On the Dynamic Characteristic of Thermoelastic Waves in Thermoelastic Plates with Thermal Relaxation Times

Document Type : Research Paper


Department of Mathematics, Government Post-Graduate College Hamirpur


In this paper, analysis for the propagation of general anisotropic media of finite thickness with two thermal relaxation times is studied. Expression of displacements, temperature, thermal stresses, and thermal gradient for most general anisotropic thermoelastic plates of finite thickness are obtained in the analysis. The calculation is then carried forward for slightly more specialized case of a monoclinic plate. Dispersion relations for symmetric and antisymmetric wave modes are obtained. Thermoelastic plates of higher symmetry are contained implicitly in the analysis. Numerical solution of the frequency equation for a representative plate of assigned thickness is carried out, and the dispersion curves for the few lower modes are presented. Coupled thermoelastic thermal motions of the medium are found dispersive and coupled with each other due to the thermal and anisotropic effects. Some special cases have also been deduced and discussed.


 [1] Chadwick P., 1960, Progress in Solid Mechanics, edited by R. Hill and I. N. Sneddon 1, North Holland Publishing Co., Amsterdam.
[2] Kraut E.A., 1963, Advances in the theory of anisotropic elastic wave propagation, Reviews of Geophysics 3: 401-448.
[3] Fedorov F.I., 1968, Theory of Elastic Waves in Crystals, Plenun Press, New York.
[4] Achenbach J.D, 1973, Wave Propagation in Elastic Solids, North-Holland, Amsterdam.
[5] Auld B.A, 1973, Acoustic Fields and Waves in Solids 1, John Wiley and Sons, New York.
[6] Rose J.L., 1999, Ultrasonic Waves in Solid Media, Cambridge, New York, Cambridge University Press.
[7] Brekhovskikh L.M., 1960, Waves in Layered Media, Academic Press, New York.
[8] Ewing, E. Jardetzky W.S., Press F., 1957, Elastic Waves in Layered Media, McGraw-Hill, New York.
[9] Kennett B.L.N, 1983, Seismic Wave Propagation in Stratified Media, Cambridge University Press, Cambridge.
[10] Thomson W.T., 1950, Transmission of elastic waves through a stratified solid medium, Journal of Applied Physics 21: 89-93.
[11] Nayfeh A.H., 1995, Wave propagation in layered anisotropic media with application to composites, Applied Mathematics and Mechanics, North-Holland, Amsterdam.
[12] Biot, M.A., 1956, Thermoelasticity and irreversible thermodynamics, Journal of Applied Physics 27:240-253.
[13] Nowacki, W., 1975, Dynamic Problems of Thermoelasticity, Noordhoff, Leyden, Netherlands.
[14] Nowacki, W. 1986, Thermoelasticity, 2nd edition, Pergamon Press, Oxford.
[15] Chandrasekharaiah D.S., 1986, Thermoelasticity with second sound-A Review, Applied Mechanics Review 39: 355-376.
[16] Chandrasekharaiah D.S., 1998, Hyperbolic thermoelasticity.-A review of recent literature, Applied Mechanics Review 51:705-729.
[17] Lord H.W., Shulman Y., 1967, A generalized dynamical theory of thermoelasticity, Journal of Mechanics and Physics of Solids 15: 299-309.
[18] Green A.E., Lindsay K.A., 1972, Thermoelasticity, Journal of Elasticity 2: 1-7.
[19] Banerjee D.K., Pao Y.K., 1974, Thermoelastic waves in anisotropy solids, The Journal of the Acoustical Society of America 56: 1444-1454.
[20] Dhaliwal R.S., Sherief H.H., 1980, Generalized thermoelasticity for anisotropic media, Applied Mathematics 38:1-8.
[21] Puri P., 1975, Plane waves in generalized thermoelasticity-errata, International Journal of Engineering Science 13: 339-340.
[22] Agarwal Y.K.,1979, On surface waves in generalized thermoelasticity, Journal of Elasticity 8: 171-177.
[23] Massalas C.V., Kalpakidis , V.K., 1987, Thermoelastic waves in a thin plate with mixed boundary conditions and thermal relaxation, Archive of Applied Mechanics 57: 401-412.
[24] Verma K.L., Hasebe N., 1999, On the propagation of Generalized thermoelastic vibrations in plates. Quarterly Journal of the Polish Academy of Science, Engineering Transactions 47: 299-319.
[25] Massalas C.V., Kalpakidis V.K., 1987, Thermoelastic waves in a waveguide, International Journal of Engineering Science 25: 1207-1218.
[26] Nayfeh A.H., Hawwa M.A, 1996, Thermoelastic waves in laminated composites plate with a second sound effect, Journal of Applied Physics 80: 2733-2738.
[27] Tao D.J., Prevost H., 1984, Relaxation effects on generalized thermoelastic waves, Journal of Thermal Stresses 7:79-89.
[28] Nayfeh A.H., Hawwa M.A., 1995, The general problem of thermoelastic waves in anisotropic periodically laminated composites, Composite Engineering 5:1499-1517.
[29] Verma K.L., Hasebe N., 2001, wave propagation in plates of general anisotropic media in generalized thermoelasticity, International Journal of Engineering Science 39: 1739-1763.
[30] Verma K. L., 2002, on the propagation of waves in layered anisotropic media in generalized thermoelasticity, International Journal of Engineering Science 40: 2077-2096.
[31] Verma K.L., 2001, Thermoelastic vibrations of transversely isotropic plate with thermal relaxations, International Journal of Solids and Structures 38: 8529-8546.
[32] Verma K.L., Hasebe N., 2002, wave propagation in transversely isotropic plates in generalized thermoelasticity, Archive of Applied Mechanics 72:470-482.
[33] Jabbari M., Dehbani H., 2010, An exact solution for Lord-Shulman generalized coupled thermoporoelasticity in spherical coordinates, Journal of Solid Mechanics 2(3): 214-230.
[34] Verma K.L., Hasebe N., 2004, On Theflexural and extensional thermoelastic waves in orthotropic plates with thermal relaxation time, Journal of Applied Mathematics 1: 69-83.
[35] Nayfeh A.H., Chementi D.E., 1989, Free wave propagation in plates of general anisotropic media, Journal of Applied Mechanics 56: 881-886.
[36] Chadwick P., Seet L.T.C., 1970, Wave propagation in a transversely isotropic heat-conducting elastic material, Mathematika 17: 255-274.