2010
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4
4
113
Electromagnetothermomechanical Behaviors of a Radially Polarized FGPM Thick Hollow Sphere
2
2
In this study an analytical method is developed to obtain the response of electromagnetothermoelastic stress and perturbation of a magnetic field vector for a thickwalled spherical functionally graded piezoelectric material (FGPM). The hollow sphere, which is placed in a uniform magnetic field, is subjected to a temperature gradient, inner and outer pressures and a constant electric potential difference between its inner and outer surfaces. The thermal, piezoelectric and mechanical properties except the Poisson’s ratio are assumed to vary with the power law functions through the thickness of the hollow sphere. By solving the heat transfer equation, in the first step, a symmetric distribution of temperature is obtained. Using the infinitesimal electromagnetothermoelasticity theory, then, the Navier’s equation is solved and exact solutions for stresses, electric displacement, electric potential and perturbation of magnetic field vector in the FGPM hollow sphere are obtained. Moreover, the effects of magnetic field vector, electric potential and material inhomogeneity on the stresses and displacements distributions are investigated. The presented results indicate that the material inhomogeneity has a significant influence on the electromagnetothermomechanical behaviors of the FGPM hollow sphere and should therefore be considered in its optimum design.
1

305
315


A
Ghorbanpour Arani
Department of Mechanical Engineering, Faculty of Engineering, University of Kashan
Department of Mechanical Engineering, Faculty
Iran
aghorban@kashanu.ac.ir


J
Jafari Fesharaki
Department of Mechanical Engineering, Faculty of Engineering, University of Kashan
Department of Mechanical Engineering, Faculty
Iran


M
Mohammadimehr
Department of Mechanical Engineering, Faculty of Engineering, University of Kashan
Department of Mechanical Engineering, Faculty
Iran


S
Golabi
Department of Mechanical Engineering, Faculty of Engineering, University of Kashan
Department of Mechanical Engineering, Faculty
Iran
FGPM
Thick hollow sphere
Electromagnetothermomechanic
Perturbation of the magnetic field vector
[[1] Chen W.Q., Lu Y., Ye J. R., Cai J.B., 2002, 3D electroelastic fields in a functionally graded piezoceramic hollow sphere under mechanical and electric loading, Archive of Applied Mechanics 72: 3951.##[2] Lim C.W., He L.H., 2001, Exact solution of a compositionally graded piezoelectric layer under uniform stretch, bending and twisting, International Journal of Mechanical Sciences 43: 24792492.##[3] Shi Z. F., Chen Y., 2004, Functionally graded piezoelectric cantilever beam under load, Archive of Applied Mechanics 74: 237247.##[4] Wu C. P., Syu Y.S., 2007, Exact solution of functionally graded piezoelectric shells under cylindrical bending, International Journal of Solids and Structures 44: 64506472.##[5] Dai H.L., Fu Y.M., Yang J.H., 2007, Electromagnetoelastic behaviors of functionally graded piezoelectric solid cylinder and sphere, Acta Mechanica Sinica 23: 5563.##[6] Ootao Y., Tanigawa Y., 2007, Transient piezothermoelastic analysis for a functionally graded thermopiezoelectric hollow sphere, Composite Structures 81: 540549.##[7] Khoshgoftar M.J., Ghorbanpour Arani A., Arefi M., 2009, Thermoelastic analysis of a thick walled cylinder made of functionally graded piezoelectric material, Smart Materials and Structures 18: 115007.##[8] Ghorbanpour Arani A., Loghman A., Abdollahitaheri A., Atabakhshian V., 2010, Electrothermomechanical behaviors of a radially polarized rotating functionally graded piezoelectric cylinder, Journal of Mechanics of Materials and Structures, in press.##[9] Ghorbanpour Arani A., Salari M., Khademizadeh H., Arefmanesh A., 2010, Magnetothermoelastic stress and perturbation of magnetic field vector in a functionally graded hollow sphere, Archive of Applied Mechanics 80: 189200.##[10] Ghorbanpour Arani A., Salari M., Khademizadeh H., Arefmanesh A., 2009, Magnetothermoelastic transient response of a functionally graded thick hollow sphere subjected to magnetic and thermoelastic fields, Archive of Applied Mechanics 79: 481497.##[11] Dai H.L., Hong L., Fu Y.M., Xiao X.,2010, Analytical solution for electromagnetothermoelastic behaviors of a functionally graded piezoelectric hollow cylinder, Applied Mathematical Modelling 34: 343357.##[12] Kraus J.D., 1984, Electromagnetic, McGrawHill, New York.##[13] Dai H.L., Wang X., 2004, Dynamic responses of piezoelectric hollow cylinders in an axial magnetic field, International Journal of Solids and Structures 41: 52315246.##[14] Heyliger P., 1996, A note on the static behavior of simplysupported laminated piezoelectric cylinders, International Journal of Solids and Structures 34: 37813794.##[15] Wang H.M., Xu Z.X., 2010, Effect of material inhomogeneity on electromechanical behaviors of functionally graded piezoelectric spherical structures, Computational Materials Science 48: 440445.##]
Stress Analysis of Twodirectional FGM Moderately Thick Constrained Circular Plates with Nonuniform Load and Substrate Stiffness Distributions
2
2
In the present paper, bending and stress analyses of twodirectional functionally graded (FG) circular plates resting on nonuniform twoparameter foundations (WinklerPasternak foundations) are investigated using a firstorder sheardeformation theory. To enhance the accuracy of the results, the transverse stress components are derived based on the three dimensional theory of elasticity. The solution is obtained by employing the differential transform method (DTM). The material properties are assumed to vary in both transverse and radial directions according to power and exponential laws, respectively. Intensity of the transverse load is considered to vary according to a secondorder polynomial. The performed convergence analysis and the comparative studies demonstrate the high accuracy and high convergence rate of the approach. A sensitivity analysis consisting of evaluating effects of different parameters (e.g., exponents of the material properties, thickness to radius ratio, trend of variations of the foundation stiffness, and edge conditions) is carried out. Results reveal that in contrast to the available constitutivelawbased solutions, present solution guarantees continuity of the transverse stresses at the interfaces between layers and may also be used for stress analysis of the sandwich panels. The results are reported for the first time and are discussed in detail.
1

