979, ThreeDimensional Problems of the Mathematical Theory of Elasticity and Thermoelasticity, NorthHolland, Company, Amsterdam, New York, Oxford.##]
1

An Approximate Solution of Functionally Graded Timoshenko Beam Using BSpline Collocation Method
http://jsm.iauarak.ac.ir/article_665909.html
10.22034/jsm.2019.665909
1
Collocation methods are popular in providing numerical approximations to complicated governing equations owing to their simplicity in implementation. However, point collocation methods have limitations regarding accuracy and have been modified upon with the application of Bspline approximations. The present study reports the stress and deformation behavior of shear deformable functionally graded cantilever beam using Bspline collocation technique. The material grading is along the beam height and varies according to power law. Poisson’s ratio is assumed to be a constant. The equations are derived using virtual work principle in the framework of Timoshenko beams to obtain a unified formulation for such beams. A sixth order basis function is used for approximation and collocation points are generated using Greville abscissa. Deformation and stresses; bending (axial) stresses and transverse (shear) stresses, and position of neutral axis are studied for a wide range of power law index values. The results are reported along the beam crosssection and beam length.
0

297
310


D
Mahapatra
BRSMCAET, IGKV, Mungeli, India
India


Sh
Sanyal
Department of Mechanical Engineering, NIT Raipur, India
India


Sh
Bhowmick
Department of Mechanical Engineering, NIT Raipur, India
India
sbhowmick.mech@nitrr.ac.in
Functionally graded beams
Bspline collocation
Timoshenko beams
Power law index
[[1] Miyamoto Y., Kaysser W.A., Rabin B.H., Kawasaki A., Ford R.G., 1999, Functionally Graded Materials, Materials Technology Series, Springer US, Boston.##[2] Suresh S., Mortensen A., 1998, Fundamentals of Functionally Graded Materials, London.##[3] Rasheedat M.M., Akinlabi E.T., 2012, Functionally graded material: An overview, Proceedings of the World Congress in Engineering, London, UK.##[4] Udupa G., Rao S.S., Gangadharan K.V., 2014, Functionally graded composite materials: An overview, Procedia Materials Science 5: 12911299.##[5] Kieback B., Neubrand A., Riedel H., 2003, Processing techniques for functionally graded materials, Materials Science and Engineering 362: 81106.##[6] Birman V., Byrd L.W., 2007, Modeling and analysis of functionally graded materials and structures, Applied Mechanics Reviews 60: 195.##[7] Reddy J.N., Chin C.D., 1998, Thermomechanical analysis of functionally graded cylinders and plates, Journal of Thermal Stresses 21: 593626.##[8] Reddy J.N., 2000, Analysis of functionally graded plates, International Journal for Numerical Methods in Engineering 47: 663684.##[9] Sankar B.V., 2001, An elasticity solution for functionally graded beams, Composites Science and Technology 61: 689696.##[10] Sankar B.V., Tzeng J.T., 2002, Thermal stresses in functionally graded beams, AIAA Journal 40: 12281232.##[11] Zhu H., Sankar B.V., 2004, A combined fourier series–Galerkin method for the analysis of functionally graded beams, Journal of Applied Mechanics 71: 421.##[12] Chakraborty A., Gopalakrishnan S., Reddy J.N., 2003, A new beam finite element for the analysis of functionally graded materials, International Journal of Mechanical Sciences 45: 519539.##[13] Aydogdu M., Taskin V., 2007, Free vibration analysis of functionally graded beams with simply supported edges, Materials & Design 28: 16511656.##[14] Zhong Z., Yu T., 2007, Analytical solution of a cantilever functionally graded beam, Composites Science and Technology 67: 481488.##[15] Kadoli R., Akhtar K., Ganesan N., 2008, Static analysis of functionally graded beams using higher order shear deformation theory, Applied Mathematical Modelling 32: 25092525.##[16] Benatta M.A., Mechab I., Tounsi A., Adda Bedia E.A., 2008, Static analysis of functionally graded short beams including warping and shear deformation effects, Computational Materials Science 44: 765773.##[17] Sina S.A., Navazi H.M., Haddadpour H., 2009, An analytical method for free vibration analysis of functionally graded beams, Materials & Design 30: 741747.##[18] Şimşek M., 2010, Fundamental frequency analysis of functionally graded beams by using different higherorder beam theories, Nuclear Engineering and Design 240: 697705.##[19] Giunta G., Belouettar S., Carrera E., 2010, Analysis of FGM beams by means of classical and advanced theories, Mechanics of Advanced Materials and Structures 17: 622635.##[20] Tahani M., Torabizadeh M.A., Fereidoon A., 2006, Nonlinear analysis of functionally graded beams, Journal of Achievements in Materials and Manufacturing Engineering 18: 315318.##[21] Reddy J.N., 2011, Microstructuredependent couple stress theories of functionally graded beams, Journal of the Mechanics and Physics of Solids 59: 23822399.##[22] Zhang D.G., 2013, Nonlinear bending analysis of FGM beams based on physical neutral surface and high order shear deformation theory, Composite Structures 100: 121126.##[23] Yaghoobi H., Fereidoon A., 2010, Influence of neutral surface position on deflection of functionally graded beam under uniformly distributed load, World Applied Sciences Journal 10: 337341.##[24] Mohanty S.C., Dash R.R., Rout T., 2011, Parametric instability of a functionally graded Timoshenko beam on Winkler’s elastic foundation, Nuclear Engineering and Design 241: 26982715.##[25] Mohanty S.C., Dash R.R., Rout T., 2012, Static and dynamic stability analysis of a functionally graded Timoshenko beam, International Journal of Structural Stability and Dynamics 12: 1250025.##[26] Li X.F., 2008, A unified approach for analyzing static and dynamic behaviors of functionally graded Timoshenko and Euler–Bernoulli beams, Journal of Sound and Vibration 318: 12101229.##[27] Kadalbajoo M.K., Yadaw A.S., 2011, Finite difference, finite element and bspline collocation methods applied to two parameter singularly perturbed boundary value problems1, Jnaiam 5: 163180.##[28] Chawla T.C., Leaf G., Chen W., 1975, A collocation method using bsplines for onedimensional heat or masstransfercontrolled moving boundary problems, Nuclear Engineering and Design 35: 163180.##[29] Chawla T.C., Chan S.H., 1979, Solution of radiationconduction problems with collocation method using bsplines as approximating functions, International Journal of Heat and Mass Transfer 22: 16571667.##[30] Bert C.W., Sheu Y., 1996, Static analyses of beams and plates by spline collocation method, Journal of Engineering Mechanics 122: 375378.##[31] Sun W., 2001, Bspline collocation methods for elasticity problems, Scientific Computing and Applications 2001: 133141.##[32] Hsu M.H., 2009, Vibration analysis of nonuniform beams resting on elastic foundations using the spline collocation method, Tamkang Journal of Science and Engineering 12: 113122.##[33] Hsu M.H., 2009, Vibration analysis of pretwisted beams using the spline collocation method, Journal of Marine Science and Technology 17: 106115.##[34] Wu L.Y., Chung L.L., Huang H.H., 2008, Radial spline collocation method for static analysis of beams, Applied Mathematics and Computing 201: 184199.##[35] Provatidis C., 2014, Finite element analysis of structures using C 1 continuous cubic bsplines or equivalent hermite elements, Journal of Structural 2014: 19.##[36] Cottrell J.A., Hughes T.J.R., Bazilevs Y., 2009, Isogeometric Analysis: Toward Integration of CAD and FEA, Wiley, Chichester.##[37] Auricchio F., Da Veiga L.B., Hughes T.J.R., Reali A., Sangalli G., 2010, Isogeometric collocation methods, Mathematical Models and Methods in Applied Sciences 20: 20752107.##[38] Reali A., Gomez H., 2015, An isogeometric collocation approach for Bernoulli–Euler beams and Kirchhoff plates, Computer Methods in Applied Mechanics and Engineering 284: 623636.##[39] Patlashenko I., 1993, Cubic bspline collocation method for nonlinear static analysis of panels under mechanical and thermal loadings, Computers & Structures 49: 8996.##[40] Patlashenko I., Weller T., 1995, Two dimensional spline collocation method for nonlinear analysis of laminated panels, Computers & Structures 57: 131139.##[41] Mizusawa T., Kito H., 1995,Vibration of cross ply laminated cylindrical panels by spline strip method, Computers & Structures 57: 253267.##[42] Mizusawa T., 1996, Vibration of thick laminated cylindrical panels by spline strip method, Computers & Structures 61: 441457.##[43] Akhras G., Li W., 2011, Stability and free vibration analysis of thick piezoelectric composite plates using finite strip method, Journal of Mechanical Sciences 53: 575584.##[44] Loja M.A.R., Mota Soares C.M., Barbosa J.I., 2013, Analysis of functionally graded sandwich plate structures with piezoelectric skins, using bspline finite strip method, Computers & Structures 96: 606615.##[45] Provatidis C.G., 2017, Bsplines collocation for plate bending eigen analysis, Journal of Mechanics of Materials and Structures 12: 353371.##[46] Johnson R.W., 2005, Higher order bspline collocation at the Greville abscissae, Applied Numerical Mathematics 52: 6375.##]
1

Modelling of Random Geometrical Imperfections and Reliability Calculations for Thin Cylindrical Shell Subjected to Lateral Pressure
http://jsm.iauarak.ac.ir/article_665559.html
10.22034/jsm.2019.665559
1
It is well known that it is very difficult to manufacture perfect thin cylindrical shell. Initial geometrical imperfections existing in the shell structure is one of the main determining factor for load bearing capacity of thin cylindrical shell under uniform lateral pressure. As these imperfections are random, the strength of same size cylindrical shell will also random and a statistical method can be preferred to find the allowable load of these shell structures and therefore a In this work the cylindrical shell of size R/t = 228, L/R = 2 and t=1mm is taken for study. The random geometrical imperfections are modeled by linearly adding the first 10 eigen mode shapes using 2kfullfactorial design matrix of DoE. By adopting this method 1024 FE random imperfect cylindrical shell models are generated with tolerance limit of ± 1 mm. Nonlinear static FE analysis of ANSYS is used to find the buckling strength of these 1024 models. FE results of 1024 models are used to predict the reliability based on MVFOSM method.
0

311
322


N
Rathinam
Department of Mechanical Engineering, Pondicherry Engineering College, Pillaichavady Puducherry, India
India
rathinam_80@pec.edu


