Study of Phase Lags and Memory Effect in Hyperbolic Two Temperature Thermoelastic Circular Plate with Temperature-Dependent Material Properties Using Eigenvalue Approach

This work examines the effects of memory and phase lags on an infinite elastic circular plate with finite width subjected to axisymmetric thermal and mechanical loadings, utilizing the hyperbolic two-temperature three-phase lag model of generalized thermoelasticity with temperature-dependent material properties. For the two-dimensional problem under consideration, governing equations are determined. At uniform temperature, the plate is first thought to be unstressed and unstrained. The governing equations are reduced to a non-dimensional form and simplified using potential functions. The combined Laplace and Hankel transforms are employed to simplify the problem into ordinary differential equations. The eigenvalue approach is utilized to address the problem, and the arbitrary constants in the solution are determined by applying the loading conditions on the boundary surfaces. In the Laplace and Hankel transform domain, the temperature fields and normal stress are calculated analytically in compact form. To obtain the field quantities in the original region, a numerical inversion technique is employed.