Nonlocal theory of propagation and reflection of plane waves in higher order thermo diffusive semiconducting medium

Abstract

Abstract The present article is related to propagation and reflection of elastic wave through a nonlocal generalized thermo-diffusive semiconducting elastic solid. The non-local theory is employed to study the wave behavior. Three phase lag model with higher order fractional order derivative is incorporated to discuss heat propagation through the medium, in addition with two phase lags diffusion equation. The Helmholz vector rule is applied to decompose the system into longitudinal and transverse components. The frequency dispersion relation indicates the presence of four coupled longitudinal and one un-coupled shear vertical wave. The speed of the waves is plotted against angular frequency for local and nonlocal medium. The cutoff frequency of the waves is also depicted graphically. The longitudinal P-wave is taken to be an incident wave at the free surface of the solid to compute the reflection coefficients. The influences of fractional order and nonlocal parameters on amplitude ratios are also studied. The effect of these parameters is found to be significant. The results are proved in the context of energy conservation. The results obtained from the current investigation are very useful for scientists working on problems of geophysics and various fields of mechanics.