B
Prabu
Department of Mechanical Engineering ,
Pondicherry Engineering College,
Pondicherry
India
prabu@pec.edu
Design of Experiments
Thin cylindrical shell
Random geometrical imperfections
reliability
Mvfosm
[[1] Prabu B., Rathinam N., Srinivasan R., Naarayen K.A.S., 2009, Finite element analysis of buckling of thin cylindrical shell subjected to uniform external pressure, Journal of Solid Mechanics 2(2): 148158.##[2] Rathinam N., Prabu B., 2015, Numerical study on influence of dent parameters on critical buckling pressure of thin cylindrical shell subjected to uniform lateral pressure, Thin Walled Structures 88: 115.##[3] Ranganathan R., 2000, Structural Reliability: Analysis & Design, Jaico Publishing House, New Delhi, India.##[4] Caitriona de P., Kevin C., James P. G., Denis K., 2012, Statistical characterisation and modelling of random geometric imperfections in cylindrical shells, Thin Walled Structures 58: 917.##[5] Sadovsky Z., Teixeira A.P., Guedes Soares C., 2005, Degradation of the compressive strength of rectangular plates due to initial deflections, ThinWalled Structures 43: 6582.##[6] Sadovsky Z., Teixeira A.P., Guedes Soares C., 2006, Degradation of the compressive strength of square plates due to initial deflections, Journal of Constructional Steel Research 62: 369377.##[7] Athiannan K., Palaninathan R., 2004, Experimental investigations of buckling of cylindrical shells under axial compression and transverse shear, Sadhana 29: 93115.##[8] Singer J., 1999, On the importance of shell buckling experiment, Journal of Applied Mechanics Review 52(6): 1725.##[9] Schneider M.H. Jr., 1996, Investigation of stability of imperfect cylinders using structural models, Engineering Structures 18(10): 792800.##[10] Arbocz J., Hol J.M.A.M., 1991, Collapse of axially compressed cylindrical shells with random imperfections, AIAA Journal 29(12): 22472256.##[11] Kirkpatrick S.W., Holmes B.S., 1989, Axial buckling of a thin cylindrical shell: Experiments and calcualtions, Computational Experiments 176: 6774.##[12] Featherston C.A., 2003, Imperfection sensitivity of curved panels under combined compression and shear, International Journal of NonLinear Mechanics 38: 225238.##[13] Kim S.E., Kim Ch.S., 2002, Buckling strength of the cylindrical shell and tank subjected to axially compressive loads, ThinWalled Structures 40: 329353.##[14] Khelil A., 2002, Buckling of steel shells subjected to nonuniform axial and pressure loadings, ThinWalled Structures 40: 955970.##[15] Teng J.G., Song C.Y., 2001, Numerical models for nonlinear analysis of elastic shells with eigen modeaffine imperfections, International Journal of Solids and Structure 38: 32633280.##[16] Ikeda K., Kitada T., Matsumura M., Yamakawa Y., 2007, Imperfection sensitivity and ultimate buckling strength of elasticplastic square plates under compression, International Journal of NonLinear Mechanics 42: 529541.##[17] Khamlichi A., Bezzazi M., Limam A., 2004, Buckling of elastic cylindrical shells considering the effect of localized axisymmetric imperfections, ThinWalled Structures 42: 10351047.##[18] Pircher M., Berry P.A., Ding X., Bridge R.Q., 2001, The shape of circumferential weldinduced imperfections in thin walled steel silos and tanks, ThinWalled Structures 39(12): 9991014.##[19] Chrysanthopoulos M.K., 1998, Probabilistic buckling analysis of plates and shells, ThinWalled Structures 30(14): 135157.##[20] Elishakoff I., 1979, Buckling of a stochastically imperfect finite column on a nonlinear elastic foundation: A reliability study, Journal of Applied MechanicsTransactions of ASME 46: 411416.##[21] Elishakoff I., Van Manen S., Vermeulen P.G., Arbocz J., 1987, Firstorder secondmoment analysis of the buckling of shells with random imperfections, AIAA Journal 25(8): 11131117.##[22] Chryssanthopoulos M.K., Baker M.J., Dowling P.J., 1991, Imperfection modeling for buckling analysis of stiffened cylinders, Journal of Structural Engineering Division 117(7): 19982017.##[23] Sadovsky Z., Bulaz I., 1996, Tolerance of initial deflections of welded steel plates and strength of I cross section in compression and bending, Journal of Constructional Steel Research 38(3): 219238.##[24] Warren J.E. Jr., 1997, Nonlinear Stability Analysis of FrameType Structures with Random Geometric Imperfections Using a TotalLagrangian Finite Element Formulation, Ph.D. Thesis, Virginia Polytechnic Institute and State University, USA.##[25] Náprstek J., 1999, Strongly nonlinear stochastic response of a system with random initial imperfections, Probabilistic Engineering Mechanics 14(12): 141148.##[26] Bielewicz E., Gorski J., 2002, Shells with random geometric imperfections simulation  based approach, International Journal of NonLinear Mechanics 37: 777784.##[27] Schenk C.A., Schueller G.I., 2003, Buckling analysis of cylindrical shells with random geometric imperfections, International Journal of NonLinear Mechanics 38: 11191132.##[28] Papadopoulos V., Papadrakakis M., 2004, Finiteelement analysis of cylindrical panels with random initial imperfections, Journal of Engineering Mechanics 130(8): 867876.##[29] Craig K.J., Roux W.J., 2007, On the investigation of shell buckling due to random geometrical imperfections implemented using KarhunenLoève expansions, International Journal for Numerical Methods in Engineering 73(12): 17151726.##[30] Sadovsky Z., Guedes Soares C., Teixeira A.P., 2007, Random field of initial deflections and strength of thin rectangular plates, Reliability Engineering & System Safety 92: 16591670.##[31] Papadopoulos V., Stefanou G., Papadrakakis M., 2009, Buckling analysis of imperfect shells with stochastic nonGaussian material and thickness properties, International Journal of Solids and Structures 46: 28002808.##[32] Rzeszut K., Garstecki A., 2009, Modeling of initial geometrical imperfections in stability analysis of thinwalled structures, Journal of Theoretical and Applied Mechanics 47(3): 667684.##[33] Bahaoui J.El., Khamlichi A., Bakkali L.El., Limam A., 2010, Reliability assessment of buckling strength for compressed cylindrical shells with interacting localized geometric imperfections, American Journal of Engineering and Applied Sciences 3(4): 620628.##[34] Brar G. S., Hari Y., Dennis K. W., 2012, Calculation of working pressure for cylindrical vessel under external pressure, Proceedings of the ASME 2012 Pressure Vessels & Piping Division Conference.##[35] Chryssanthopoulos M.K., Poggi C., 1995, Probabilistic imperfection sensitivity analysis of axially compressed composite cylinders, Engineering Structures 17(6): 398406.##[36] Croll J.G.A., 2006, Stability in shells, Nonlinear Dynamics 43: 1728.##[37] Combescure A., Gusic G., 2001, Nonlinear buckling of cylinders under external pressure with non axisymmetric thickness imperfections using the COMI axisymmetric shell element, International Journal of Solids and Structures 38: 62076226.##[38] Windernburg D.F., Trilling C., 1934, Collapse by instability of thin cylindrical shells under external pressure, ASME Transactions 56(11): 81925.##[39] Forde W. R. B., Stiemer S. F., 1987, Improved arc length orthogonality methods for nonlinear finite element analysis, Computers & Structures 27(5): 625630.##[40] Verderaime V., 1994, Illustrated Structural Application of Universal First Order Reliability Method, NASA Technical Paper 3501.##]
1

Coupled AxialRadial Vibration of SingleWalled Carbon Nanotubes Via Doublet Mechanics
http://jsm.iauarak.ac.ir/article_665256.html
10.22034/jsm.2019.665256
1
This paper investigates the coupled axialradial (CAR) vibration of singlewalled carbon nanotubes (SWCNTs) based on doublet mechanics (DM) with a scale parameter. Two coupled forth order partial differential equations that govern the CAR vibration of SWCNTs are derived. It is the first time that DM is used to model the CAR vibration of SWCNTs. To obtain the natural frequency and dynamic response of the CAR vibration, the equations of motion are solved and the relation between natural frequencies and scale parameter is derived. It is found that there are two frequencies in the frequency spectrum and these CAR vibrational frequencies are complicated due to coupling between two vibration modes. The advantage of these analytical formulas is that they are explicitly dependent to scale parameter and chirality effect. The influence of changing some geometrical and mechanical parameters of SWCNT on its CAR frequencies has been investigated, too. It is shown that the chirality and scale parameter play significant role in the CAR vibration response of SWCNTs. The scale parameter decreases the higher band CAR frequency compared to the predictions of the classical continuum models. However, with increase in tube radius and length, the effect of the scale parameter on the natural frequencies decreases. The lower band CAR frequency is nearly independent to scale effect and tube diameter. The CAR frequencies of SWCNTs decrease as the length of the tube increases. This decreasing is higher for higher band CAR frequency. To show the accuracy and ability of this method, the results obtained herein are compared with the existing theoretical and experimental results and good agreement is observed.
0

323
340


Z
Azimzadeh
Young Researchers and Elite Club, YadegareImam Khomeini (RAH) ShahreRey Branch, Islamic Azad University, Tehran, Iran
Iran


