Analysis of wave motion and deformation in elastic plate based on two temperature theory of thermoelasticity.

This article explores the effects of two temperatures on the combined problem of wave propagation and thermomechanical loading in a homogeneous isotropic plate. The governing equations are converted to non-dimensional form, and the potential functions are introduced to simplify the problem. The plate's surfaces are assumed to be traction-free, rigidly fixed, thermally insulated and isothermal to study the wave propagation phenomenon. Secular equations in closed form and isolated mathematical conditions for symmetric and skew-symmetric wave mode propagation are derived. The phase velocity and attenuation coefficient are examined for the first problem. The results for uncoupled, coupled, Lord-Shulman (LS) and Green-Lindsay (GL) theories of thermoelasticity have been attained as special cases and agree with that in literature for one temperature theory. In the second part, thermo-mechanical loading has been considered to obtain the expressions of stress and displacement components, conductive and thermodynamic temperatures. The obtained analytical results are computed numerically as well as displayed graphically for copper material to demonstrate the impacts of two temperature theory and compared theoretically as well as numerically with one temperature Lord and Shulman theory. [ABSTRACT FROM AUTHOR]