Journal of Applied Mathematics
Volume 2004 (2004), Issue 1, Pages 69-83
doi:10.1155/S1110757X04308041
On the flexural and extensional thermoelastic waves in orthotropic plates with two thermal relaxation times
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.
Abstract
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.