A
FatahiVajari
Young Researchers and Elite Club, YadegareImam Khomeini (RAH) ShahreRey Branch, Islamic Azad University, Tehran, Iran
Iran
alirezafatahi@shriau.ac.ir
Coupled axialradial vibration
Doublet mechanics
Natural frequency
Scale parameter
singlewalled carbon nanotubes
[[1] FatahiVajari A., Imam A., 2016, Torsional vibration of singlewalled carbon nanotubes using doublet mechanics, Zeitschrift für angewandte Mathematik und Physik 67:81.##[2] Banks H. T., Hu S., Kenz Z. R., 2011, A brief review of elasticity and viscoelasticity for solids, Advances in Applied Mathematics and Mechanics 3(1): 151.##[3] Granik V.T., Ferrari M., 1993, Microstructural mechanics of granular media, Mechanics of Materials 15: 301322.##[4] Eringen A.C., 1972, Nonlocal polar elastic continua, International Journal of Engineering Science 10: l16.##[5] Yang Y., Lim C.W., 2012, Nonclassical stiffness strengthening size effects for free vibration of a nonlocal nanostructure, International Journal of Mechanical Sciences 54: 5768.##[6] Mindlin R.D., Eshel N.N., 1968, On first straingradient theories in linear elasticity, International Journal of Solids and Structures 4: 109124.##[7] Dell’Isola F., Della Corte A., Giorgio I., 2017, Highergradient continua: The legacy of Piola, Mindlin, Sedov and Toupin and some future research perspectives, Mathematics and Mechanics of Solids 22(4): 852872.##[8] Polizzotto C., 2014, Stress gradient versus strain gradient constitutive models within elasticity, International Journal of Solids and Structures 51: 18091818.##[9] Ramasubramaniam A., Carter E.A., 2007, Coupled quantum–atomistic and quantum–continuum mechanics methods, Materials Research 32: 913918.##[10] Dove M.T., 2007, An introduction to atomistic simulation methods, Seminarios de la SEM 4: 737.##[11] Carcaterra A., 2015, Quantum euler beam—QUEB: modeling nanobeams vibration, Continuum Mechanics and Thermodynamics 27: 145156.##[12] Friak M., Hickel T. Grabowski B., Lymperakis L., Udyansky A., Dick A., Ma D., Roters F., Zhu L.F., Schlieter A., Kuhn U., Ebrahimi Z., Lebensohn R.A., Holec D., Eckert J., Emmerich H., Raabe D., Neugebauer J., 2011, Methodological challenges in combining quantummechanical and continuum approaches for materials science applications, The European Physical Journal Plus 126(101): 122.##[13] Khodabakhshi P., Reddy J. N., 2016, A unified beam theory with strain gradient effect and the von Karman nonlinearity, ZAMM 97: 7091.##[14] Beheshti A., 2017, Generalization of straingradient theory to finite elastic deformation for isotropic materials, Continuum Mechanics and Thermodynamics 29: 493507.##[15] Kiani K., 2014, Axial buckling analysis of vertically aligned ensembles of singlewalled carbon nanotubes using nonlocal discrete and continuous models, Acta Meccanica 225: 35693589.##[16] FatahiVajari A. , Azimzadeh Z., 2018, Analysis of nonlinear axial vibration of singlewalled carbon nanotubes using Homotopy perturbation method, Indian Journal of Physics 92: 14251438.##[17] Kiani K., 2014, In and outofplane dynamic flexural behaviors of twodimensional ensembles of vertically aligned singlewalled carbon nanotubes, Physica B, Condensed Matter 449: 164180.##[18] Aydogdu M., 2012, Axial vibration analysis of nanorods (carbon nanotubes) embedded in an elastic medium using nonlocal elasticity, Mechanics Research Communications 43: 3440.##[19] Kiani K., 2018, Application of nonlocal higherorder beam theory to transverse wave analysis of magnetically affected forests of singlewalled carbon nanotubes, International Journal of Mechanical Sciences 138139: 116.##[20] Ferrari M., Granik V.T., Imam A., Nadeau J., 1997, Advances in Doublet Mechanics, SpringerVerlag, Berlin.##[21] FatahiVajari A., Imam A., 2016, Axial vibration of singlewalled carbon nanotubes using doublet mechanics, Indian Journal of Physics 90(4): 447455.##[22] Granik V.T., 1978, Microstructural Mechanics of Granular Media, Institute of Mechanics of Moscow State University, Russian.##[23] Kojic M., Vlastelica I., Decuzzi P., Granik V.T., Ferrari M., 2011, A ﬁnite element formulation for the doublet mechanics modeling of microstructural materials, Computer Methods in Applied Mechanical Engineering 200: 14461454.##[24] Xin J., Zhou L.X., Ru W.J., 2009, Ultrasound attenuation in biological tissue predicted by the modified doublet mechanics model, Chinese Physics Letters 26(7): 074301.1074301.4.##[25] Gentile F., Sakamoto J., Righetti R., Decuzzi P., Ferrari M., 2011, A doublet mechanics model for the ultrasound characterization of malignant tissues, Journal of Biomedical Science and Engineering 4: 362374.##[26] Fang J.Y., Jue Z., Jing F., Ferrari M., 2004, Dispersion analysis of wave propagation in cubictetrahedral assembly by doublet mechanics, Chinese Physics Letters 21(8): 15621565.##[27] Sadd M.H., Dai Q., 2005, A comparison of micromechanical modeling of asphalt materials using ﬁnite elements and doublet mechanics, Mechanics of Materials 37: 641662.##[28] FatahiVajari A., Imam A., 2016, Lateral vibrations of singlelayered graphene sheets using doublet mechanics, Journal of Solid Mechanics 8(4): 875894.##[29] Lin S.S., Shen Y.C., 2005, Stress fields of a halfplane caused by moving loadsresolved using doublet mechanics, Soil Dynamics and Earthquake Engineering 25: 893904.##[30] Sadd M.H., 2005, Elasticity Theory, Applications, and Numeric, Elsevier ButterworthHeinemann, Burlington.##[31] Lee A.P., Lee J., Ferrari M., 2006, BioMEMS and Biomedical Nanotechnology, Biological and Biomedical Nanotechnology, Springer, New York.##[32] FatahiVajari A., 2018, A new method for evaluating the natural frequency in radial breathing like mode vibration of doublewalled carbon nanotubes, ZAMM 98(2): 255269.##[33] Maultzsch J., Telg H., Reich S., Thomsen C., 2005, Radial breathing mode of singlewalled carbon nanotubes: Optical transition energies and chiralindex assignment, Physical Review B 72: 205438.1205438.16.##[34] Basirjafari S., EsmaielzadehKhadem S., Malekfar R., 2013,Validation of shell theory for modeling the radial breathing mode of a singlewalled carbon nanotube, International Journal of Engineering: Transactions A 26(4): 447454.##[35] Szabó A., Perri C., Csató A., Giordano G., Vuono D., Nagy J.B., 2010, Synthesis methods of carbon nanotubes and related materials, Materials 3: 30923140.##[36] Prasek J., Drbohlavova J., Chomoucka J., Hubalek J., Jasek O., Adamc V., Kizek R., 2011, Methods for carbon nanotubes synthesis, Journal of Materials Chemistry 21: 1587215884.##[37] Hongjie D., 2002, Carbon nanotubes: synthesis, integration, and properties, American Chemical Society 35: 10351044.##[38] Zhang Y. Y., Wang C. M., Tan V. B. C., 2009, Assessment of timoshenko beam models for vibrational behavior of singlewalled carbon nanotubes using molecular dynamics, Advances in Applied Mathematics and Mechanics 1(1): 89106.##[39] Kiani K., 2018, Nonlocal free dynamic analysis of periodic arrays of singlewalled carbon nanotubes in the presence of longitudinal thermal and magnetic fields, Computers and Mathematics with Applications 75: 38493872.##[40] Ghorbanpour Arani A., Mosallaie Barzoki A. A., Kolahchi R., Loghman A., 2011, Pasternak foundation effect on the axial and torsional waves propagation in embedded DWCNTs using nonlocal elasticity cylindrical shell theory, Journal of Mechanical Science and Technology 25(9): 23852391.##[41] Basirjafari S., EsmaeilzadehKhadem S., Malekfar R., 2013, Radial breathing mode frequencies of carbon nanotubes for determination of their diameters, Current Applied Physics 13: 599609.##[42] Kiani K., 2014, Nonlocal discrete and continuous modeling of free vibration of stocky ensembles of vertically aligned singlewalled carbon nanotubes, Current Applied Physics 14(8): 11161139.##[43] Das S.L., Mandal T., Gupta S.S., 2013, Inextensional vibration of zigzag singlewalled carbon nanotubes using nonlocal elasticity theories, International Journal of Solids and Structures 50: 27922797.##[44] FatahiVajari A., Imam A., 2016, Analysis of radial breathing mode vibration of singlewalled carbon nanotubes via doublet mechanics, ZAMM 96(9): 10201032.##[45] Li C.F., Zhou S.H., Liu J., Wen B.C., 2014, Coupled lateraltorsionalaxial vibrations of a helical gearrotorbearing system, Acta Mechanica Sinica 30(5): 746761.##[46] Kiani K., 2014, Nanoparticle delivery via stocky singlewalled carbon nanotubes: A nonlinearnonlocal continuumbased scrutiny, Composite Structures 116: 254272.##[47] Gupta S.S., Batra R.C., 2008, Continuum structures equivalent in normal mode vibrations to singlewalled carbon nanotubes, Computational Materials Science 43: 715723.##[48] Lin S.Y., 1995, Coupled vibration and natural frequency analysis of isotropic cylinders or disks of finite dimensions, Journal of Sound and Vibration 185(2): 193199.##[49] Ren F., Wang B., Chen S., Yao Z., Bai B., 2016, Nonlinear model and qualitative analysis for coupled axial/torsional vibrations of drill string, Shock and Vibration 2016: 1646814.##[50] Subramaniyan A.K., Sun C.T., 2008, Continuum interpretation of virial stress in molecular simulations, International Journal of Solids and Structures 45: 43404346.##]
1

Bifurcation and Chaos in SizeDependent NEMS Considering Surface Energy Effect and Intermolecular Interactions
http://jsm.iauarak.ac.ir/article_665396.html
10.22034/jsm.2019.665396
1
The impetus of this study is to investigate the chaotic behavior of a sizedependent nanobeam with doublesided electrostatic actuation, incorporating surface energy effect and intermolecular interactions. The geometrically nonlinear beam model is based on EulerBernoulli beam assumption. The influence of the smallscale and the surface energy effect are modeled by implementing the consistent couple stress theory proposed by Hadjesfandiari and Dargush together with GurtinMurdoch elasticity theory. The governing differential equation of motion is derived using Hamilton’s principle and discretized to a set of nonlinear ODE through Galerkin’s method. Nonlinearities stemmed from different sources such as midplane stretching, electrostatic and interatomic forces lead to an intensive nonlinear dynamics in nanoelectromechanical devices so that the systems exhibit rich dynamic behavior such as periodic and chaotic motions. Poincaré portrait is utilized in order to present the system dynamic response in discrete statespace. Bifurcation analysis has been performed with a change in the magnitude of AC voltage corresponding to the various values of DC voltage and excitation frequency. Then, we compare some ranges of AC voltage amplitude, in which the system response becomes stable for these cases. Fast Fourier transformation is also carried out to analyze the frequency content of the system response.
0

341
360


S
Rahmanian
School of Mechanics Engineering, Iran University of Science and Technology, Narmak, Tehran, Iran
Iran


