Acta Mechanica Solida Sinica

, Volume 24, Issue 2, pp 135–143

# Guided thermoelastic wave propagation in layered plates without energy dissipation

Article

## Abstract

In this paper, the propagation of guided thermoelastic waves in laminated orthotropic plates subjected to stress-free, isothermal boundary conditions is investigated in the context of the Green-Naghdi (GN) generalized thermoelastic theory (without energy dissipation). The coupled wave equations and heat conduction equation are solved by the Legendre orthogonal polynomial series expansion approach. The validity of the method is confirmed through a comparison. The dispersion curves of thermal modes and elastic modes are illustrated simultaneously. Dispersion curves of the corresponding pure elastic plate are also shown to analyze the influence of the thermoelasticity on elastic modes. The displacement and temperature distributions are shown to discuss the differences between the elastic modes and thermal modes.

## Key words

guided thermoelastic waves without energy dissipation layered plates orthotropic materials Legendre polynomial dispersion curves

## References

1. [1]
Al-Qahtani, H. and Datta, S., Thermoelastic waves in an anisotropic infinite plate. Journal of Applied Physics, 2004, 96(7): 3645–3658.
2. [2]
Massalas, C.V., Thermoelastic waves in a thin plate. Acta Mechanica, 1986, 65(1–4): 51–61.
3. [3]
Daimaruya, M. and Naitoh, M., Dispersion and energy dissipation of thermoelastic waves in a plate. Journal of Sound and Vibration, 1987, 117(3): 511–518.
4. [4]
Massalas, C.V. and Kalpakidis, V.K., Thermoelastic waves in a waveguide. International Journal of Engineering Science, 1987, 25(15): 1207–1218.
5. [5]
Sharma, J.N., Singh, D. and Kumar, R., Generalized thermoelastic waves in homogeneous isotropic plates. The Journal of the Acoustical Society of America, 2000, 108(2): 848–851.
6. [6]
Verma, K.L. and Hasebe, N., Dispersion of thermoelastic waves in a plate with and without energy dissipation. International Journal of Thermophysics, 2001, 22(3): 957–978.
7. [7]
Verma, K.L. and Hasebe, N., Wave propagation in plates of general anisotropic media in generalized thermoelasticity. International Journal of Engineering Science, 2001, 39(15): 1739–1763.
8. [8]
Verma, K.L. and Hasebe, N., Wave propagation in transversely isotropic plates in generalized thermoelasticity. Archive of Applied Mechanics, 2002, 72(6–7): 470–482.
9. [9]
Rajneesh, K. and Tarun, K., Propagation of Lamb waves in transversely isotropic thermoelastic diffusive plate. International Journal of Solids and Structures, 2008, 45(22–23): 5890–5913.
10. [10]
Rajneesh, K. and Tarun, K., Rayleigh-Lamb waves in transversely isotropic thermoelastic diffusive layer. International Journal of Thermophysics, 2009, 30(2): 710–733.
11. [11]
Al-Qahtani, H., Extensional thermoelastic waves in transversely isotropic plate according to a higher order theory. Acta Mechanica, 2009, 208(1–2): 27–38.
12. [12]
Sharma, J.N. and Pathania, V., Generalized thermoelastic wave propagation in circumferential direction of transversely isotropic cylindrical curved plates. Journal of Sound and Vibration, 2005, 281(3–5): 1117–1131.
13. [13]
Yu, J.G., Wu, B. and He, C.F., Circumferential thermoelastic waves in orthotropic cylindrical curved plates without energy dissipation. Ultrasonics, 2010, 5(3): 416–423.Google Scholar
14. [14]
Yu, J.G. and Xue, T.L., Generalized thermoelastic waves in spherical curved plates without energy dissipation. Acta Mechanica, 2010, 212(1–2): 39–50.
15. [15]
Yu, J.G., Zhang, X.M. and Xue, T.L., Generalized thermoelastic waves in functionally graded plates without energy dissipation. Composite Structures, 2010, 93(1): 32–39.
16. [16]
Wang, Y.Z., Li, F.M., Kishimoto, K., Wang, Y.S. and Huang, W.H., Wave localization in randomly disordered layered three-component phononic crystals with thermal effects. Archive of Applied Mechanics, 2010, 80(6): 629–640.
17. [17]
Hawwa, M.A. and Nayfeh, A.H., The general problem of thermoelastic waves in anisotropic periodically laminated composites. Composites Engineering, 1995, 5(12): 1499–1517.
18. [18]
Hawwa, M.A. and Nayfeh, A.H., Thermoelastic waves in a laminated composite with a second sound effect. Journal of Applied Physics, 1996, 80(5): 2733–2738.
19. [19]
Verma, K.L., On the propagation of waves in layered anisotropic media in generalized thermoelasticity. International Journal of Engineering Science, 2002, 40(18): 2077–2096.
20. [20]
Lefebvre, J.E., Zhang, V., Gazalet, J. and Gryba, T., Legendre polynomial approach for modeling freeultrasonic waves in multilayered hollow cylinders. Journal of Applied Physcis, 1999, 85: 3419–3427.
21. [21]
Sharma, J.N. and Pathania, V., Generalized thermoelastic waves in anisotropic plates sandwiched between liquid layers. Journal of Sound and Vibration, 2004, 278(1–2): 383–411.