316
331


M.M
Alipour
Faculty of Mechanical Engineering, K.N. Toosi University of Technology
Faculty of Mechanical Engineering, K.N. Toosi
Iran


M
Shariyat
Faculty of Mechanical Engineering, K.N. Toosi University of Technology
Faculty of Mechanical Engineering, K.N. Toosi
Iran
m_shariyat@yahoo.com
Bending stress analysis
threedimensional theory of elasticity
twodirectional functionally graded materials
Circular plates
Elastic foundation
Differential transform method
[[1] Reddy J.N., Wang C.M., Kitipornchai S., 1999, Axisymmetric bending of functionally graded circular and annular plates, European Journal of Mechanics A/Solids 18: 185199.##[2] Ma L.S., Wang T.J., 2004, Relationships between axisymmetric bending and buckling solutions of FGM circular plates based on thirdorder plate theory and classical plate theory, International Journal of Solids and Structures 41: 85101.##[3] Saidi A.R., Rasouli A., Sahraee S., 2009, Axisymmetric bending and buckling analysis of thick functionally graded circular plates using unconstrained thirdorder shear deformation plate theory, Composite Structures 89: 110119.##[4] Sahraee S., Saidi A.R., 2009, Axisymmetric bending analysis of thick functionally graded circular plates using fourthorder shear deformation theory, European Journal of Mechanics A/Solids 28: 974984.##[5] Jomehzadeh E., Saidi A.R., Atashipour S.R., 2009, An analytical approach for stress analysis of functionally graded annular sector plates, Materials and Design 30: 36793685.##[6] Golmakani M.E., Kadkhodayan M., 2011, Nonlinear bending analysis of annular FGM plates using higherorder shear deformation plate theories, Composite Structures 93: 973982.##[7] Nie G., Zhong Z., 2007, Axisymmetric bending of twodirectional functionally graded circular and annular plates, Acta Mechanica Solida Sinica 20: 289295.##[8] Li X.Y., Ding H.J., Chen W.Q., 2008, Elasticity solutions for a transversely isotropic functionally graded circular plate subject to an axisymmetric transverse load qrk, International Journal of Solids and Structures 45: 191210.##[9] Li X.Y., Ding H.J., Chen W.Q., 2008, Threedimensional analytical solution for functionally graded magneto–electroelastic circular plates subjected to uniform load, Composite Structures 83: 381390.##[10] Yang B., Ding H.J., Chen W.Q., 2008, Elasticity solutions for a uniformly loaded annular plate of functionally graded materials, Structural Engineering and Mechanics 30(4): 501512.##[11] Lei Z., Zheng Z., 2009, Exact solution for axisymmetric bending of functionally graded circular plate, Tsinghua Science and Technology 14: 6468.##[12] Wang Y., Xu R.Q., Ding H.J., 2010, Threedimensional solution of axisymmetric bending of functionally graded circular plates, Composite Structures 92: 16831693.##[13] Nie G.J., Zhong Z., 2010, Dynamic analysis of multidirectional functionally graded annular plates, Applied Mathematical Modelingl. 34(3): 608616.##[14] Sepahi O., Forouzan M.R., Malekzadeh P., 2010, Large deflection analysis of thermomechanical loaded annular FGM plates on nonlinear elastic foundation via DQM, Composite Structures 92(10): 23692378.##[15] Sburlati R., Bardella L., 2010, Threedimensional elastic solutions for functionally graded circular plates, European Journal of Mechanics A/Solids 2011, dx.doi.org/10.1016/j.euromechsol.2010.12.008.##[16] Shariyat M., Alipour M.M., 2011, Differential transform vibration and modal stress analyses of circular plates made of twodirectional functionally graded materials, resting on elastic foundations, Archive of Applied Mechanics 81: 12891306.