Application of Asymptotic Method to Study Flexural Wave Motion in Transversely Isotropic Thermoelastic Media

Flexural wave motion in an infinite transversely isotropic, thermoelastic plate in the context of conventional coupled thermoelasticity (CT), Lord-Shulman (LS) and Green-Lindsay (GL) theories of generalized thermoelasticity has been studied by asymptotic method. The asymptotic operator plate model for flexural motion in a transversely isotropic thermoelastic plate leads to fifth degree polynomial secular equation that governs frequency and phase velocity of various possible modes of wave propagation at all wavelengths. The governing secular equation of the frequency, expression of group velocity and asymptotic differential equation of flexural wave motion are also derived. The special cases, such as the approximations for short and long wavelength waves of the secular equation are also discussed. The numerical results in respect of phase velocity and attenuation coefficients have been obtained when wave inclined at 0 75 with the axis of symmetry and presented graphically for CT theory. The deviations of these quantities in LS and GL models vis-à-vis CT model has also been presented in graphically for first two wave modes of considered motion for comparison purpose.