Thermoelastic interactions on thick granular plate with three-phase-lag model under axisymmetric temperature distribution

Abstract

The theory of thermoelasticity with three-phase-lag is used to study the phase lag effects on wave propagation in granular medium. A two-dimensional thick granular plate with axisymmetric temperature distribution is considered under the type III and three-phase-lag thermoelasticity. The plate’s lower and upper surfaces are assumed to be stress free and subjected to a thermal condition. The analytical solution of the different fields like temperature, displacement, stresses, rotation, and couple stresses is obtained by the Laplace together with the Hankel transform method. The characteristic features of the underlying theory are analyzed by the small-time approximation method with Boley’s theorem and by comparing these results with their counterparts in other generalized thermoelasticity theories (GN III and Lord Shulman theory). The numerical values are evaluated and displayed graphically in the middle plane for different models, and comparison is made.