##[17] Alipour M.M., Shariyat M., Shaban M., 2010, A semianalytical solution for free vibration of variable thickness twodirectionalfunctionally graded plates on elastic foundations, International Journal of Mechanics and Materials in Design 6(4): 293304.##[18] Reddy J.N., 2007, Theory and Analysis of Elastic Plates and shells, Second Edition, CRC/Taylor and Francis, Philadelphia.##[19] Shen, H.S., 2009, Functionally Graded Materials: Nonlinear Analysis of Plates and Shells, CRC Press, Taylor and Francis Group, Boca Raton.##[20] Ugural A.C., Fenster S.K, 2003, Advanced Strength and Applied Elasticity, Forth Edition, Prentice Hall, New Jersey.##[21] Reddy J.N., Wang C.M., Kitipornchai S., 1999, Axisymmetric bending of functionally graded circular and annular plates, European Journal of Mechanics A/Solids 18: 185199.##[22] Nosier A., Fallah F., 2008, Reformulation of Mindlin–Reissner governing equations of functionally graded circular plates, Acta Mechanica 198: 209233.##[23] Shariyat M., 2011, Nonlinear dynamic thermomechanical buckling analysis of the imperfect laminated and sandwich cylindrical shells based on a globallocal theory inherently suitable for nonlinear analyses, International Journal of NonLinear Mechanics46(1):253271.##[24] Shariyat M., 2011, A doublesuperposition globallocal theory for vibration and dynamic buckling analyses of viscoelastic composite/sandwich plates: A complex modulus approach, Archive of Applied Mechanics81: 12531268.##[25] LezgyNazargah M., Shariyat M., BeheshtiAval S.B., 2011, A refined highorder globallocal theory for finite element bending and vibration analyses of the laminated composite beams, Acta Mechanica217: 219242.##[26] LezgyNazargah M., BeheshtiAval S.B., Shariyat M., 2011, A refined mixed globallocal finite element model for bending analysis of multilayered rectangular composite beams with small widths, ThinWalled Structures49: 351362.##[27] Hosseini S.M., Sladek J., Sladek V., 2011, Meshless local Petrov–Galerkin method for coupled thermoelasticity analysis of afunctionally graded thick hollow cylinder, Engineering Analysis with Boundary Elements. 35: 827835.##]
Elastic Buckling Analysis of Ring and Stringerstiffened Cylindrical Shells under General Pressure and Axial Compression via the Ritz Method
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2
Elastic stability of ring and stringerstiffened cylindrical shells under axial, internal and external pressures is studied using Ritz method. The stiffeners are rings, stringers and their different arrangements at the inner and outer surfaces of the shell. Critical buckling loads are obtained using Ritz method. It has been found that the cylindrical shells with outside rings are more stable than those with inside rings under axial compressive loading. The critical buckling load for inside rings is reducing by increasing the eccentricity of the rings, while for outside ring stiffeners the magnitude of eccentricity does not affect the critical buckling load. It has also been found that the shells with inside stringers are more stable than those with outside one. Moreover, the stability of cylindrical shells under internal and external pressures is almost the same for inside and outside arrangements of stringers. The results are verified by comparing with the results of Singer at the same loading and boundary conditions.
1

