Rayleigh waves in thermoelasticity: Triple porous media in local thermal non-equilibrium

Abstract

Assuming the hypothesis of local thermal non-equilibrium, this work investigates the propagation of Rayleigh surface waves in a thermoelastic half-space, isotropic, homogeneous and structured with a triple level of porosity. Its surface is supposed to be stress-free, thermally insulated and characterized by null pressure boundary conditions. A class of wave solutions is highlighted for the differential system of the model, each solution satisfying suitable asymptotic conditions in the depth of the considered half-space. Then, the Rayleigh wave solution is sought as a linear combination of the elements of this class, and, moreover, by means of the selected boundary conditions, the associated secular equation is found. By solving the secular equation, the characteristics of the wave solution are determined: the propagation speed as well as the damping in time. With the purpose of clearly highlighting the characteristics of the model, the secular equation is solved numerically and significant graphical representations are provided, using the software packages Mathematica and MATLAB. This suggests an increase of the Rayleigh wave propagation speed, corroborated with the appearance of the damping in time of its amplitude.

Theory of elastic wave propagation in a fluid-saturated multi-porous medium with multi-permeability

“…The theories of double and triple porosity, as well as the concepts of uniqueness and stability, have been extensively explored and discussed by Straughan [66,67]. Arusoaie & Chirita [68] have investigated compressional wave behaviour in triple-porosity media, while Zampoli & Chirita [69] have examined Rayleigh waves in a triple thermo-poroelastic medium. In continuation to the previous development in single, double and triple porosity, one can extend the concept of multi-porosity for a better understanding of porous media by considering a greater number of distinct pore structures.…”