Asymptotic Analysis for the Generalized Thermoelastic Equations Near the Cut-off Frequencies in Heat Conducting Isotropic Plates

Abstract: Asymptotic analysis of the generalized thermoelasticity equations is carried out for zero surface traction and heat conducting isotropic plates in the vicinity of the cut-off frequencies. Thickness of shear resonance frequencies are also studied in the context of generalized thermoelasticity. The exact dispersion relations are also derived giving frequency as a function of wave number. On taking the thermal relaxation time zero, the obtained results in the analysis reduce to the conventional coupled theory of thermoelasticity. Similarly when the coupling constant is taken identically equal to zero, the strain and thermal fields are uncoupled from each other. In this case, the results can be obtained from the uncoupled theory of thermoelasticity.