On plane wave scattering at the piezothermoelastic half-space with impedance boundary condition

Abstract

Piezothermoelasticity and wave interaction studies hold immense significance in designing functional devices ranging from transducers to sensors for a variety of purposes like energy harvesting and structural health monitoring. These applications catalyze interest in this article which addresses the problem of reflection of plane wave at the boundary of piezothermoelastic half-space. Through this study, the effect of impedance parameter on amplitude and energy ratios of the reflected waves is studied. Four wave modes are indicated upon reflection and a linear system of equations is formed to obtain a closed-form expression for amplitude and energy ratios. These equations are solved by suitable mathematical tools leading to expression for amplitude ratios as a function of incidence angle. For a suitable piezothermoelastic medium, the ratios are plotted against incidence angle and the findings are compared for two well-known theories of thermoelasticity, namely, Lord–Shulman (LS theory) and Green–Lindsay (GL theory). The analytical outcomes suggest approximate values of impedance and incidence angle for preferred energy division between reflected waves. It is recognized that adding impedance increases the amplitude of the quasi-longitudinal (qP) wave and decreases that of the quasi-transverse wave, making it suitable for devices that require a more robust qP wave signal detection.