Plane harmonic waves in a thermoelastic solid with double porosity

Abstract

Propagation of time harmonic plane waves in an infinite thermoelastic solid medium with double porosity is studied in this paper. It is found that there may exist five basic waves consisting of four sets of coupled longitudinal waves and an independent transverse wave traveling at different speeds. Each set of coupled longitudinal waves is found to be dispersive, attenuating and depends upon the presence of both types of voids and thermal properties in the medium. The lone transverse wave is found to be non-dispersive and non-attenuating, and does not depend on the presence of voids and thermal properties, and travels with the speed of the shear wave of classical elasticity. Two sets of the coupled longitudinal waves face critical frequencies, below which these waves do not propagate in the medium. These critical frequencies depend upon the presence of voids and thermal parameters of the medium. The reflection phenomenon of a set of incident coupled longitudinal wave from the stress-free and thermally insulated boundary surface of a half-space has been studied. For a particular model, the phase speeds, attenuation coefficients, amplitude ratios and energy ratios have been computed numerically, presented graphically and discussed.