Sh
Hosseini Hashemi
School of Mechanics Engineering, Iran University of Science and Technology, Narmak, Tehran, Iran
Iran
shh@iust.ac.ir
Sizedependent NEMS
Bifurcation
Chaos
Poincaré portrait
FFT analysis
[[1] Mayoof F. N., Hawwa M. A., 2009, Chaotic behavior of a curved carbon nanotube under harmonic excitation, Chaos, Solitons & Fractals 42(3):18601867.##[2] Amorim T. D., Dantas W. G., Gusso A., 2015, Analysis of the chaotic regime of MEMS/NEMS fixed–fixed beam resonators using an improved 1DOF model, Nonlinear Dynamics 79(2): 967981.##[3] Sabarathinam S., Thamilmaran K., 2016, Implementation of analog circuit and study of chaotic dynamics in a generalized Duffingtype MEMS resonator, Nonlinear Dynamics 2016:112.##[4] Hu W., Song M., Deng Z., Zou H., Wei B., 2017, Chaotic region of elastically restrained singlewalled carbon nanotube, Chaos: An Interdisciplinary Journal of Nonlinear Science 27(2): 023118.##[5] Bienstman J., Vandewalle J., Puers R., 1998, The autonomous impact resonator: a new operating principle for a silicon resonant strain gauge, Sensors and Actuators A: Physical 66(1): 4049.##[6] Luo A. C., Wang F.Y., 2002, Chaotic motion in a microelectro–mechanical system with nonlinearity from capacitors, Communications in Nonlinear Science and Numerical Simulation 7(1): 3149.##[7] Luo A. C., Wang F.Y., 2004, Nonlinear dynamics of a microelectromechanical system with timevarying capacitors, Journal of Vibration and Acoustics 126(1): 7783.##[8] DeMartini B. E., Butterfield H. E., Moehlis J., Turner K. L., 2007, Chaos for a microelectromechanical oscillator governed by the nonlinear Mathieu equation, Journal of Microelectromechanical Systems 16(6): 13141323.##[9] Wang Y. C., Adams S. G., Thorp J. S., MacDonald N. C., Hartwell P., Bertsch F., 1998, Chaos in MEMS, parameter estimation and its potential application, IEEE Transactions on Circuits and Systems, Fundamental Theory and Applications 45(10): 10131020.##[10] Zhang W.M., Tabata O., Tsuchiya T., Meng G., 2011, Noiseinduced chaos in the electrostatically actuated MEMS resonators, Physics Letters A 375(32): 29032910.##[11] Aghababa M. P., 2012, Chaos in a fractionalorder microelectromechanical resonator and its suppression, Chinese Physics B 21(10): 100505.##[12] Li H., Liao X., Ullah S., Xiao L., 2012, Analytical proof on the existence of chaos in a generalized Duffingtype oscillator with fractionalorder deflection, Nonlinear Analysis: Real World Applications 13(6): 27242733.##[13] Miandoab E. M., YousefiKoma A., Pishkenari H. N., Tajaddodianfar F., 2015, Study of nonlinear dynamics and chaos in MEMS/NEMS resonators, Communications in Nonlinear Science and Numerical Simulation 22(1): 611622.##[14] Seleim A., Towfighian S., Delande E., AbdelRahman E., Heppler G., 2012, Dynamics of a closeloop controlled MEMS resonator, Nonlinear Dynamics 69(12): 615633.##[15] Han J., Zhang Q., Wang W., 2015, Design considerations on large amplitude vibration of a doubly clamped microresonator with two symmetrically located electrodes, Communications in Nonlinear Science and Numerical Simulation 22(1): 492510.##[16] Haghighi H. S., Markazi A. H., 2010, Chaos prediction and control in MEMS resonators, Communications in Nonlinear Science and Numerical Simulation 15(10): 30913099.##[17] Yau H.T., Wang C.C., Hsieh C.T., Cho C.C., 2011, Nonlinear analysis and control of the uncertain microelectromechanical system by using a fuzzy sliding mode control design, Computers & Mathematics with Applications 61(8): 19121916.##[18] Zhankui S., Sun K., 2013, Nonlinear and chaos control of a microelectromechanical system by using secondorder fast terminal sliding mode control, Communications in Nonlinear Science and Numerical Simulation 18(9): 25402548.##[19] Tusset A., Balthazar J. M., Bassinello D., Pontes Jr B., Felix J. L. P., 2012, Statements on chaos control designs, including a fractional order dynamical system, applied to a “MEMS” combdrive actuator, Nonlinear Dynamics 69(4): 18371857.##[20] Tusset A. M., Bueno A. M., Nascimento C. B., dos Santos Kaster M., Balthazar J. M., 2013, Nonlinear state estimation and control for chaos suppression in MEMS resonator, Shock and Vibration 20(4): 749761.##[21] Tajaddodianfar F., Hairi Yazdi M. R., Pishkenari H. N., 2015, On the chaotic vibrations of electrostatically actuated arch micro/nano resonators: a parametric study, International Journal of Bifurcation and Chaos 25(08): 1550106.##[22] Ni X., Ying L., Lai Y.C., Do Y., Grebogi C., 2013, Complex dynamics in nanosystems, Physical Review E 87(5): 052911.##[23] Hu W., Deng Z., Wang B., Ouyang H., 2013, Chaos in an embedded singlewalled carbon nanotube, Nonlinear Dynamics 72(12): 389398.##[24] Coluci V., Legoas S., de Aguiar M., Galvao D., 2005, Chaotic signature in the motion of coupled carbon nanotube oscillators, Nanotechnology 16(4): 583.##[25] Hawwa M., Mayoof F., 2009, Nonlinear oscillations of a carbon nanotube resonator, International Symposium on Mechatronics and its Applications, Sharjah.##[26] Hawwa M. A., AlQahtani H. M., 2010, Nonlinear oscillations of a doublewalled carbon nanotube, Computational Materials Science 48(1): 140143.##[27] Joshi A. Y., Sharma S. C., Harsha S., 2012, Chaotic response analysis of singlewalled carbon nanotube due to surface deviations, Nanotechnology 7(02): 1250008.##[28] Ashhab M., Salapaka M., Dahleh M., Mezić I., 1999, Melnikovbased dynamical analysis of microcantilevers in scanning probe microscopy, Nonlinear Dynamics 20(3): 197220.##[29] Ashhab M., Salapaka M. V., Dahleh M., Mezić I., 1999, Dynamical analysis and control of microcantilevers, Automatica 35(10): 16631670.##[30] Basso M., Giarre L., Dahleh M., Mezic I., 1998, Numerical analysis of complex dynamics in atomic force microscopes, Proceedings of the 1998 IEEE International Conference 2: 10261030.##[31] Balthazar J. M., Tusset A. M. Bueno A., 2014, TMAFM nonlinear motion control with robustness analysis to parametric errors in the control signal determination, Journal of Theoretical and Applied Mechanics 52: 93106.##[32] Jamitzky F., Stark M., Bunk W., Heckl W., Stark R., 2006, Chaos in dynamic atomic force microscopy, Nanotechnology 17(7): S213.##[33] Raman A., Hu S., 2006, Chaos in dynamic atomic force microscopy, International Symposium on Nonlinear Theory and Its Applications, Bologna, Italy.##[34] Lin W.H., Zhao Y.P., 2005, Nonlinear behavior for nanoscale electrostatic actuators with Casimir force, Chaos, Solitons & Fractals 23(5): 17771785.##[35] AbdelRahman E. M., Nayfeh A. H., 2003, Secondary resonances of electrically actuated resonant microsensors, Journal of Micromechanics and Microengineering 13(3): 491.##[36] Ouakad H. M., Younis M. I., 2010, Nonlinear dynamics of electrically actuated carbon nanotube resonators, Journal of Computational and Nonlinear Dynamics 5(1): 011009.##[37] Nayfeh A. H., Balachandran B., 1995, Applied Nonlinear Dynamics: Analytical, Computational, and Experimental Methods, Wiley Series in Nonlinear Sciences, John Wiley & Sons, Inc New York.##[38] Younis M. I., 2011, MEMS Linear and Nonlinear Statics and Dynamics, Springer Science & Business Media.##[39] Kivi A. R., Azizi S., Norouzi P., 2017, Bifurcation analysis of an electrostatically actuated nanobeam based on modified couple stress theory, Sensing and Imaging 18(1): 32.##[40] Chen X., Meguid S., 2017, Dynamic behavior of microresonator under alternating current voltage, International Journal of Mechanics and Materials in Design 13: 481497.##[41] Nikpourian A., Ghazavi M. R., Azizi S., 2018, On the nonlinear dynamics of a piezoelectrically tuned microresonator based on nonclassical elasticity theories, International Journal of Mechanics and Materials in Design 14: 119.##[42] Pourkiaee S. M., Khadem S. E., Shahgholi M., 2016, Parametric resonances of an electrically actuated piezoelectric nanobeam resonator considering surface effects and intermolecular interactions, Nonlinear Dynamics 84: 19431960.##[43] Hajnayeb A., Khadem S., 2011, Nonlinear vibrations of a carbon nanotube resonator under electrical and van der Waals forces, Journal of Computational and Theoretical Nanoscience 8(8): 15271534.##[44] Hajnayeb A., Khadem S., 2012, Nonlinear vibration and stability analysis of a doublewalled carbon nanotube under electrostatic actuation, Journal of Sound and Vibration 331(10): 24432456.##[45] Batra R. C., Porfiri M., Spinello D., 2008, Effects of van der Waals force and thermal stresses on pullin instability of clamped rectangular microplates, Sensors 8(2): 10481069.##[46] Lamoreaux S. K., 2004, The Casimir force: background, experiments, and applications, Reports on Progress in Physics 68(1): 201.##[47] Gupta R. K., 1998, Electrostatic pullin test structure design for insitu mechanical property measurements of microelectromechanical systems (MEMS, Thesis Ph. D. Massachusetts Institute of Technology, Department of Electrical Engineering and Computer Science.##[48] Huang J.M., Liew K., Wong C., Rajendran S., Tan M., Liu A., 2001, Mechanical design and optimization of capacitive micromachined switch, Sensors and Actuators A: Physical 93(3): 273285.##[49] Mindlin R., Tiersten H., 1962, Effects of couplestresses in linear elasticity, Archive for Rational Mechanics and Analysis 11(1): 415448.##[50] Stölken J., Evans A., 1998, A microbend test method for measuring the plasticity length scale, Acta Materialia 46(14): 51095115.##[51] Hadjesfandiari A. R., Dargush G. F., 2011, Couple stress theory for solids, International Journal of Solids and Structures 48(18): 24962510.##[52] Osterberg P. M., Senturia S. D., 1997, MTEST: a test chip for MEMS material property measurement using electrostatically actuated test structures, Journal of Microelectromechanical Systems 6(2): 107118.##[53] Gurtin M. E., Murdoch A. I., 1975, A continuum theory of elastic material surfaces, Archive for Rational Mechanics and Analysis 57(4): 291323.##[54] Gurtin M. E., Murdoch A. I., 1978, Surface stress in solids, International Journal of Solids and Structures 14(6): 431440.##[55] Ru C., 2010, Simple geometrical explanation of GurtinMurdoch model of surface elasticity with clarification of its related versions, Science China Physics, Mechanics and Astronomy 53(3): 536544.##[56] Azizi S., Ghazavi M.R., Khadem S. E., Rezazadeh G., Cetinkaya C., 2013, Application of piezoelectric actuation to regularize the chaotic response of an electrostatically actuated microbeam, Nonlinear Dynamics 73(12): 853867.##[57] Zhu R., Pan E., Chung P. W., Cai X., Liew K. M., Buldum A., 2006, Atomistic calculation of elastic moduli in strained silicon, Semiconductor Science and Technology 21(7): 906.##[58] Akgöz B., Civalek Ö., 2011, Strain gradient elasticity and modified couple stress models for buckling analysis of axially loaded microscaled beams, International Journal of Engineering Science 49(11): 12681280.##[59] Alemansour H., Miandoab E. M., Pishkenari H. N., 2017, Effect of size on the chaotic behavior of nano resonators, Communications in Nonlinear Science and Numerical Simulation 44: 495505.##[60] Chen Y., 1993, Bifurcation and Chaos Theory of Nonlinear Vibration Systems, Higher Education, Beijing, China.##[61] Guckenheimer J., Holmes P. J., 2013, Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields, Springer Science & Business Media.##]
1

Reliability of the Rubber Tube of Automotive Hydraulic Braking System Under Fatigue Failures Considering Random Variation of Load and the Process of Aging of Material
http://jsm.iauarak.ac.ir/article_665910.html
10.22034/jsm.2019.665910
1
This paper presents the approach for the assessing of the operational reliability of a multilayer thickwalled tube made of rubber with textile reinforcement. The analysis of the fatigue accumulation process is carried out within the framework of the concept of the continuum mechanics of damage. The mathematical model, which takes into account the accumulation of damages in case of a random spread of the strength characteristics of the material, as well as the process of stochastic aging for the elastomeric matrix of the composite and possible random variation of the workload has been developed. In this case, the aging process is modelled as a reduction of the endurance limit of the material. In this paper, the mean equivalent strains of the tube and their possible statistical variation in operation have been investigated on the basis of the finite element method. To solve the above problems, a submodeling method has been employed in this work. The probability of nonfailure operation of the tube has been determined using the methods and models proposed. The influence of the rate of the aging process on the lifetime of the tube has been estimated.
0

361
374


O
Larin
National Technical University, Kharkiv Polytechnic Institute, Kharkiv, Ukraine
Ukraine


K
Potopalska
National Technical University, Kharkiv Polytechnic Institute, Kharkiv, Ukraine
Ukraine
ks.potopalskaya@gmail.com


