Guided thermoelastic waves in functionally graded plates with two relaxation times

Functionally graded material (FGM) is a promising heat insulation material. Wave propagation in FGM structures has received much attention for the purpose of non-destructive testing and evaluation. Few literatures dealt with the thermoelastic wave in FGM structures although the thermal effect would cause attenuations of elastic waves. In this paper, guided thermoelastic waves in FGM plates subjected to stress-free, isothermal boundary conditions are investigated in the context of the Green–Lindsay (GL) generalized thermoelastic theories (with two relaxation times). Coupled wave equations and heat conduction equation are solved by the Legendre polynomial approach. Dispersion curves for a pure elastic graded plate are calculated to make a comparison with the published data. For the thermoelastic graded plate, dispersion curves of thermal modes and elastic modes are illustrated simultaneously. Attenuation curves for graded plates with different relaxation times are compared. The influences of different material gradient shapes are discussed. Two homogeneous thermoelastic plates with different volume fractions are obtained to show their differences from graded plates. Finally, thermoelastic wave dispersion curves for a homogeneous plate and a graded plate are calculated in the context of the classical coupled thermoelastic theory (CT) to show its differences and similarities to the generalized theory.