Rayleigh waves in isotropic strongly elliptic thermoelastic materials with microtemperatures

TL;DR

This paper investigates Rayleigh surface waves in isotropic thermoelastic materials with microtemperatures, using Green and Naghdi's entropy balance, deriving a secular equation, and numerically analyzing wave behavior.

Contribution

It introduces a detailed analysis of Rayleigh waves in microtemperature thermoelastic materials, deriving explicit secular equations and numerical solutions.

Findings

Rayleigh wave behavior depends on microtemperature effects

Explicit secular equations are obtained for special cases

Numerical solutions illustrate wave characteristics

Abstract

This paper is concerned with the linear theory of thermoelasticity with microtemperatures, based on the entropy balance proposed by Green and Naghdi, which permits the transmission of heat as thermal waves of finite speed. We analyze the behavior of Rayleigh waves in an unbounded isotropic homogeneous strongly elliptic thermoelastic material with microtemperatures. The related solution of the Rayleigh surface wave problem is expressed as a linear combination of the elements of the bases of the kernels of appropriate matrices. The secular equation is established and afterwards an explicit form is written when some coupling constitutive coefficients vanish. Then, we solve numerically the secular equation by mean of a grafical metod and by taking arbitrary data for strongly elliptic thermoelastic material.