Analysis of Reflection and Transmission of Inhomogeneous Waves at the Interface Between Two Transversely Isotropic Thermoelastic Diffusive Half‐Spaces

ABSTRACT

This paper investigates the reflection and transmission of inhomogeneous plane waves at a planar interface separating two transversely isotropic thermoelastic diffusive half‐spaces. The mixed specification of the complex slowness vector is employed to describe the incident inhomogeneous wave, while the component specification is used for reflected and transmitted waves. The governing field equations are solved to obtain the characteristic equation, which yields four complex wave modes: quasi‐elastodiffusive, quasi‐mass diffusive, quasi‐thermodiffusive and quasi‐transverse. Closed‐form expressions for the amplitude and energy reflection/transmission coefficients are derived, including the necessary interference contributions to ensure energy conservation. Numerical simulations were performed using copper‐like material parameters. Key findings include a frequency threshold ( Hz) below which homogeneous waves cannot propagate; propagation angles are significantly smaller than the corresponding attenuation angles for all reflected/transmitted waves; the sum of all energy ratios (including interference terms) equals unity, confirming energy conservation. The present results provide new physical insights into inhomogeneous wave propagation in dissipative anisotropic media and may serve as benchmarks for experimental validation in geophysical exploration and non‐destructive testing.