On the propagation of waves in layered anisotropic media in generalized thermoelasticity. (English) Zbl 1211.74139

Summary: In view of the increased usage of anisotropic materials in the development of advanced engineering materials such as fibers and composite and other multilayered, propagation of thermoelastic waves in arbitrary anisotropic layered plate is investigated in the context of the generalized theory of thermoelasticity. Beginning with a formal analysis of waves in a heat-conducting \(N\)-layered plate of an arbitrary anisotropic media, the dispersion relations of thermoelastic waves are obtained by invoking continuity at the interface and boundary conditions on the surfaces of layered plate. The calculation is then carried forward for more specialized case of a monoclinic layered plate. The obtained solutions which can be used for material systems of higher symmetry (orthotropic, transversely isotropic, cubic, and isotropic) are contained implicitly in our analysis. The case of normal incidence is also considered separately. Some special cases have also been deduced and discussed. We also demonstrate that the particle motions for SH modes decouple from rest of the motion, and are not influenced by thermal variations if the propagation occurs along an in-plane axis of symmetry. The results of the strain energy distribution in generalized thermoelasticity are useful in determining the arrangements of the layer in thermal environment.


74J99 Waves in solid mechanics
74E10 Anisotropy in solid mechanics
74F05 Thermal effects in solid mechanics
Full Text: DOI


[1] Ewing, W.M.; Jardetsky, W.S.; Press, F., Elastic waves in layered media, (1957), McGraw-Hill New York · Zbl 0083.23705
[2] Brekhovskikh, L.M, Waves in layered media, (1960), Academic Press New York · Zbl 0558.73018
[3] Caviglia, G.; Morro, A., Wave propagation in multilayered anisotropic solids, Int. J. engng. sci., 38, 1377-1395, (2000) · Zbl 1210.74093
[4] Liu, G.R.; Tani, J.; Watanabe, K.; Ohyoshi, T., Lamb propagation waves in anisotropic laminates, ASME, J. appl. mech., 57, 923-929, (1990)
[5] Padvan, J., Thermoelasticity of anisotropic half space, J. appl. mech., 41, 935, (1974) · Zbl 0294.73009
[6] Padvan, J., Thermoelasticity of anisotropic generally laminated slabs subject to spatially periodic loads, ASME, J. appl. mech., 42, 341, (1975)
[7] Bufler, H., Theory of elasticity of a multilayered medium, J. elast., 19, 125, (1971)
[8] Bahar, L.Y., Transfer matrix approach to layered system, ASCE, J. engng. mech. div., 98, 1159, (1972)
[9] Thangjitham, S.; Choi, H.J., Thermal stresses in a multilayered anisotropic medium, ASME, J. appl. mech., 58, 1021, (1991) · Zbl 0744.73014
[10] Lord, H.W.; Shulman, Y.A., A generalized dynamical theory of thermoelasticity, J. mech. phys. solids, 15, 299-309, (1967) · Zbl 0156.22702
[11] Dhaliwal, R.S.; Sherief, H.H., Generalized thermoelasticity for anisotropic media, Q. appl. math., 38, 1-8, (1980) · Zbl 0432.73013
[12] Sharma, J.N.; Sidhu, R.S., On the wave propagation of plane harmonic waves in anisotropic generalized thermoelasticity, Int. J. engng. sci., 24, 1511-1516, (1986) · Zbl 0594.73012
[13] K.L. Verma, Propagation of generalized thermoelastic free waves in plate of anisotropic media, in: Proceedings of Second International Symposium on Thermal Stresses and Related Topics, Thermal Stresses, 1997, pp. 199-201
[14] Verma, K.L.; Hasebe, N., Wave propagation in plates of general anisotropic media in generalized thermoelasticity, Int. J. engng sci., 39, 1739-1763, (2001)
[15] K.L. Verma, N. Hasebe, R. Sethuraman, Dynamic distribution of displacements and thermal stresses in multilayered media in generalized thermoelasticity, Proceedings of third International Congress on Thermal Stresses, Thermal Stresses, 1999, pp. 577-580
[16] Nayfeh, A.H.; Chementi, D.E., General problem of elastic wave propagation in multilayered anisotropic media, J. acoust. soc. am., 89, 1521-1531, (1991)
[17] Nayfeh, A.H.; Chementi, D.E., Free wave propagation in plates of general anisotropic media, J. appl. mech., 56, 881-886, (1989) · Zbl 0724.73053
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