A three-dimensional generalized shock plate problem with four thermoviscoelastic relaxations

Abstract

The three-dimensional generalized thermoviscoelastic shock plate problem is presented. Four thermoviscoelastic relaxations are used during this study, three of them are due to the generalized thermoelasticity models and the fourth is due to the viscosity parameter. The plate is thermally isolated at its bottom surface while its upper one is under a thermal shock. The transient thermal shock plate problem is presented according to a unified theory of generalized thermoelasticity. The classical coupled thermoelasticity model is used and two of its generalizations, namely Green–Lindsay and Lord–Shulman models, are also used. Normal mode analysis is adopted to get an analytical general solution of the present plate problem. The distributions of all variables are investigated along the plate directions. Different thermoelasticity theories are compared to present suitable conclusions. Some special findings are pointed out to show the effects of viscosity and other thermal relaxation parameters on thermoelastic interactions. Numerical results are plotted and tabulated to serve as benchmark results for future comparisons.