R
Mygushchenko
National Technical University, Kharkiv Polytechnic Institute, Kharkiv, Ukraine
Ukraine
Rubber pipe
Composite
Fatigue
Lifetime
[[1] Renu R., Visotsky D., Knackstedt S., Mocko G., Summers J.D., Schulte J., 2016, A knowledge based FMEA to support identification and management of vehicle flexible component issues, Procedia CIRP 44: 157162.##[2] Moon S., Cho I., Woo C., Kim W., 2011, Study on determination of durability analysis process and fatigue damage parameter for rubber component, Journal of Mechanical Science and Technology 25: 1159.##[3] Cho J.R., Yoon Y.H., Seo C.W., Kim Y.G., 2015, Fatigue life assessment of fabric braided composite rubber hose in complicated large deformation cyclic motion, Finite Elements in Analysis and Design 100: 6576.##[4] Cho JR., Yoon YH., 2016, Large deformation analysis of anisotropic rubber hose along cyclic path by homogenization and path interpolation methods, Journal of Mechanical Science and Technology 30: 789795.##[5] Budinski M.K., 2013, Failure analysis of a rubber hose in anhydrous ammonia service, Case Studies in Engineering Failure Analysis 1: 156164.##[6] Chandran D., Ng H.K., Lau H.L.N., Gan S., Choo Y.M., 2016, Investigation of the effects of palm biodiesel dissolved oxygen and conductivity on metal corrosion and elastomer degradation under novel immersion method, Applied Thermal Engineering 104: 294308.##[7] Pierce S.O., Evans J.L., 2012, Failure analysis of a metal bellows flexible hose subjected to multiple pressure cycles, Engineering Failure Analysis 22: 1120.##[8] Reza Kashyzadeh K., Farrahi G.H., Shariyat M., Ahmadian M.T., 2018, Experimental accuracy assessment of various highcycle fatigue criteria for a critical component with a complicated geometry and multiinput random nonproportional 3D stress components, Engineering Failure Analysis 90: 534553.##[9] Krismer S., 2003, Hydraulic hose failures caused by corrosion of the reinforcing strands, Practical Failure Analysis 3: 3339.##[10] Pavloušková Z., Klakurková L., Man O., Čelko L., Švejcar J., 2015, Assessment of the cause of cracking of hydraulic hose clamps, Engineering Failure Analysis 56: 1419.##[11] Noda N.A., Yoshimura S., Kawahara H., Tuyunaru S., 2008, FEM Analysis for Sealing Performance of Hydraulic Brake Hose Crimped Portion and Its Life Estimation, Transactions of the Japan Society of Mechanical Engineers Series A 74(748): 15381543.##[12] Kwak S., Choi N., 2009, Microdamage formation of a rubber hose assembly for automotive hydraulic brakes under a durability test, Engineering Failure Analysis 16: 12621269.##[13] Mars W.V., Fatemi A., 2002, A literature survey on fatigue analysis approaches for rubber, International Journal of Fatigue 24(9): 949961.##[14] Fedorko G., Molnar V., Dovica M., Toth T., Fabianova J., 2015, Failure analysis of irreversible changes in the construction of the damaged rubber hoses, Engineering Failure Analysis 58: 3143.##[15] Hansaka M., Ito M., 1999, Investigation on aging of train rubber hose, Quarterly Report of RTRI 40(2):105111.##[16] Haseeb A.S.M.A., Jun T.S, Fazal M.A., Masjuki H.H., 2011, Degradation of physical properties of different elastomers upon exposure to palm biodiesel, Energy 36(3): 18141819.##[17] Lee G., Kim H., Park J., Jin H., Lee Y., Kim J., 2011, An experimental study and finite element analysis for finding leakage path in high pressure hose assembly, International Journal of Precision Engineering and Manufacturing 12: 537542.##[18] Larin O.O., 2015, Probabilistic model of fatigue damage accumulation in rubberlike materials, Strength of Materials 47(6): 849858.##[19] Larin O., Vodka O., 2015, A probability approach to the estimation of the process of accumulation of the highcycle fatigue damage considering the natural aging of a material, International Journal of Damage Mechanics 24(2): 294310.##[20] Wei Y., Nasdala L., Rothert H., Xie Z., 2004, Experimental investigations on the dynamic mechanical properties of aged rubbers, Polymer Testing 23: 447453.##[21] Huang D., LaCount B.J., Castro J.M., IgnatzHoover F., 2001, Development of a servicesimulating, accelerated aging test method for exterior tire rubber compounds i. cyclic aging, Polymer Degradation and Stability 74(2): 353362.##[22] Coronado M., Montero G., Valdez B., Stoytcheva M., Eliezer A., García C., Campbell H., Pérez A., 2014, Degradation of nitrile rubber fuel hose by biodiesel use, Energy 68: 364369.##[23] Larin O.O., Vodka O.O., Trubayev O.I., 2014, The fatigue lifetime propagation of the connection elements of longterm operated hydro turbines considering material degradation, PNRPU Mechanics Bulletin 1(1):167193.##[24] Bellander M., Gedde U.W., 2016, Degradation of carbonblack fi lled acrylonitrile butadiene rubber in alternative fuels, Transesteri fied and hydrotreated vegetable oils, Polymer Degradation and Stability 123: 6979.##[25] Barlow T.J., Latham S., Mccrae I.S., Boulter P.G., A Reference Book of Driving Cycles for Use in the Measurement of Road Vehicle Emissions, Published Project Report PPR354.##]
1

Dynamic Behavior Analysis of a Geometrically Nonlinear Plate Subjected to a Moving Load
http://jsm.iauarak.ac.ir/article_665267.html
10.22034/jsm.2019.665267
1
In this paper, the nonlinear dynamical behavior of an isotropic rectangular plate, simply supported on all edges under influence of a moving mass and as well as an equivalent concentrated force is studied. The governing nonlinear coupled PDEs of motion are derived by energy method using Hamilton’s principle based on the large deflection theory in conjuncture with the vonKarman straindisplacement relations. Then the Galerkin’s method is used to transform the equations of motion into the three coupled nonlinear ordinary differential equations (ODEs) and then are solved in a semianalytical way to get the dynamical responses of the plate under the traveling load. A parametric study is conducted by changing the size of moving mass/force and its velocity. Finally, the dynamic magnification factor and normalized time histories of the plate central point are calculated for various load velocity ratios and outcome nonlinear results are compared to the results from linear solution.
0

375
387


A
Mamandi
Department of Mechanical Engineering, Parand Branch, Islamic Azad University, Parand, Iran
Iran
am_2001h@yahoo.com


R
Mohsenzadeh
Department of Mechanical Engineering, Science and Research Branch, Islamic Azad University, Tehran, Iran
Iran
Moving load
Nonlinear response
Plate
Galerkin’s method
[[1] Amabili M., 2004, Nonlinear vibrations of rectangular plates with different boundary conditions: theory and experiments, Computers and Structures 82: 25872605.##[2] Eftekhari S.A., Jafari A.A., 2012, Vibration of an initially stressed rectangular plate due to an accelerated traveling mass, Scientia Iranica 19(5):11951213.##[3] Fryba L., 1999, Vibration of Solids and Structures under Moving Loads, Thomas Telford Publishing, London.##[4] Gbadeyan J.A., Oni S.T., 1995, Dynamic behaviour of beams and rectangular plates under moving loads, Journal of Sound and Vibration 182(5): 677695.##[5] Ghafoori E., Kargarnovin M.H., Ghahremani A.R., 2010, Dynamic responses of rectangular plate under motion of an oscillator using a semianalytical method, Journal of Vibration and Control 17(9): 13101324.##[6] Kiani K.A., Nikkhoo A., Mehri B., 2009, Prediction capabilities of classical and shear deformable beam models excited by a moving mass, Journal of Sound and Vibration 320: 632648.##[7] Leissa A.W., 1969, Vibration of Plates, US Government Printing Office, Washington.##[8] Mamandi A., Kargarnovin M.H., Younesian D., 2010, Nonlinear dynamics of an inclined beam subjected to a moving load, Nonlinear Dynamics 60(3): 277293.##[9] Mamandi A., Kargarnovin M.H., 2014, An investigation on dynamic analysis of a Timoshenko beam with geometrical nonlinearity included resting on a nonlinear viscoelastic foundation and traveled by a moving mass, Shock and Vibration 242090:110.##[10] Mamandi A., Kargarnovin M.H., Farsi S., 2014, Nonlinear vibration solution of an inclined Timoshenko beam under the action of a moving force with constant/nonconstant velocity, Journal of Mathematical Sciences 201(3): 361383.##[11] Mamandi A., Kargarnovin M.H., 2011, Nonlinear dynamic analysis of an inclined Timoshenko beam subjected to a moving mass/force with beam’s weight included, Shock and Vibration 18(6): 875891.##[12] Mamandi A., Kargarnovin M.H., 2011, Dynamic analysis of an inclined Timoshenko beam travelled by successive moving masses/forces with inclusion of geometric nonlinearities, Acta Mechanica 218(1):929.##[13] Mamandi A., Kargarnovin M.H., Farsi S., 2010, An investigation on effects of a traveling mass with variable velocity on nonlinear dynamic response of an inclined Timoshenko beam with different boundary conditions, International Journal of Mechanical Sciences 52(12):16941708.##[14] Mamandi A., Kargarnovin M.H., 2013, Nonlinear dynamic analysis of an axially loaded rotating Timoshenko beam with extensional condition included subjected to general type of force moving along the beam length, Journal of Vibration and Control 19(16): 24482458.##[15] Meirovitch L., 1997, Principles and Techniques of Vibrations, PrenticeHall Inc., New Jersey.##[16] Nayfeh A.H., Mook D.T., 1995, Nonlinear Oscillations, WileyInterscience, New York.##[17] Nikkhoo A., Rofooei F.R., 2012, Parametric study of the dynamic response of thin rectangular plates traversed by a moving mass, Acta Mechanica 223: 1527.##[18] Shadnam M.R., Mofid M., Akin J.E., 2001,On the dynamic response of rectangular plate with moving mass, Thinwalled Structures 39: 797806.##[19] Timoshenko S.P., 1959, Theory of Plates and Shells, Mc GrawHill, New York.##[20] Vaeseghi Amiri J., Nikkhoo A., Davoodi M.R., Ebrahimzadeh Hassanabadi M., 2013, Vibration analysis of a Mindlin elastic plate under a moving mass excitation by eigenfunction expansion method, ThinWalled Structures 62: 5364.##[21] Wu J.J., 2007,Vibration analyses of an inclined flat plate subjected to moving loads, Journal of Sound and Vibration 299: 373387.##[22] Yanmeni Wayou A.N., Tchoukuegno R., Woafo P., 2004, Nonlinear dynamics of an elastic beam under moving loads, Journal of Sound and Vibration 273: 11011108.##[23] Mamandi A., Kargarnovin M.H., Mohsenzadeh R., 2015, Nonlinear dynamic analysis of a rectangular plate subjected to accelerated/decelerated moving load, Journal of Theoretical and Applied Mechanics 53(1):151166.##]
1

Strain Hardening Analysis for MP Interaction in Metallic Beam of TSection
http://jsm.iauarak.ac.ir/article_665161.html
10.22034/jsm.2019.665161
1
This paper derives kinematic admissible bending moment – axial force (MP) interaction relations for mild steel by considering strain hardening idealisations. Two models for strain hardening – Linear and parabolic have been considered, the parabolic model being closer to the experiments. The interaction relations can predict strains, which is not possible in a rigid, perfectly plastic idealization. The relations are obtained for all possible cases pertaining to the locations of neutral axis. One commercial rolled steel Tsection has been considered for studying the characteristics of interaction curves for different models. On the basis of these interaction curves, most significant cases for the position of neutral axis which are enough for the establishment of interaction relations have been suggested. The influence of strain hardening in the interaction study has been highlighted. The strains and hence the strain rates due to bending and an axial force can be separated only for the linearelastic case because the principle of superposition is not valid for the nonlinear case. The difference between the interaction curves for linear and parabolic hardening for the particular material is small.
0

388
408


M
Hosseini
Department of Civil Engineering, Faculty of Engineering, Lorestan University, Iran
Iran
hoseini.m@lu.ac.ir


