Wave propagation at the boundary surface of an elastic and thermoelastic diffusion media with fractional order derivative

Abstract

The purpose of this research is to study the reflection and refraction of obliquely incident plane wave at the interface of elastic and thermoelastic diffusion media with fractional order derivative. Lord–Shulman [1] theory of thermoelasticity using the methodology of fractional calculus is used to investigate the problem. It is noticed that three type of longitudinal waves and one transverse wave propagate in an isotropic thermoelastic diffusion medium. The amplitude and energy ratios of various reflected and refracted waves are obtained and it is found that these are the functions of incidence angle and frequency of that incident wave. The variation of modulus of amplitude ratios and energy ratios with the angle of incidence for different fractional orders are computed numerically using continuous boundary conditions for the copper material. The computed numerical results are depicted graphically for the variation of energy ratios with the angle of incidence. It has been verified that the sum of energy ratios is equal to unity at the interface. Some particular cases of interest are also deduced from the present investigation.