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Generalized Coupled Thermoelasticity of a Layer

The generalized thermoelasticity based on the Lord-Shulman (LS), Green-Lindsay (GL), and Green-Naghdi (GN) theories admit the second sound effect. By introducing some parameters all these theories are combined and a unified set of equations is rendered. These equations are then solved for a layer of isotropic and homogeneous material to study the thermal and mechanical wave propagations. The disturbances are generated by a sudden application of temperature to the boundary. The non-dimensionalized form of the governing equations are solved utilizing the Laplace transform method in time domain. Closed form solutions are obtained for the layer in Laplace transform domain, and a numerical inverse Laplace transform method is used to obtain the temperature, displacement, and stress fields in the physical time domain. The thermo-mechanical wave propagations and reflections from the layer boundaries are investigated.