Modeling reflection of plane waves in bio-thermoplastic diffusion with initial stress and temperature dependence via the MGT equation

Abstract

This work explores how initial stresses, temperature-dependent material parameters, and impedance conditions affect the propagation and reflection of plane waves in a bio-thermoelastic diffusion half-space described by the Moore–Gibson–Thompson (MGT) heat conduction theory. The governing equations for a two-dimensional setting are nondimensionalized and reformulated using potential functions. By applying the reflection technique, it is shown that the medium supports four interacting longitudinal waves along with a single transverse mode, each traveling at different speeds. Expressions for the amplitude ratios of the reflected longitudinal (P), thermal (T), chemical potential (Pₒ), and shear vertical (SV) waves are obtained as functions of the incident angle under impedance boundary conditions. The effects of initial stress, thermal dependence of material properties, and impedance parameters on these amplitude ratios are illustrated through graphical results and interpreted in detail. Several limiting cases are also analyzed to verify the formulation. The findings contribute to a deeper understanding of wave behavior in bio-engineered materials, seismic environments, and broader thermoelastic wave propagation applications.