Plane wave reflection in micropolar hygro-thermoelastic half-space

Abstract

The research problem aims to investigate the effect of heat and moisture on the propagation of plane waves in a micropolar hygro-thermoelastic medium. The governing equations of a hygro-thermoelastic micropolar medium are developed and solved to determine the velocity equation. The plane-wave solution reveals that the medium is propagated by two coupled transverse displacement waves, namely Coupled Transverse Micropolar wave (CTM-wave) and Coupled Transverse Displacement wave (CTD-wave). Additionally, three coupled longitudinal waves are observed: thermal diffusion TD-wave, longitudinal displacement P-wave, and moisture diffusion mD-wave. To assess the characteristics of these waves in the micropolar hygrothermal medium, the speed and distance of propagation are calculated for each wave type. This analysis provides information on how fast and how far the P-wave, TD-wave, mD-wave, CTM-wave, and CTD-wave can travel in the medium. Furthermore, the research problem determines the equations for the coefficient of reflection and energy ratio when a coupled plane wave is incident on the medium. These coefficients quantify the amount of reflected energy compared to the incident energy and provide insights into the wave behavior at the interface of the medium. Finally, the variations in energy ratio and reflection coefficient are depicted graphically, allowing for a visual representation of how these quantities change with different parameters or conditions. These graphs provide a comprehensive understanding of the wave behavior and the effects of heat and moisture on the propagation characteristics in the micropolar hygrothermal medium.