H
Hatami
Department of Mechanical Engineering , Faculty of Engineering, Lorestan University, Iran
Iran
Axial force
Bending moment
T–Section
MP interaction
Strain hardening
[[1] Menkes S.B., Opat H.J., 1973, Broken beams, Experimental Mechanics 13: 480486.##[2] Jones N., 1976, Plastic failure of ductile beams loaded dynamically, Journal of Engineering for Industry 98: 131136.##[3] Liu J.H., Jones N., 1987, Experimental investigation of clamped beams struck transversely by a mass, International Journal of Impact Engineering 6(4): 303335.##[4] Liu J.H., Jones N., 1988, Plastic Failure of a Clamped Beams Struck Transversely by a Mass, University of Liverpool, Department of Mechanical Engineering Report ES/13/87.##[5] Jones N., Soares C.G., 1977, Higher model dynamic, plastic behavior of beam loaded impulsively, International Journal of Mechanical Sciences 20: 135147.##[6] Shen W.Q., Jones N. A., 1992, Failure criterion for beams under impulsive loading, International Journal of Impact Engineering 12(1): 101121.##[7] Alves M., Jones N., 2002, Impact failure of beams using damage mechanics: Part II – Application, International Journal of Impact Engineering 27(8): 86390.##[8] Symonds P.S., Genna F., Ciullini A., 1991, Special cases in study of anomalous dynamic elasticplastic response of beams by a simple model, International Journal of Solids and Structures 27(3): 299314.##[9] Qian Y., Symonds P.S., 1996, Anomalous dynamic elasticplastic response of a Galerkin beam model, International Journal of Mechanical Sciences 38(7): 687708.##[10] Bassi A., Genna F., Symonds P.S., 2003, Anomalous elasticplastic responses to short pulse loading of circular plates, International Journal of Impact Engineering 28(1): 6591.##[11] Lellep J., Torn K., 2005, Shear and bending response of a rigidplastic beam subjected to impulsive loading, International Journal of Impact Engineering 31(9): 10811105.##[12] Ma G. W., Shi H. J., Shu D. W., 2007, P–I diagram method for combined failure modes of rigidplastic beams, International Journal of Impact Engineering 34(6): 10811094.##[13] Ghaderi S. H., Kazuyuki H., Masahiro F., 2009, Analysis of stationary deformation behavior of a semiinfinite rigidperfect plastic beam subjected to moving distributed loads of finite width, International Journal of Impact Engineering 36(1): 115121.##[14] Li Q. M., Liu Y. M., 2003, Uncertain dynamic response of a deterministic elastic–plastic beam, International Journal of Impact Engineering 28(6): 643651.##[15] Li Q. M., Liu Y. M., Ma G. W., 2006, The anomalous region of elastic–plastic beam dynamics, International Journal of Impact Engineering 32(9): 13571369.##[16] Xi F., Liu F., Li Q. M., 2012, Large deflection response of an elastic, perfectly plastic cantilever beam subjected to a step loading, International Journal of Impact Engineering 48: 3345.##[17] Brake M. R., 2012, An analytical elasticperfectly plastic contact model, International Journal of Solids and Structures 49(22): 31293141.##[18] Hosseini M., Abbas H., 2013, Strain hardening in M–P interaction for metallic beam of Isection, ThinWalled Structures 62: 243256.##[19] Alves M., Jones N., 2002, Impact failure of beams using damage mechanics, Part I – Analytical model, International Journal of Impact Engineering 27(8): 83761.##]
1

Buckling and Thermomechanical Vibration Analysis of a Cylindrical Sandwich Panel with an Elastic Core Using Generalized Differential Quadrature Method
http://jsm.iauarak.ac.ir/article_665367.html
10.22034/jsm.2019.665367
1
In this paper, the vibrational and buckling analysis of a cylindrical sandwich panel with an elastic core under thermomechanical loadings is investigated. The modeled cylindrical sandwich panel as well as its equations of motions and boundary conditions is derived by Hamilton’s principle and the firstorder shear deformation theory (FSDT). For the first time in the present study, various boundary conditions is considered in the cylindrical sandwich panel with an elastic core. In order to obtain the temperature distribution in the cylindrical sandwich panel in the absence of a heatgeneration source, temperature distribution is obtained by solving the steadystate heattransfer equation. The accuracy of the presented model is verified using previous studies and the results obtained by the Navier analytical method. The novelty of the present study is considering thermomechanical loadings as well as satisfying various boundary conditions. The generalized differential quadrature method (GDQM) is applied to discretize the equations of motion. Then, some factors such as the influence of lengthtoradius ratio, circumferential wave numbers, thermal loadings, and boundary conditions are examined on the dynamic and static behavior of the cylindrical sandwich panel.
0

409
424


A.R
Pourmoayed
Department of Mechanical Engineering, KhatamulAnbiya Air Defense University, Tehran, Iran
Iran
pourmoayed@mut.ac.ir


K
Malekzadeh
Faculty of Structural Analysis and Simulation Centre, MalekAshtar University,Tehran, Iran
Iran


M
Shahravi
Faculty of Structural Analysis and Simulation Centre, MalekAshtar University,Tehran, Iran
Iran


H
Safarpour
Department of Mechanics, Imam Khomeini International University, Qazvin, Iran
Iran
Heattransfer equation
Buckling and vibration behavior
GDQM
Cylindrical sandwich panel
Various boundary conditions
[[1] Lim C., Ma Y., Kitipornchai S., Wang C., Yuen R., 2003, Buckling of vertical cylindrical shells under combined end pressure and body force, Journal of Engineering Mechanics 129: 876884.##[2] Librescu L., Marzocca P., 2003, Thermal Stresses, Virginia Polytechnic Institute and State University, Blacksburg.##[3] Noor A. K., Burton W. S., 1992, Computational models for hightemperature multilayered composite plates and shells, Applied Mechanics Reviews 45: 419446.##[4] Lam K., Loy C., 1995, Effects of boundary conditions on frequencies of a multilayered cylindrical shell, Journal of Sound and vibration 188: 363384.##[5] Li X., Chen Y., 2002, Transient dynamic response analysis of orthotropic circular cylindrical shell under external hydrostatic pressure, Journal of Sound and Vibration 257: 967976.##[6] Loy C., Lam K., 1999, Vibration of thick cylindrical shells on the basis of threedimensional theory of elasticity, Journal of Sound and Vibration 226: 719737.##[7] Young P., 2000, Application of a threedimensional shell theory to the free vibration of shells arbitrarily deep in one direction, Journal of Sound and Vibration 238: 257269.##[8] Shariyat M., 1997, Elastic, plastic, and creep buckling of imperfect cylinders under mechanical and thermal loading, Journal of Pressure Vessel Technology 119: 2736.##[9] Eslami M., Ziaii A., Ghorbanpour A., 1996, Thermoelastic buckling of thin cylindrical shells based on improved stability equations, Journal of Thermal Stresses 19: 299315.##[10] Radhamoman S., Enkataramana J., 1975,Thermal buckling of orthotropic cylindrical shells, AIAA Journal 13: 397399.##[11] Alibeigloo A., 2014, Threedimensional thermoelasticity solution of sandwich cylindrical panel with functionally graded core, Composite Structures 107: 458468.##[12] Thangaratnam R. K., Palaninathan R., Ramachandran J., 1990,Thermal buckling of laminated composite shells, AIAA Journal 28: 859860.##[13] Bert C., 1993, Buckling and postbuckling of composite plates and shells subjected to elevated temperature, Journal of Applied Mechanics 60(2): 514519.##[14] MohammadAbadi M., Daneshmehr A., 2015, Modified couple stress theory applied to dynamic analysis of composite laminated beams by considering different beam theories, International Journal of Engineering Science 87: 83102.##[15] Dumir P., Nath J., Kumari P., Kapuria S., 2008, Improved efficient zigzag and third order theories for circular cylindrical shells under thermal loading, Journal of Thermal Stresses 31: 343367.##[16] Kant T., Khare R., 1994, Finite element thermal stress analysis of composite laminates using a higherorder theory, Journal of Thermal stresses 17: 229255.##[17] Khdeir A., Rajab M., Reddy J., 1992, Thermal effects on the response of crossply laminated shallow shells, International Journal of Solids and Structures 29: 653667.##[18] Khare R. K., Kant T., Garg A. K., 2003, Closedform thermomechanical solutions of higherorder theories of crossply laminated shallow shells, Composite Structures 59: 313340.##[19] Sheng G., Wang X., 2007, Effects of thermal loading on the buckling and vibration of ringstiffened functionally graded shell, Journal of Thermal Stresses 30: 12491267.##[20] Sheng G., Wang X., 2010, Thermoelastic vibration and buckling analysis of functionally graded piezoelectric cylindrical shells, Applied Mathematical Modelling 34: 26302643.##[21] Shiau L.C., Kuo S.Y., 2004, Thermal postbuckling behavior of composite sandwich plates, Journal of Engineering Mechanics 130: 11601167.##[22] JengShian C., 1990, FEM analysis of buckling and thermal buckling of antisymmetric angleply laminates according to transverse shear and normal deformable high order displacement theory, Computers & Structures 37: 925946.##[23] Rao K. M., 1985, Buckling analysis of anisotropic sandwich plates faced with fiberreinforced plastics, AIAA Journal 23: 12471253.##[24] Noor A. K., Starnes Jr J. H., Peters J. M., 1997, Curved sandwich panels subjected to temperature gradient and mechanical loads, Journal of Aerospace Engineering 10: 143161.##[25] Chang C.C., 2012, Thermoelastic behavior of a simply supported sandwich panel under large temperature gradient and edge compression, Journal of the Aerospace Sciences 2012: 480.##[26] Huang H., 2003, The initial postbuckling behavior of facesheet delaminations in sandwich composites, Journal of Applied Mechanics 70: 191199.##[27] Huang H., Kardomateas G. A., 2002, Buckling and initial postbuckling behavior of sandwich beams including transverse shear, AIAA Journal 40: 23312335.##[28] Frostig Y., Thomsen O. T., 2008, Nonlinear thermal response of sandwich panels with a flexible core and temperature dependent mechanical properties, Composites Part B: Engineering 39: 165184.##[29] Khalili S., Mohammadi Y., 2012, Free vibration analysis of sandwich plates with functionally graded face sheets and temperaturedependent material properties: A new approach, European Journal of MechanicsA/Solids 35: 6174.##[30] Leonenko D., Starovoitov E., 2016, Vibrations of cylindrical sandwich shells with elastic core under local loads, International Applied Mechanics 52: 359367.##[31] Malekzadeh F. K., Malek M. H., 2017, Free vibration and buckling analysis of sandwich panels with flexible cores using an improved higher order theory, Journal of Solid Mechanics 9(1): 3953.##[32] Jabbari M., Zamani N. M., Ghannad M., 2017, Stress analysis of rotating thick truncated conical shells with variable thickness under mechanical and thermal loads, Journal of Solid Mechanics 9(1): 100114.##[33] Saviz M., 2016, Coupled vibration of partially fluidfilled laminated composite cylindrical shells, Journal of Solid Mechanics 8: 823839.##[34] Golpayegani I. F., 2018, Calculation of natural frequencies of bilayered rotating functionally graded cylindrical shells, Journal of Solid Mechanics 10: 216231.##[35] Saadatfar M., Aghaie K. M., 2015, On the magnetothermoelastic behavior of a functionally graded cylindrical shell with pyroelectric layers featuring interlaminar bonding imperfections rested in an elastic foundation, Journal of Solid Mechanics 7(3): 344363.##[36] Ghasemi A., Hajmohammad M., 2017, Evaluation of buckling and post buckling of variable thickness shell subjected to external hydrostatic pressure, Journal of Solid Mechanics 9: 239248.##[37] HosseiniHashemi S., Abaei A., Ilkhani M., 2015, Free vibrations of functionally graded viscoelastic cylindrical panel under various boundary conditions, Composite Structures 126: 115.##[38] Thinh T. I., Nguyen M. C., Ninh D. G., 2014, Dynamic stiffness formulation for vibration analysis of thick composite plates resting on nonhomogenous foundations, Composite Structures 108: 684695.##[39] Tauchert T. R., 1974, Energy Principles in Structural Mechanics, McGrawHill Companies.##[40] Reddy J. N., 2004, Mechanics of Laminated Composite Plates and Shells: Theory and Analysis, CRC Press.##[41] Ghadiri M., SafarPour H., 2017, Free vibration analysis of sizedependent functionally graded porous cylindrical microshells in thermal environment, Journal of Thermal Stresses 40: 5571.##[42] Bellman R., Casti J., 1971, Differential quadrature and longterm integration, Journal of Mathematical Analysis and Applications 34: 235238.##[43] Bellman R., Kashef B., Casti J., 1972, Differential quadrature: a technique for the rapid solution of nonlinear partial differential equations, Journal of Computational Physics 10: 4052.##[44] Shu C., 2012, Differential Quadrature and its Application in Engineering, Springer Science & Business Media.##[45] Shu C., Richards B. E., 1992, Application of generalized differential quadrature to solve two‐dimensional incompressible Navier‐Stokes equations, International Journal for Numerical Methods in Fluids 15: 791798.##[46] Loy C., Lam K., Shu C., 1997, Analysis of cylindrical shells using generalized differential quadrature, Shock and Vibration 4: 193198.##[47] Loy C., Lam K., Reddy J., 1999, Vibration of functionally graded cylindrical shells, International Journal of Mechanical Sciences 41: 309324.##[48] Matsunaga H., 2009, Free vibration and stability of functionally graded circular cylindrical shells according to a 2D higherorder deformation theory, Composite Structures 88: 519531.##[49] Rabani Bidgoli M., Saeed Karimi M., Ghorbanpour Arani A., 2016, Nonlinear vibration and instability analysis of functionally graded CNTreinforced cylindrical shells conveying viscous fluid resting on orthotropic Pasternak medium, Mechanics of Advanced Materials and Structures 23: 819831.##]
1