332
347


A
Ghorbanpour Arani
Department of Mechanical Engineering, Faculty of Engineering, University of Kashan
Department of Mechanical Engineering, Faculty
Iran
aghorban@kashanu.ac.ir


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


A.A
Mosallaie Barzoki
Department of Mechanical Engineering, Faculty of Engineering, University of Kashan
Department of Mechanical Engineering, Faculty
Iran


R
Kolahchi
Department of Mechanical Engineering, Faculty of Engineering, University of Kashan
Department of Mechanical Engineering, Faculty
Iran
Buckling analysis
Stiffened cylindrical shells
Ritz method
[[1] Singer J., Baruch M., 1963, Effect of eccentricity of stiffeners on the general instability of stiffened cylindrical shells under hydrostatic pressure, International Journal of Mechanical Sciences 5: 2327.##[2] Ghorbanpour A., Golabi S., Loghman A., Daneshi H., 2007, Investigating elastic stability of cylindrical shell with an elastic core under axial compression by energy method, Journal of Mechanical Science and Technology 21(7):983996.##[3] Ojalvo I.U., Newman M., 1967, Natural vibrations of a stiffened pressurized cylinder with an attached mass, AIAA. Journal 5: 11391146.##[4] Eslami M.R., Ziaii A.R., Ghorbanpour A., 1996, Thermoelastic buckling of thin cylindrical shell based on improved stability equations, Journal of Thermal Stresses 19: 299315.##[5] Singer J., Baruch M., Harari O., 1967, The stability of eccentrically stiffened cylindrical shells under axial compression, International Journal of Solids and Structures 3: 445470.##[6] Hubner A., Albiez M., Kohler D., Saal H., 2007, Buckling of long steel cylindrical shells subjected to external pressure, ThinWalled Structures 45: 17.##[7] Buermann P., Rolfes R., Tessmer J., Schagerlet M., 2006, A semi analytical model for local postbuckling analysis of stringer and framestiffened cylindrical panels, ThinWalled Structures 44: 102114.##[8] Ding H., 2003, Strength and stability of double cylindrical shell structure subjected to hydrostatic external pressure—II: stability, Marine Structures 16: 397415.##[9] Andrianova V.M., Verbonolb J., Awrejcewiczc I.V., 2006, Buckling analysis of discretely stringerstiffened cylindrical shells, International Journal of Mechanical Sciences 48: 15051515.##[10] Timoshenko S.P., Gere J.M., 1985, Theory of Elastic Stability, McGraw Hill, NewYork.##[11] Galletly G.D, 1955, On the invacuo vibrations of simply supported ringstiffened cylindrical shells, ASME Proceedings of 2nd U.S. National Congress of Applied Mechanics:225231.##[12] Wang Y.G., Zeng G.W., 1983, Calculation of critical pressure of ring stiffened cylindrical shells through function minimization, China Ship Building 4: 2938.##[13] Bushnell D., 1985, Computerized Buckling Analysis of Shells, Martinus Nijhoff Publishers, Lancaster.##]
Boundary Value Problems in Generalized Thermodiffusive Elastic Medium
2
2
In the present study, the boundary value problems in generalized thermodiffusive elastic medium has been investigated as a result of inclined load. The inclined load is assumed to be a linear combination of normal load and tangential load. Laplace transform with respect to time variable and Fourier transform with respect to space variable are applied to solve the problem. As an application of the approach, distributed sources and moving force have been taken. Expressions of displacement, stresses, temperature and concentration in the transformed domain are obtained by introducing potential functions. The numerical inversion technique is used to obtain the solution in the physical domain. Graphical representation due to the response of different sources and use of angle of inclination are shown. Some particular cases are also deduced.
1

