Wave propagation in transversely isotropic plates in generalized thermoelasticity K. L. Verma, N. Hasebe Summary In this paper, the boundary value problem in generalized thermoelasticity con- cerning the propagation of plane harmonic waves in a thin, flat, infinite homogeneous, transversely isotropic plate of finite width is solved. The frequency equations corresponding to the symmetric and antisymmetric modes of vibration of the plate are obtained. The limiting and special cases of the frequency equations have also been discussed. Finally, a numerical solution of the frequency equations for a NaF crystal is carried out, and the dispersion curves for the lowest six modes of the symmetric and antisymmetric vibrations are represented graphically at different values of thermal relaxation time. Keywords Thermoelasticity, Frequency equation, NaF crystal, Thermal relaxation time, Vibration, Harmonic wave 1 Introduction The dynamical theory of generalized thermoelasticity proposed in [1] has aroused much in- terest in recent years. This theory is the generalization of the classical coupled thermoelasticity, [2], which includes the time needed for acceleration of the heat flow. The new theory, which has been named the ‘Generalized Theory of Thermoelasticity’ and received much attention, [2–6], eliminates the paradox of an infinite velocity of propagation and admits finite speed for the propagation of thermoelastic disturbances. Extensive theoretical efforts have been made so far to model thermoelastic waves in solids. The propagation of generalized thermoelastic waves in plates of isotropic media has con- sidered by [7–11]. In [12], the propagation of thermoelastic waves in infinite plates has studied in the context of generalized thermoelasticity and linear theory of thermoelasticity without energy dissipation. The generalized theory of thermoelasticity has been extended to heat conducting anisotropic elastic solids by [13, 14]. Propagation of plane harmonic waves in a homogeneous anisotropic generalized thermoelastic solid was discussed [15]. It was found that four dispersive wave modes are possible namely, three quasi-elastic wave modes (E) and one quasi-thermal wave mode (T), which in coupled thermoelasticity is diffusive but now becomes wave-like with the finite velocity of propagation. In [16], the propagation of thermoelastic waves was studied in bilaminated periodic waveguides in the context of the generalized theory of thermoelasticity. The same authors studied the propagation of harmonic waves in a laminated composite consisting of an arbitrary number of layered anisotropic plates, [17]. The present paper is a continuation of our previous work [12]. Its aim is to study in generalized thermoelasticity the propagation of plane harmonic waves in a thin, flat, infinite Archive of Applied Mechanics 72 (2002) 470 – 482 Ó Springer-Verlag 2002 DOI 10.1007/s00419-002-0215-z 470 Received 17 July 2000; accepted for publication 26 March 2002 K. L. Verma (&) Department of Mathematics, Government Post Graduate College, Hamirpur, (H.P.) 177005 India e-mail: klverma@netscape.net N. Hasebe Department of Civil Engineering, Nogoya Institute of Technology, Gokiso-Cho, Showa-Ku, Nagoya 466, Japan