Nonlocal analysis of Rayleigh wave with double porosity and dual-phase-lag model

<p>The purpose of this article is to develop the propagation of Rayleigh waves in a nonlocal thermoelastic isotropic material with double porosity whose surface is subjected to stress free, thermally insulated/isothermal boundary conditions. Linear theory of nonlocal thermoelastic material with double porosity structure is developed within the context of Eringen’s theory of nonlocal thermoelasticity. Dual-phase-lag (DPL) model and LordShulman (LS) model of hyperbolic thermoelasticity is developed in the context of nonlocal and double porosity. Energy density function is constructed from the basic variables, and then, constitutive relations are derived, which are used to develop the field equations for an isotropic homogeneous nonlocal thermoelastic material with double porosity. The vector matrix differential equation is obtained by applying the normal mode analysis to the considered equations. Some special cases are also derived from this study which are also compared with the existing results of the various researchers. The effects of voids and nonlocality on different characteristics of Rayleigh waves are presented graphically. This theory seems to be an adequate tool to describe the behaviour of granular materials like rock, soils and manufactured porous bodies. Numerical results for the different characteristics of Rayleigh waves like propagation speed, attenuation coefficient, specific loss and penetration depth are computed numerically. The computer simulated results for copper materials in respect of determinant of Rayleigh wave secular equation, Rayleigh wave velocity, attenuation coefficient, specific loss and propagation speed have been presented graphically.</p>