348
362


K
Sharma
Department of Mechanical Engineering, N.I.T Kurukshetra
Department of Mechanical Engineering, N.I.T
Iran
kunal_nit90@rediffmail.com
Generalized thermodiffusion
Inclined load
Distributed sources
Moving force
concentration
[[1] Danilouskaya V., 1950, Thermal stresses in elastic half space due to sudden heating of its boundary, Pelageya Yakovlevna Kochina 14: 316321 (in Russian).##[2] Biot M., 1956,Thermoelasticity and irreversible thermodynamics, Journal of Applied Physics 27: 240253.##[3] Lord H.W., Shulman Y., 1967, A generalized dynamical theory of thermoelasticity , Journal of the Mechanics and Physics of Solids 15: 299309.##[4] Nowacki W.,1974, Dynamical problems of thermo diffusion in solids I, Bulletin of the Polish Academy of Sciences  Technical Sciences 22: 5564 (a).##[5] Nowacki W.,1974, Dynamical problems of thermo diffusion in solids II, Bulletin of the Polish Academy of Sciences  Technical Sciences 22: 129135 (b).##[6] Nowacki W.,1974, Dynamical problems of thermo diffusion in solids III, Bulletin of the Polish Academy of Sciences  Technical Sciences 22: 257266 (c).##[7] Nowacki W.,1976, Dynamical problems of thermo diffusion in solids, Engineering fracture mechanics 8: 261266.##[8] Olesiak Z.S., Pyryev Y.A., 1995,A coupled quasistationary problem of thermodiffusion for an elastic cylinder, International Journal of Engineering Science 33: 773780.##[9] Sherief H.H., Saleh H., Hamza F., 2004, The theory of generalized thermoelastic diffusion, International Journal of Engineering Science 42: 591608.##[10] Sherief H.H., Saleh H., 2005, A half space problem in the theory of generalized thermoelastic diffusion, International Journal of Solid and Structures 42 : 44844493.##[11] Singh B., 2006,Reflection of P and SV waves from free surface of an elastic soild with generalized thermodiffusion, Journal of Earth System Science 114 (2): 764778.##[12] Singh B.,2006, Reflection of SV waves from free surface of an elastic solid in generalized thermoelastic diffusion, Journal of Sound and Vibration 291: 764778.##[13] Aouadi M., 2006,Variable electrical and thermal conductivity in the theory of generalized thermodiffusion, ZAMP 57(2): 350366.##[14] Aouadi M.,2006, A generalized thermoelastic diffusion problem for an infinitely long solid cylinder, International Journal of Mathematics and Matematical Sciences, Article ID 25976, 15 pages.##[15] Aouadi M.,2007, A problem for an infinite elastic body with a spherical cavity in the theory of generalized thermoelastic diffusion, International Journalof Solids and Structures 44: 57115722.##[16] Aouadi M., 2007, Uniqueness and recipocity theorem in the theory of generalized thermoelasic diffusion, Journal of Thermal Streses 30: 665678.##[17] Aouadi M.,2008, Generalized theory of thermoelasic diffusion for an anisotropic media, Journal of Thermal Streses 31:270285.##[18] Sharma N.,Ram P., Kumar R., 2008, Plane strain deformation in generalized thermoelastic diffusion, International Journal of Thermophysics 29: 15031522.##[19] Sharma N.,Ram P., Kumar R. ,2008, Dynamical behaviour of generalized thermoelastic diffusion with two relaxation times in frequency domain, Structural Engineering and Mechanics 28(1) :1938.##[20] Kumar R., Kansal T., 2009, RayleighLamb waves in transversely isotropic themoelastic diffusive layer, International Journal of Thermophysics 30(2): 701733.##[21] Kumar R., Rani L., 2005, Deformation due to inclined load in thermoelastic half space with voids, Archive of Mechanics 57(1): 724.##[22] Kumar R., Aliwalia P., 2005, Interactions due to inclined load at micropolar elastic halfspace with voids, International Journal of Applied Mechanics and Engineering 10(1): 109122.##[23] Kumar R., Gupta R.R., 2007,Boudary value problems in orthotropic micropolar thermoelastic medium with one relaxation time, Journal of the Mechanical Behaviour of Materials 18: 317337.##[24] Sharma J.N., Kumari N., Sharma K.K., 2009, Disturbance due to thermal and mass loads in generalized elastothermodiffusive solids, International Journal of Thermophysics 30: 16971723.##[25] Sharma J.N., Kumar V., 1997, Plain strain problems of transversely isotropic thermoelastic media, Journal of Thermal Stresses 20: 463476.##[26] Sherief H.H., ElMaghraby N.M.,2009, A thick plate problem in the theory of generalized thermoelastic diffusion, International Journal of Thermophysics 30: 2044205.##[27] Honig G., Hirdes U., 1984, A method for the numerical inversion of Laplace transforms, Journal of Computational and Applied Mathematics 10: 113132.##[28] Press W.H., Teukolshy S.A.., Vellerling W.T., Flannery B.P., 1986, Numerical Recipes in Fortran, Second Edition, Cambridge University Press, Cambridge.##[29] Eringen A.C., 1984, Plane waves in nonlocal micropolar elasticity, International Journal of Engineering Science 22: 11131121.##[30] Thomas L., 1980, Fundamental of Heat Transfer, Prentice hall IncEnglewmd Diffs, Newjersey.## ##]
Wave Propagation at the Boundary Surface of Elastic Layer Overlaying a Thermoelastic Without Energy Dissipation Halfspace
2
2
The present investigation is to study the surface wave propagation at imperfect boundary between an isotropic thermoelastic without energy dissipation halfspace and an isotropic elastic layer of finite thickness. The penetration depth of longitudinal, transverse, and thermal waves has been obtained. The secular equation for surface waves in compact form is derived after developing the mathematical model. The components of temperature distribution, normal and tangential stress are computed at the interface and presented graphically. The effect of stiffness is shown on the resulting amplitudes and the effect of thermal is shown on the penetration depth of various waves. A particular case of interest is also deduced. Some special cases of interest are also deduced from the present investigation.
1

