Reflection of plane waves in thermoelastic medium with double porosity

Abstract

Purpose The purpose of this paper is to study the reflection of plane waves in thermoelastic medium with double porosity structure. Design/methodology/approach A two-dimensional model is considered of an isotropic thermoelastic half-space with double porosity. Thermoelasticity with one relaxation time given by Lord and Shulman (1967) has been used to study the problem. It is found that there exists four coupled longitudinal waves, namely, longitudinal wave (P), longitudinal thermal wave (T), longitudinal volume fractional wave corresponding to pores (PVI) and longitudinal volume fractional wave corresponding to fissures (PVII), in addition to an uncoupled transverse wave (SV). Findings The formulae for amplitude ratios of various reflected waves are obtained in closed form. It is found that these amplitude ratios are functions of angle of incidence. Effect of porosity and thermal relaxation time is shown graphically on the amplitude ratios with angle of incidence for a particular model. Originality/value Reflection of plane waves is of great practical importance. There are many organic and inorganic deposits beneath the earth surface. Wave propagation is the simplest and most economical technique to detect these. The model discussed in the present paper can provide useful information for experimental researchers working in the field of geophysics and earthquake engineering, along with seismologist working in the field of mining tremors and drilling into the crust of the earth.

Lord–Shulman Thermoelasticity with Microtemperatures

“…On the other side, the study of elastic materials with voids was proposed by Cowin and Nunziato [9,10,35]. These materials has deserved big attention in the last forty years [4,12,13,24,25,28,29,33,34,36,37]. There are interesting physical applications of the thermoelasticity with voids, so we can recall the study of solids with small distributed porous, in particular we mention, for instance, rocks, soils, woods, ceramics or even biological materials as bones.…”

An a priori error analysis of a type III thermoelastic problem with two porosities

“…Even more, this approach has been also considered in alternative contexts as viscoelasticity [2,3,18,[20][21][22]33]. It is worth saying that in several recent contributions the authors provide explicit values for the constitutive parameters (see [1,[23][24][25][26]39]).…”

An a priori error analysis of a Lord–Shulman poro-thermoelastic problem with microtemperatures

“…Rocks, soils, woods, ceramics or biological materials as bones are examples where this theory can be applied. We can recall several contributions concerning this theory [27][28][29][30][31][32][33][34][35][36][37][38][39][40]20,[41][42][43].…”