Reflection of thermoelastic coupled plane waves under the MGL model

Abstract

The present study is concerned with the reflection phenomenon of thermoelastic plane waves at the thermally insulated stress-free surface of a homogeneous isotropic thermally conducting elastic half-space in the frame of modified Green-Lindasy (MGL) model of generalized thermoelasticity with strain rate. The thermoelastic coupling effect creates two types of coupled longitudinal waves which are dispersive in nature as well as exhibit attenuation. Different from the thermoelastic coupling effect, there also exist one independent vertically shear-type (SV-type) wave. In contrast to the classical Green-Lindsay (GL) and the Lord-Shulman (LS) theories of generalized thermoelasticity, the SV-type wave is not only dispersive in nature but also experiences attenuation. Analytical expressions for the amplitude ratios and their respective energy ratios for the reflected thermoelastic waves are determined when a coupled longitudinal wave is made incident on a surface. The paper concludes with the numerical results on the phase speeds, amplitude ratios and their respective energy ratios for specific parameter choices. Various graphs are plotted to analyzed the analytical solution. The characteristics of employing the MGL model are discussed by comparing the numerical results obtained for the MGL model with those obtained in case of the GL, LS and the coupled thermoelasticity (CTE) models.

Keywords:

• Attenuation
• dispersion
• energy partition
• generalized thermoelasticity
• plane waves
• reflection

Acknowledgments

The authors would like to thank the Editor and the anonymous referee for their suggestions and comments to improve the manuscript.

Disclosure statement

The author declare that they have no conflict of interest.

Funding

The author received no financial support for the research.