363
375


R
Kumar
Department of Mathematics, Kurukshetra University
Department of Mathematics, Kurukshetra University
Iran
rajneesh_kuk@rediffmail.com


V
Chawla
Department of Mathematics, Kurukshetra University
Department of Mathematics, Kurukshetra University
Iran
Thermoelasticity without energy dissipation
Stiffness
Amplitudes
[[1] Benveniste Y., 1984, The effective mechanical behavior of composite materials with imperfect contact between the constituents, Mechanics of Materials 4: 197208.##[2] Achenbaeh J.D., Zhu H., 1989, Effect of interfacial zone on mechanical behaviour and failure of reinforced composites, Journal of the Mechanics and Physics of Solids 37: 381393.##[3] Hashin Z., 1990, Thermoelastic properties of fiber composites with imperfect interface, Mechanics of Materials 8: 333348.##[4] Hashin Z., 1991, The spherical inclusion with imperfect interface, ASME Journal of Applied Mechanics 58:444449.##[5] Zhong Z., Meguid S. A., 1996, On the eigenstrain problem of a spherical inclusion with an imperfectly bonded interface, ASME Journal of Applied Mechanics 63: 877883.##[6] Pan E., 2003, Threedimensional Green’s function in anisotropic elastic bimaterials with imperfect interfaces, ASME Journal of Applied Mechanics 70: 180190.##[7] Yu H.Y., 1998, A new dislocationlike model for imperfect interfaces and their effect on Lord transfer composites, Composite Part A: Applied Science and Manufacturing 29(910): 10571062.##[8] Yu H.Y., Wei Y.N., Chiang F.P., 2002, Lord transfer at imperfect interfaces dislocationlike model, International Journal of Engineering Science 40: 16471662.##[9] Benveniste Y., 1999, On the decay of end effects in conduction phenomena: A sandwich strip with imperfect interfaces of low or high conductivity, Journal of Applied Physics 86: 12731279.##[10] Joseph D.D., Preziosi L., 1989, Heat waves, Reviews of Modern Physics 61: 4173.##[11] Dreyer W., Struchtrup H., 1993, Heat pulse experiments revisited, Continuum Mechanics and Thermodynamics 5(1): 350.##[12] Caviglia G., Morro A., Straughan B., 1992, Thermoelasticity at cryogenic temperatures, International Journal of Nonlinear Mechanics 27: 251261.##[13] Chandrasekharaiah D.S., 1986, Thermoelasticity with second sound: A review, Applied Mechanics Review 39: 355376.##[14] Chandrasekharaiah D.S., 1998, Hyperbolic thermoelasticity: A review of recent literature, Applied Mechanics Review 51: 705729.##[15] Muller I., Ruggeri T., 1998, Rational and extended thermodynamics, SpringerVerlag, New York.##[16] Hetnarski R.B., Ignazack J., 1999, Generalized thermoelasticity, Journal of Thermal Stresses 22: 451470.##[17] Green A.E., Naghdi P.M., 1995, A unified procedure for construction of theories of deformable media. I. Classical continuum physics, II. Generalized continua, III. Mixtures of interacting continua, Proceedings of Royal Society London A 448: 335356, 357377, 379388.##[18] Green A.E., Naghdi P.M., 1991, A reexamination of the basic posulales of thermomechanics, Proceedings of Royal Society London A 432: 171194.##[19] Green A.E., Naghdi P.M., 1992, On undamped heat waves in an elastic solid, Journal of Thermal Stresses 15: 253264.##[20] Green A.E., Naghdi P.M., 1993, Thermoelasticity without energy dissipation, Journal of Elasticity 31: 189208.##[21] Bullen K.E., 1963, An introduction of the theory of seismology, Cambridge University Press, Cambridge.##[22] Scott N.H., 1996, Energy and dissipation of inhomogeneous plane waves in thermoelasticity, Wave Motion 23: 393406.##[23] Ciarletta M., 1999, Atheory of micropolar thermoelasticity without energy dissipation, Journal of Thermal Stresses 22: 581594.##[24] Kalpakides V.K., Maugin G.A., 2004, Canonical formulation and conservation laws of thermoelasticity without energy dissipation, Reports of Mathematical Physics 23: 371391.##[25] Othman M. I.A., Song Y., 2007, Reflection of plane waves from an elastic solid halfspace under hydrostatic intial stress without energy dissipation, International Journal of Solids and Structures 44: 56515664.##[26] Chirit S., Ciarletta M., 2010, Spatial behavior for some nonstandard problems in linear thermoelasticity without energy dissipation,Journal of Mathematical Analysis and Applications 367: 5868.##[27] Jiangong Y., Zhang X.., Xue T., 2010, Generalized thermoelastic waves in a functionally graded plates without energy dissipation, Composites Structures 93: 3239.##[28] Jiangong Y., Bin W., Cunfu H., 2010, Circumferential thermoelastic waves in orthotropic cylindrical curved plates without energy dissipation, Ultrasonics 50: 416423.##[29] Youssef H.M., 2011, Theory of two temperature thermoelasticity without energy dissipation, Journal of Thermal Stresses 34: 138146.##[30] Jiangong Y., Bin W., Cunfu H., 2011, Guided thermoelastic wave propagation in layered plates without energy dissipation, Acta Mechanica Solida Sinica 24: 135143.##[31] Aki K., Richards P.G., 1980, Quantitative Seismology Theory and Methods, Volume 1, Freeman, New York.##[32] Dhaliwal R.S., Singh A., 1980, Dynamical Coupled Thermoelasticity, Hindustan Publishing Corporation, Delhi, India.## ##]
Threedimensional Free Vibration Analysis of a Transversely Isotropic Thermoelastic Diffusive Cylindrical Panel
2
2
The present paper is aimed to study an exact analysis of the free vibrations of a simply supported, homogeneous, transversely isotropic, cylindrical panel based on threedimensional generalized theories of thermoelastic diffusion. After applying the displacement potential functions in the basic governing equations of generalized thermoelastic diffusion, it is noticed that a purely transverse mode is independent of thermal and concentration fields and gets decoupled from the rest of motion. The equations for free vibration problem are reduced to four equations of secondorder and one fourthorder ordinary differential equation after expanding the displacement potential, temperature change and concentration functions with an orthogonal series. The formal solution of this system of equations can be expressed by using modified Bessel function with complex arguments. The numerical results for lowest frequency have been obtained and presented graphically. The effect of diffusion on lowest frequency has also been presented graphically. Some special cases of secular equation are also discussed.
1

376
392


R
Kumar
Department of Mathematics, Kurukshetra University
Department of Mathematics, Kurukshetra University
Iran
rajneesh_kuk@rediffmail.com


