The present investigation is concerned with the study of extensional and transversal wave motions in an infinite homogenous transversely isotropic, thermoelastic plate by using asymptotic method in the context of coupled thermoelasticity, Lord and Shulman (1967, “The Generalized Dynamical Theory of Thermoelasticity,” J. Mech. Phys. Solids, 15, pp. 299–309), and Green and Lindsay (1972, “Thermoelasticity,” J. Elast., 2, pp. 1–7) theories of generalized thermoelasticity. The governing equations for extensional, transversal, and flexural motions have been derived from the system of three-dimensional dynamical equations of linear thermoelasticity. The asymptotic operator plate model for extensional motion in a homogeneous transversely isotropic thermoelastic plate leads to sixth degree polynomial secular equation that governs frequency and phase velocity of various possible modes of wave propagation at all wavelengths. It is shown that the purely transverse motion (SH mode), which is not affected by thermal variations, gets decoupled from rest of the motion. The Rayleigh–Lamb frequency equation for the plate is expanded in power series in order to obtain polynomial frequency equation and velocity dispersion relations. Their validation has been established with that of asymptotic method. The special cases of short and long wavelength waves are also discussed. The expressions for group velocity of extensional and transversal modes have been derived. Finally, the numerical solution is carried out for homogeneous transversely isotropic plate of single crystal of zinc material. The dispersion curves of phase velocity and attenuation coefficient are presented graphically.
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November 2011
Research Papers
Extensional and Transversal Wave Motion in Transversely Isotropic Thermoelastic Plates by Using Asymptotic Method
S. K. Rana
S. K. Rana
Department of Mathematics,
e-mail: sanjeevrananit@gmail.com
National Institute of Technology
, Hamirpur 177005, India
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S. K. Rana
Department of Mathematics,
National Institute of Technology
, Hamirpur 177005, India
e-mail: sanjeevrananit@gmail.com
J. Appl. Mech. Nov 2011, 78(6): 061022 (11 pages)
Published Online: September 30, 2011
Article history
Received:
April 1, 2010
Revised:
November 19, 2010
Accepted:
February 28, 2011
Online:
September 30, 2011
Published:
September 30, 2011
Citation
Sharma, J. N., Sharma, P. K., and Rana, S. K. (September 30, 2011). "Extensional and Transversal Wave Motion in Transversely Isotropic Thermoelastic Plates by Using Asymptotic Method." ASME. J. Appl. Mech. November 2011; 78(6): 061022. https://doi.org/10.1115/1.4003721
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