Modelling Mechanical Properties of AISI 439430Ti Ferritic Stainless Steel Sheet
http://jsm.iauarak.ac.ir/article_665911.html
10.22034/jsm.2019.665911
1
The comprehension of the anisotropy impacts on mechanical properties of the rolled steel sheets was investigated using a nonquadratic anisotropic yield function. In this study, experimental and modelling determination regarding the behaviour of an industrial rolled sheet for a ferritic stainless lowcarbon steel were carried out. The parameters of the associated yield equation, derived from the three orthotropic yield functions proposed by Hill48, Yld96 and Yld20002d, were determined. Predictions and the evolution of normalized yield stress and normalized Lankford parameters (plastic strain ratio) obtained by the presented investigative are considered. The forecasts given by the YLD20002d criterion are consistent with that of the experience. In order to describe the path of strain behavior, the isotropic hardening function is described using the following four empirical standard formulae based on: Hollomon, Ludwick, Swift and Voce law. More accurately, the anisotropy coefficients of three yield functions are represented as a function of the longitudinal equivalent plastic strain.
0

425
439


N
Brinis
Engineering Sciences and Advanced Materials Laboratory (ISMA), LaghrourAbbes University of Khenchela, Algeria
Algeria


B
Regaiguia
Engineering Sciences and Advanced Materials Laboratory (ISMA), LaghrourAbbes University of Khenchela, Algeria
Metallurgy and Engineering Materials, BadjiMokhtar University of Annaba, Algeria
Algeria


O
Chahaoui
Engineering Sciences and Advanced Materials Laboratory (ISMA), LaghrourAbbes University of Khenchela, Algeria
Algeria
oualid.chahaoui@gmail.com


N
Maatougui
National School of Mines and MetallurgyAnnaba, Algeria
Algeria


M.L
Fares
Metallurgy and Engineering Materials, BadjiMokhtar University of Annaba, Algeria
Algeria
Constitutive model
Sheet Metal Forming
Anisotropy evolution
Orthotropic yield criterion
Isotropic hardening function
[[1] Liu W., Guines D., Leotoing L. , Ragneau E., 2015, Identification of sheet metal hardening for large strains with an inplane biaxial tensile test and a dedicated cross specimen, International Journal of Mechanical Sciences 101–102: 387398.##[2] Chahaoui O., Fares M. L., Piot D., Montheillet F., 2011, Monoclinic effects and orthotropic estimation for the behaviour of rolled sheet, Journal of Materials Science 46: 16551667.##[3] Chahaoui O., Fares M. L., Piot D., and Montheillet F., 2013, Mechanical modeling of macroscopic behavior for anisotropic and heterogeneous metal alloys, Metals and Materials International 19: 10051019.##[4] Hill R., 1948, A theory of yielding and plastic flow of anisotropic materials, Proceedings: Mathematical, Physical and Engineering Science, Royal Society London 193: 281297.##[5] Hosford W.F., 1972, A generalized isotropic Yield criterion, Journal of Applied Mechanics 39: 607609.##[6] Barlat F., Lian J., 1989, Plastic behavior and stretchability of sheet metals: Part I. A yield function for orthotropic sheets under plane stress conditions, International Journal of Plasticity 5: 5166.##[7] Barlat F., Lege D. J., Brem J. C., 1991, A sixcomponent yield function for anisotropic materials, International Journal of Plasticity 7: 693712.##[8] Barlat F., Becker R.C., Hayashida Y., Maeda Y., Yanagawa M., Chung K., Brem J.C., Lege D.J., Matsui K., Murtha S.J., Hattori S., 1997, Yielding description of solution strengthened aluminium alloys, International Journal of Plasticity 13: 185401.##[9] Barlat F., Maeda Y., Chung K., Yanagawa M., Brem J.C., Hayashida Y., Leged D.J., Matdui K., Murtha S.J., Hattori S., Becker R.C., Makosey S., 1997, Yield function development for aluminum alloy sheets, Journal of the Mechanics and Physics of Solids 45: 17271763.##[10] Barlat F., Brem J.C., Yoon J.W., Chung K., Dick R.E., Lege D.J., Pourboghrat F., Choi S.H., Chu E., 2003, Plane stress yield function for aluminum alloy sheets—part 1: Theory, International Journal of Plasticity 19: 12971319.##[11] Barlat F., Aretz H., Yoon J. W., Karabin M.E., Brem J.C., Dick R.E., 2005, Linear transfomationbased anisotropic yield functions, International Journal of Plasticity 21: 10091039.##[12] Aretz H., Aegerter J., Engler O., 2010, Analysis of earing in deep drawn cups, AIP Conference Proceedings 1252(1): 417424.##[13] Zhang S., Leotoing L., Guines D., Thuillier S., Zang S.l., 2014, Calibration of anisotropic yield criterion with conventional tests or biaxial test, International Journal of Mechanical Sciences 85: 142151.##[14] Zang S. L., Thuillier S., Le Port A., Manach J. Y., 2011, Prediction of anisotropy and hardening for metallic sheets in tension, simple shear and biaxial tension, International Journal of Mechanical Sciences 53: 338347.##[15] Wang H., Wan M., Wu X., Yan Y., 2009, The equivalent plastic straindependent Yld20002d yield function and the experimental verification, Computational Materials Science 47: 1222.##[16] Cazacu O., Barlat F., 2001, Generalization of Drucker’s yield criterion to orthotropy, Mathematics and Mechanics of Solids 6: 613630.##[17] Kawka M., Makinouchi A., 1996, Plastic anisotropy in FEM analysis using degenerated solid element, Journal of Materials Processing Technology 60: 239242.##[18] Taejoon P., Kwansoo C., 2012, Nonassociated flow rule with symmetric stiffness modulus for isotropickinematic hardening and its application for earing in circular cup drawing, International Journal of Solids and Structures 49: 35823593.##[19] Basak S., Bandyopadhyay K., Panda S. K., Saha P., 2015, Prediction of formability of Biaxial Prestrained dual phase steel sheets using stress based forming limit diagram, Advances in Material Forming and Joining, Springer 2015: 167192.##[20] Basak S., Bandyopadhyay K., Panda S. K., Saha P., 2014, Use of stress based forming limit diagram to predict formability in twostage forming of tailorwelded blanks, Materials and Design 67: 558570.##[21] Watson M., Robert R., Huang Y.H., Lockley A., Cardoso R., Santos R., 2016, Benchmark 1 – failure prediction after cup drawing, reverse redrawing and expansion, Journal of Physics: Conference Series 734: 4022001.##]
1

Influence of Viscoelastic Foundation on Dynamic Behaviour of the Double Walled Cylindrical Inhomogeneous Micro Shell Using MCST and with the Aid of GDQM
http://jsm.iauarak.ac.ir/article_665264.html
10.22034/jsm.2019.665264
1
In this article, dynamic modeling of double walled cylindrical functionally graded (FG) microshell is studied. Size effect of double walled cylindrical FG microshell are investigated using modified couple stress theory (MCST). Each layer of microshell is embedded in a viscoelastic medium. For the first time, in the present study, has been considered, FG length scale parameter in double walled cylindrical FG microshells, which this parameter changes along the thickness direction. Taking into consideration the firstorder shear deformation theory (FSDT), double walled cylindrical FG microshell is modeled and its equations of motions are derived using Hamilton's principle. The novelty of this study is considering the effects of double layers and MCST, in addition to considering the various boundary conditions of double walled cylindrical FG microshell. Generalized differential quadrature method (GDQM) is used to discretize the model and to approximate the equation of motions and boundary conditions. Also, for confirmation, the result of current model is validated with the results obtained from molecular dynamics (MD) simulation. Considering length scale parameter (l=R/3) on MCST show, the results have better agreement with MD simulation. The results show that, length, thickness, FG power index, Winkler and Pasternak coefficients and shear correction factor have important role on the natural frequency of double walled cylindrical FG microshell.
0

440
453


A
Mohammadi
Faculty of Engineering, Department of Mechanics, Islamic Azad University of South Tehran Branch, Tehran, Iran
Iran


H
Lashini
Faculty of Mechanic and Manufacturing, University Putra Malaysia, Serdang, Malaysia
Malaysia


M
Habibi
Center of Excellence in Design, Robotics and Automation, School of Mechanical Engineering, Sharif University of Technology, Tehran, Iran
Iran