T
Kansal
Department of Mathematics, Kurukshetra University
Department of Mathematics, Kurukshetra University
Iran
Cylindrical panel
Thermoelastic diffusion
Circumferential wave number
Secular equations
Free vibrations
Lowest frequency
[[1] Aouadi M., 2007, Uniqueness and reciprocity theorems in the theory of generalized thermoelastic diffusion, Journal of Thermal Stresses 30: 665678.##[2] Aouadi M., 2008, Generalized theory of thermoelastic diffusion for anisotropic media, Journal of Thermal Stresses 31: 270285.##[3] Bert C.W., Baker J.K., Egle D.M., 1969, Free vibrations of multilayer anisotropic cylindrical shells, Journal of Composite Materials 3: 11731186.##[4] Buchwald V.P., 1961, Rayleigh waves in transversely isotropic media, Quarterly Journal of Mechanics and Applied Mathematics, 14: 193304.##[5] Chau K.T., 1994, Vibrations of transversely isotropic circular cylinders, ASME Journal of Applied Mechanics 61: 964970.##[6] Fan J.R.., Ding K.W., 1993, Analytical solution for thick closed laminated cylindrical shells, International Journal of Mechanical Sciences 35: 657668.##[7] Gawinecki J.A.., Kacprzyk P., BarYoseph P., 2000, Initial boundary value problem for some coupled nonlinear parabolic system of partial differential equations appearing in thermoelastic diffusion in solid body, J. Anal. Appl, 19: 121130.##[8] Gawinecki J. A., Szymaniec A., 2002, Global solution of the cauchy problem in nonlinear thermoelastic diffusion in solid body, Proceedings in Applied Mathematics and Mechanics 1: 446447.##[9] Green A.E., Lindsay K.A., 1972, Thermoelasticity, Journal of Elasticity 2: 17.##[10] Ip K.H., Chan W.K., Tse P.C., Lai T.C., 1996, Vibration analysis of orthotropic cylindrical shells with free ends by RayleighRitz method, Journal of Sound and Vibration 195: 117135.##[11] Jiang X.Y.,1997, 3D vibration analysis of fiber reinforced composite laminated cylindrical shells, Journal of Vibration and Acoustics 119: 4651.##[12] Jones R.M., Margan H., 1975, Buckling and vibration of cross ply laminated circular cylindrical shells, AIAA Journal 13: 664671.##[13] Kumar R., Kansal T., 2008, Propagation of lamb waves in transversely isotropic thermoelastic diffusive plate, International Journal of Solids and Structures 45: 58905913.##[14] Lord H.W., Shulman Y., 1967, A generalized dynamical theory of thermoelasticity, Journal of Mechanics and Physics of Solids 15: 299309.##[15] Mirsky I., 1965, Wave propagation in transversely isotropic circular cylinders (part I and II), Journal of the Acoustical Society of America 37: 10161026.##[16] Nowacki W., 1974, Dynamical problems of thermodiffusion in solidsI, Bulletin of Polish Academy of Sciences Series, Science and Technology 22: 55 64.##[17] Nowacki W., 1974, Dynamical problems of thermodiffusion in solidsII, Bulletin of Polish Academy of Sciences Series, Science and Technology 22: 129135.##[18] Nowacki W., 1974,Dynamical problems of thermodiffusion in solidsIII, Bulletin of Polish Academy of Sciences Series, Science and Technology 22: 257266.##[19] Nowacki W., 1976, Dynamical problems of thermodiffusion in solids, Engineering Fracture Mechanics 8: 261266.##[20] Sharma J.N., Sharma P.K., 2002, Free vibration analysis of homogeneous transversely isotropic thermoelastic cylindrical panel, Journal of Thermal Stresses 25: 169182.##[21] Sherief H.H., Hamza F., Saleh H., 2004, The theory of generalized thermoelastic diffusion, International Journal of Engineering Science 42: 591 608.##[22] Sherief H.H., Saleh H., 2005, A half space problem in the theory of generalized thermoelastic diffusion, International Journal of Solids and Structures 42: 44844493.##[23] So J.Y., Leissa A.W., 1997, Free vibrations of thick hollow cylinders from three dimensional analysis, Journal of Vibration and Acoustics 119: 8995.##[24] Soedel W., 1983, Simplified equations and solutions for the vibration of orthotropic cylindrical shells, Journal of Sound and Vibration 87: 555566.##[25] Soldatos K.P., 1987, Influence of thickness shear deformation on free vibrations of rectangular plates and cylinders of antisymmetric angle ply construction, Journal of Sound and Vibration 119: 111137.##[26] Soldatos K.P., Hadhgeorgian V.P., Threedimensional solutions of the free vibration problem of homogeneous isotropic cylindrical shells and panels, Journal of Sound and Vibration 137: 369384.##[27] Ye J.Q., Soldatos K.P., 1994, 3D vibrations of laminated cylinders and cylindrical panels with symmetric and antisymmetric crossply layup, Composites part B: Engineering 4: 429444.## ##]
Wave Propagation in Sandwich Panel with Auxetic Core
2
2
Auxetic cellular solids in the forms of honeycombs and foams have great potential in a diverse range of applications, including as core material in curved sandwich panel composite components, radome applications, directional pass band filters, adaptive and deployable structures, filters and sieves, seat cushion material, energy absorption components, viscoelastic damping materials and fastening devices etc.In this paper, the characteristic of wave propagation in sandwich panel with auxetic core is analyzed. A threelayer sandwich panel is considered which is discretized in the thickness direction by using semianalytical finite element method. Wave propagation equations are obtained through some algebraic manipulation and applying standard finite element assembling procedures. The mechanical properties of auxetic core can be described by the geometric parameters of the unit cell and mechanical properties of the virgin core material. The characteristics of wave propagation in sandwich panel with conventional hexagonal honeycomb core and reentrant auxetic core are discussed, and effects of panel thickness, geometric properties of unit cell on dispersive curves are also discussed. Variations of Poisson’s ratio and core density with inclined angle are presented.
1

