Wave propagation in context of Moore–Gibson–Thompson thermoelasticity with Klein–Gordon nonlocality

Abstract

Understanding plane and surface waves in elastic materials is crucial in various fields, including geophysics, seismology, and materials science, as they provide valuable information about the properties of the materials they travel through and can help in earthquake detection and analysis. In the present paper, the governing equations of Moore–Gibson–Thompson (MGT) thermoelasticity are modified in context of Klein–Gordon (KG) nonlocality. For linear, homogeneous and isotropic case, the governing equations in two-dimensions are solved to obtain the dispersion relations for possible plane waves. It is found that there exists one transverse and two coupled longitudinal waves in a two-dimensional model of MGT weakly nonlocal thermoelastic medium and the speeds of these plane waves are found to be dependent on KG nonlocal parameters. The coupled longitudinal waves are also found to be dependent on conductivity rate parameter. For linear, homogeneous and isotropic case, the governing equations in two-dimensions are also solved to obtain a Rayleigh wave secular equation at thermally insulated surface. For a numerical example of aluminium material, the speeds of transverse wave, coupled longitudinal waves and the Rayleigh wave are computed and graphically illustrated to visualize the effects of KG nonlocality parameters, conductivity rate parameter and the angular frequency on the wave speeds.