H
Safarpour
Faculty of Engineering, Department of Mechanics, Imam Khomeini International University, Qazvin, Iran
Iran
hamed_safarpor@yahoo.com
Double walled
Functionally graded material
Modified couple stress theory
Vibration analysis
Viscoelastic foundation
[[1] Reddy J., Chin C., 1998, Thermomechanical analysis of functionally graded cylinders and plates, Journal of Thermal Stresses 21: 593626.##[2] Loy C., Lam K., Reddy J., 1999, Vibration of functionally graded cylindrical shells, International Journal of Mechanical Sciences 41: 309324.##[3] Pradhan S., Loy C., Lam K., Reddy J., 2000, Vibration characteristics of functionally graded cylindrical shells under various boundary conditions, Applied Acoustics 61: 111129.##[4] Patel B., Gupta S., Loknath M., Kadu C., 2005,Free vibration analysis of functionally graded elliptical cylindrical shells using higherorder theory, Composite Structures 69: 259270.##[5] Kadoli R., Ganesan N., 2006, Buckling and free vibration analysis of functionally graded cylindrical shells subjected to a temperaturespecified boundary condition, Journal of Sound and Vibration 289: 450480.##[6] ZhiYuan C., HuaNing W., 2007, Free vibration of FGM cylindrical shells with holes under various boundary conditions, Journal of Sound and Vibration 306: 227237.##[7] Haddadpour H., Mahmoudkhani S., Navazi H., 2007, Free vibration analysis of functionally graded cylindrical shells including thermal effects, Thinwalled Structures 45: 591599.##[8] Farid M., Zahedinejad P., Malekzadeh P., 2010,Threedimensional temperature dependent free vibration analysis of functionally graded material curved panels resting on twoparameter elastic foundation using a hybrid semianalytic, differential quadrature method, Materials & Design 31: 213.##[9] Rahaeifard M., Kahrobaiyan M., Ahmadian M., 2009, Sensitivity analysis of atomic force microscope cantilever made of functionally graded materials, International Design Engineering Technical Conferences and Computers and Information in Engineering Conference.##[10] Fu Y., Du H., Huang W., Zhang S., Hu M., 2004, TiNibased thin films in MEMS applications: a review, Sensors and Actuators A: Physical 112: 395408.##[11] Witvrouw A., Mehta A., 2005, The use of functionally graded polySiGe layers for MEMS applications, Materials Science Forum 2005: 255260.##[12] Lee Z., Ophus C., Fischer L., NelsonFitzpatrick N., Westra K., Evoy S., 2006, Metallic NEMS components fabricated from nanocomposite Al–Mo films, Nanotechnology 17: 3063.##[13] Shojaeian M., Beni Y.T., 2015, Sizedependent electromechanical buckling of functionally graded electrostatic nanobridges, Sensors and Actuators A: Physical 232: 4962.##[14] Mescher M. J., Houston K., Bernstein J. J., Kirkos G. A., Cheng J., Cross L. E., 2002, Novel MEMS microshell transducer arrays for highresolution underwater acoustic imaging applications, Proceedings of IEEE.##[15] Toupin R. A., 1962, Elastic materials with couplestresses, Archive for Rational Mechanics and Analysis 11: 385414.##[16] Koiter W., 1964, Couple stresses in the theory of elasticity, Proceedings van de Koninklijke Nederlandse Akademie van Wetenschappen.##[17] Mindlin R. D., 1964, Microstructure in linear elasticity, Archive for Rational Mechanics and Analysis 16: 5178.##[18] Asghari M., Kahrobaiyan M., Rahaeifard M., Ahmadian M., 2011, Investigation of the size effects in Timoshenko beams based on the couple stress theory, Archive of Applied Mechanics 81: 863874.##[19] Park S., Gao X., 2006, Bernoulli–Euler beam model based on a modified couple stress theory, Journal of Micromechanics and Microengineering 16: 2355.##[20] Reddy J., 2011, Microstructuredependent couple stress theories of functionally graded beams, Journal of the Mechanics and Physics of Solids 59: 23822399.##[21] Shaat M., Mahmoud F., Gao X.L., Faheem A. F., 2014, Sizedependent bending analysis of Kirchhoff nanoplates based on a modified couplestress theory including surface effects, International Journal of Mechanical Sciences 79: 3137.##[22] Miandoab E. M., Pishkenari H. N., YousefiKoma A., Hoorzad H., 2014, Polysilicon nanobeam model based on modified couple stress and Eringen’s nonlocal elasticity theories, Physica E: Lowdimensional Systems and Nanostructures 63: 223228.##[23] Karami H., Farid M., 2015, A new formulation to study inplane vibration of curved carbon nanotubes conveying viscous fluid, Journal of Vibration and Control 21: 23602371.##[24] Choi J., Song O., Kim S.k., 2013, Nonlinear stability characteristics of carbon nanotubes conveying fluids, Acta Mechanica 224: 13831396.##[25] Zhang Y.W., Yang T.Z., Zang J., Fang B., 2013, Terahertz wave propagation in a nanotube conveying fluid taking into account surface effect, Materials 6: 23932399.##[26] Chang T.P., 2013, Axial vibration of nonuniform and nonhomogeneous nanorods based on nonlocal elasticity theory, Applied Mathematics and Computation 219: 49334941.##[27] AliAsgari M., Mirdamadi H. R., Ghayour M., 2013, Coupled effects of nanosize, stretching, and slip boundary conditions on nonlinear vibrations of nanotube conveying fluid by the homotopy analysis method, Physica E: Lowdimensional Systems and Nanostructures 52: 7785.##[28] Kiani K., 2013, Vibration behavior of simply supported inclined singlewalled carbon nanotubes conveying viscous fluids flow using nonlocal Rayleigh beam model, Applied Mathematical Modelling 37: 18361850.##[29] Arani A. G., Ahmadi M., Ahmadi A., Rastgoo A., Sepyani H., 2012, Buckling analysis of a cylindrical shell, under neutron radiation environment, Nuclear Engineering and Design 242: 16.##[30] Ghorbanpour A., Mosallaie A. A., Kolahchi R., 2014, Nonlinear dynamic buckling of viscousfluidconveying PNC cylindrical shells with core resting on viscopasternak medium 6(3): 265277.##[31] Wattanasakulpong N., Ungbhakorn V., 2014, Linear and nonlinear vibration analysis of elastically restrained ends FGM beams with porosities, Aerospace Science and Technology 32: 111120.##[32] 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: 28532867.##[33] Daneshjou K., Talebitooti M., Talebitooti R., Googarchin H. S., 2013, Dynamic analysis and critical speed of rotating laminated conical shells with orthogonal stiffeners using generalized differential quadrature method, Latin American Journal of Solids and Structures 10: 349390.##[34] Daneshjou K., Talebitooti M., Talebitooti R., 2013, Free vibration and critical speed of moderately thick rotating laminated composite conical shell using generalized differential quadrature method, Applied Mathematics and Mechanics 34: 437456.##[35] Shu C., 2012, Differential Quadrature and its Application in Engineering, Springer Science & Business Media.##[36] Tadi Beni Y., Mehralian F., Zeighampour H., 2016, The modified couple stress functionally graded cylindrical thin shell formulation, Mechanics of Advanced Materials and Structures 23: 791801.##[37] Ghadiri M., Safarpour H., 2016, Free vibration analysis of embedded magnetoelectrothermoelastic cylindrical nanoshell based on the modified couple stress theory, Applied Physics A 122: 833.##[38] Barooti M. M., Safarpour H., M., 2017, Critical speed and free vibration analysis of spinning 3D singlewalled carbon nanotubes resting on elastic foundations, The European Physical Journal Plus 132: 6.##[39] Ansari R., Gholami R., Rouhi H., 2012, Vibration analysis of singlewalled carbon nanotubes using different gradient elasticity theories, Composites Part B: Engineering 43: 29852989.##]
1

Vibration, Buckling and Deflection Analysis of Cracked Thin Magneto Electro Elastic Plate Under Thermal Environment
http://jsm.iauarak.ac.ir/article_665912.html
10.22034/jsm.2019.665912
1
The MagnetoElectroElastic (MEE) material exhibits pyroelectric and pyromagnetic effects under thermal environment. The effects of such pyroelectric and pyromagnetic behavior on vibration, buckling and deflection analysis of partially cracked thin MEE plate is presented and discussed in this paper. The aim of the study is to develop an analytical model for the vibration and geometrically linear thermal buckling analysis of cracked MEE plate based on the classical plate theory (CPT). The line spring model (LSM) is modified for the crack terms to accommodate the effect of electric and magnetic field rigidities, whereas the effect of thermal environment is accommodated in the form of thermal moment and inplane forces. A classical relation for thermal buckling phenomenon of cracked MEE plate is also proposed. The governing equation for cracked MEE plate has also been solved to get central deflection which shows an important phenomenon of shift in primary resonance due to crack and temperature rise. The results evaluated for natural frequencies as affected by crack length, plate aspect ratio and critical buckling temperature are presented for first four modes of vibration. The obtained results reveal that the fundamental frequency of the cracked plate decreases with increase in temperature and crack length. Furthermore the variation of the critical buckling temperature with plate aspect ratio and crack length is also established for different modes of vibration.
0

454
474


Shashank
Soni
National Institute of Technology, Raipur, Chhattisgarh, India
India
shashanksoninitr@gmail.com


N.K
Jain
National Institute of Technology, Raipur, Chhattisgarh, India
India


P.V.
Joshi
Department of Basic Sciences and Engineering, Indian Institute of Information Technology, Nagpur, India
India
Vibration
Buckling
temperature
Crack
Magnetoelectroelastic plate
[[1] Chang T.P., 2013, On the natural frequency of transversely isotropic magnetoelectroelastic plates in contact with fluid, Applied Mathematical Modelling 37: 25032515.##[2] Liu M., 2011, An exact deformation analysis for the magnetoelectroelastic fiberreinforced thin plate, Applied Mathematical Modelling 35: 24432461.##[3] Liu M., Chang T., 2010, Closed form expression for the vibration problem of a transversely isotropic magnetoelectro elastic plate, Journal of Applied Mechanics 77: 18.##[4] Chen Z., Yu S., Meng L., Lin Y., 2006, Effective properties of layered magnetoelectroelastic composites, Composite Structures 57: 177182.##[5] Li J.Y., 2000, Magnetoelectroelastic multiinclusion and inhomogeneity problems and their applications in composite materials, International Journal of Engineering Science 38: 19932011.##[6] Xue C.X., Pan E., 2013, On the longitudinal wave along a functionally graded magnetoelectroelastic rod, International Journal of Engineering Science 62: 4855.##[7] Wu T.L., Huang J.H., 2000, Closedform solutions for the magnetoelectric coupling coefficients in fibrous composites with piezoelectric and piezomagnetic phases, International Journal of Solids and Structures 37: 29813009.##[8] Pan E., 2001, Exact solution for simply supported and multilayered magnetoelectroelastic plates, Journal of Applied Mechanics 68: 608.##[9] Pan E., Heyliger P.R., 2002, Free vibrations of simply supported and multilayered magnetoelectroelastic plates, Journal of Sound and Vibration 252: 429442.##[10] Ramirez F., Heyliger P.R., Pan E., 2006, Free vibration response of twodimensional magnetoelectroelastic laminated plates, Journal of Sound and Vibration 292: 626644.##[11] Ramirez F., Heyliger P.R., Pan E., 2006, Discrete layer solution to free vibrations of functionally graded magnetoelectroelastic plates, Mechanics of Advanced Materials and Structures 13: 249266.##[12] Simões Moita J.M., Mota Soares C.M., Mota Soares C.A., 2009, Analyses of magnetoelectroelastic plates using a higher order finite element model, Composite Structures 91: 421426.##[13] Milazzo A., 2012, An equivalent singlelayer model for magnetoelectroelastic multilayered plate dynamics, Composite Structures 94: 20782086.##[14] Milazzo A., 2014, Layerwise and equivalent single layer models for smart multilayered plates, Composites Part B: Engineering 67: 6275.##[15] Milazzo A., 2014, Refined equivalent single layer formulations and finite elements for smart laminates free vibrations, Composites Part B: Engineering 61: 238253.##[16] Kattimani S.C., Ray M.C., 2015, Control of geometrically nonlinear vibrations of functionally graded magnetoelectroelastic plates, International Journal of Mechanical Sciences 99: 154167.##[17] Li Y., Zhang J.,2014, Free vibration analysis of magnetoelectroelastic plate resting on a Pasternak foundation, Smart Materials and Structures 23: 25002.##[18] Razavi S., Shooshtari A., 2015, Nonlinear free vibration of magnetoelectroelastic rectangular plates, 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1

Dynamics of LoveType Waves in Orthotropic Layer Under the Influence of Heterogeneity and Corrugation
http://jsm.iauarak.ac.ir/article_665913.html
10.22034/jsm.2019.665913
1
The present problem deals with the propagation of Lovetype surface waves in a bedded structure comprises of an inhomogeneous orthotropic layer and an elastic halfspace. The upper boundary and the interface between two media are considered to be corrugated. An analytical method (separation of variables) is adapted to solve the second order PDEs, which governs the equations of motion. Equations for particle motion in the layer and halfspace have been formulated and solved separately. Finally, the frequency relation has been established under suitable boundary conditions at the interface of the orthotropic layer and the elastic halfspace. Obtained relation is found to be in good agreement with the classical case of Love wave propagation. Remarkable effects of heterogeneity and corrugation parameters on the phase velocity of the considered wave have been represented by the means of graphs. Moreover, the group velocity curves are also plotted to exhibit the profound effect of heterogeneity considered in the layer. Results may be useful in theoretical study of wave propagation through composite layered structure with irregular boundaries.
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475
485


S.A
Sahu
Department of Applied Mathematics, IIT(ISM), Dhanbad826004, India
India
ism.sanjeev@gmail.com


S
Goyal
Department of Applied Mathematics, IIT(ISM), Dhanbad826004, India
India


S
Mondal
Department of Applied Mathematics, IIT(ISM), Dhanbad826004, India
India
Lovetype waves
Orthotropic layer
Corrugation
Heterogeneity
Elastic halfspace
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