393
402


D
QingTian
School of Science, Chang’an University, Xi’an, China
School of Science, Chang’an University,
Iran
deng_qingtian@yahoo.com.cn


Y
ZhiChun
School of Aeronautics, Northwestern Polytechnical University
School of Aeronautics, Northwestern Polytechnical
Iran
Sandwich panel
Auxetic material
Negative Poisson’s ratio
Elastic wave
Semianalytical finite element method
[[1] Evans K.E., Nkansah M.A., Hutchinson I.J., Rogers S.C., 1991, Molecular network design, Nature 353: 12125.##[2] Alderson A., Alderson K.L., 2007, Auxetic materials, Proceeding of Institute of Mechanical Engineers, Part G: Journal of Aerospace Engineering 221: 565575.##[3] Hadjigeorgiou E.P., Stavroulakis G.E., 2004, The use of auxetic materials in smart structures, Computational Methods in Science and Technology 10(2): 147160.##[4] Yu S.D., Cleghorn W.L., 2005, Free flexural vibration analysis of symmetric honeycomb panels, Journal of Sound and Vibration 284: 189204.##[5] Remillat C., Wilcox P., Scarpa F., 2008, Lamb wave propagation in negative Poisson’s ratio composites, Proceedings of SPIE 6935.##[6] Tee K.F., Spadoni A., Scarpa F., Ruzzene M., 2010, Wave propagation in auxetic tetrachiral honeycombs, Journal of Vibration and Acoustics 132: 031007.##[7] Wan H., Ohtaki H., Kotosaka S., Hu G.M., 2004, A study of negative Poisson’s ratios in auxetic honeycombs based on a large deflection model, European Journal of Mechanics A/Solids 23: 95106.##[8] Scarpa F., Tomlinson G., 2000, Theoretical characteristics of the vibration of sandwich plates with inplane negative Poisson’s ratio values, Journal of Sound and Vibration 230(1): 4567.##[9] Ruzzene M., Mazzarella L., Tsopelas P., Scarpa F. 2002, Wave propagation in sandwich plates with periodic auxetic core, Journal of Intelligent Material Systems and Structures 13(9): 587597.##[10] Ruzzene M., Scarpa F., 2003, Control of wave propagation in sandwich beams with auxetic core, Journal of Intelligent Materials Systems and Structures 1(7): 448468.##[11] Ruzzene M., Scarpa F., Soranna, F. 2003, Wave beaming effects in two dimensional cellular structures, Smart Materials and Structures 12(3): 363372.##[12] Lira C., Innocenti P., Scarpa F. 2009, Transverse elastic shear of auxetic multireentrant honeycombs, Composite Structures 90(3): 314322.##[13] Reddy J.N., 2002, Energy Principle and Variational Methods in Applied Mechanics, Second Edition, John Wiley, New York.##[14] Cook R.D., 2001, Concepts and Applications of Finite Element Analysis, John Wiley, New York.##[15] Scarpa F., Tomlin P.J. 2000, On the transverse shear modulus of negative Poisson’s ratio honeycomb structures, Fatigue and Fracture Engineering Materials and Structures 23: 717720.##[16] Gibson L.J., Ashby M.F., 1997, Cellular Solids: Structure and Properties, Cambridge University Press, Cambridge, UK, Second Edition.##[17] Decolon C., 2002, Analysis of Composite Structures, Hermes Penton Science, London.## ##]
Twodimensional Axisymmetric Electromechanical Response of Piezoelectric, Functionally Graded and Layered Composite Cylinders
2
2
A mixed semianalytical cum numerical approach is presented in this paper which accounts for the coupled mechanical and electrical response of piezoelectric, functionally graded (FG) and layered composite hollow circular cylinders of finite length. Under axisymmetric mechanical and electrical loadings, the threedimensional problem (3D) gets reduced to a twodimensional (2D) plane strain problem of elasticity. The 2D problem is further simplified and reduced to a onedimensional (1D) by assuming an analytical solution in longitudinal direction (z) in terms of Fourier series expansion which satisfies the simply (diaphragm) supported boundary conditions exactly at the two ends z = 0, l. Fundamental (basic) dependent variables are chosen in the radial direction (thickness coordinate) of the cylinder. The resulting mathematical model is cast in the form of first order simultaneous ordinary differential equations which are integrated through an effective numerical integration technique by first transforming the BVP into a set of initial value problems (IVPs). The cylinder is subjected to internal/external pressurized mechanical and an electrical loading. Finally, numerical results are obtained which govern the active and sensory response of piezoelectric and FG cylinders. Numerical results are compared for their accuracy with available results. New results of finite length cylinders are generated and presented for future reference.
1

403
417


T
Kant
Institute Chair Professor, Department of Civil Engineering, Indian Institute of Technology Bombay
Institute Chair Professor, Department of
Iran


P
Desai
Manager (Design), S N Bhobe and Associates, Navi Mumbai
Manager (Design), S N Bhobe and Associates,
Iran
payaldesai79@gmail.com
Finite length cylinder
FGM, Laminated composites
Piezoelectricity
Boundary Value Problem
Elasticity theory
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