Reflection phenomena of waves in a rotating micro-stretch medium with temperature-dependent elastic properties in the Context of Green–Naghdi theory

Abstract

In this study, we emphasize on the reflection of elastic waves through a homogenous micro-stretch thermoelastic medium. Material and elastic properties of the medium are considered to be temperature-dependent. The medium selected is rotating about an axis with some fixed angular frequency. Initially, the governing equations are formulated with the help of generalized thermoelastic theory. Heat conduction through the medium is encountered by the model proposed by Green and Naghdi. Governing equations are decomposed into longitudinal and transverse components with the help of Helmholtz decomposition principle. Harmonic representation of wave is used to find the solution to the problem. On the basis of solution, it is concluded that after reflection five quasi-waves propagate through the medium. The quasi term basically represents that the polarization vector of particles is not purely perpendicular or parallel to the propagation vector. The rotational frequency of the medium is responsible for this special nature of waves. Some particular cases are also deduced from the present investigation. The amplitude ratios of reflected waves against incident wave are obtained analytically for general medium and represented graphically for a particular medium.