Journal of Applied Mathematics
Volume 2004 (2004), Issue 1, Pages 69-83

On the flexural and extensional thermoelastic waves in orthotropic plates with two thermal relaxation times

K. L. Verma1 and Norio Hasebe2

1Department of Mathematics, Government Post Graduate College, Pradesh 177005, Hamirpur, India
2Department of Civil Engineering, Nagoya Institute of Technology, Gokio-Cho, Showa-Ku, Nagoya 466, Japan

Received 12 August 2003

Copyright © 2004 K. L. Verma and Norio Hasebe. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Analysis for the propagation of plane harmonic thermoelastic waves in an infinite homogeneous orthotropic plate of finite thickness in the generalized theory of thermoelasticity with two thermal relaxation times is studied. The frequency equations corresponding to the extensional (symmetric) and flexural (antisymmetric) thermoelastic modes of vibration are obtained and discussed. Special cases of the frequency equations are also discussed. Numerical solution of the frequency equations for orthotropic plate is carried out, and the dispersion curves for the first six modes are presented for a representative orthotropic plate. The three motions, namely, longitudinal, transverse, and thermal, of the medium are found dispersive and coupled with each other due to the thermal and anisotropic effects. The phase velocity of the waves gets modified due to the thermal and anisotropic effects and is also influenced by the thermal relaxation time. Relevant results of previous investigations are deduced as special cases.