Analysis of phase-lag effects on wave propagation in a thick plate under axisymmetric temperature distribution

Abstract

The main objective of the present paper is to analyze the effects of phase lags on wave propagation in a two dimensional thick plate due to an axisymmetric temperature distribution. The problem is formulated by employing three recent theories of thermoelasticity in a unified way, namely thermoelasticity of type III (Green and Naghdi in J Therm Stress 15:253–264, 1992), thermoelasticity with dual phase lags (Tzou in ASME J Heat Transf 117:8–16, 1995) and thermoelasticity with three phase lags (Roychoudhuri in J Therm Stress 30:231–238, 2007). The lower and upper surfaces of the plate are assumed to be traction free and subjected to a given axisymmetric temperature distribution. A potential function approach together with the Laplace and Hankel transform method is employed to derive the solution in the transform domain. The Hankel inversion is performed analytically and the solution in the Laplace transform domain is obtained. Detailed analyses on wave propagation and discontinuities of different fields of the medium are presented by using a method due to Boley (Quart Appl Math 19:273–284, 1962). By employing a numerical method for the Laplace inversion the distributions of different fields like temperature, displacement and stresses in the middle plane of the plate have been computed and depicted graphically. Findings are analyzed along with the comparison with the corresponding results obtained in earlier works.