Inhomogeneous wave reflection from the surface of a partially saturated thermoelastic porous media

Abstract

Purpose The purpose of this paper is to study the propagation of inhomogeneous waves in a partially saturated poro-thermoelastic media through the examples of the free surface of such media.. Design/methodology/approach The mathematical model evolved by Zhou et al. (2019) is solved through the Helmholtz decomposition theorem. The propagation velocities of bulk waves in partially saturated poro-thermoelastic media are derived by using the potential functions. The phase velocities and attenuation coefficients are expressed in terms of inhomogeneity angle. Reflection characteristics (phase shift, loci of vertical slowness, amplitude, energy) of elastic waves are investigated at the stress-free thermally insulated boundary of a considered medium. The boundary can be permeable or impermeable. The incident wave is portrayed with both attenuation and propagation directions (i.e. inhomogeneous wave). Numerical computations are executed by using MATLAB. Findings In this medium, the permanence of five inhomogeneous waves is found. Incidence of the inhomogeneous wave at the thermally insulated stress-free surface results in five reflected inhomogeneous waves in a partially saturated poro-thermoelastic media. The reflection coefficients and splitting of incident energy are obtained as a function of propagation direction, inhomogeneity angle, wave frequency and numerous thermophysical features of the partially saturated poro-thermoelastic media. The energy of distinct waves (incident wave, reflected waves) accompanying interference energies between distinct pairs of waves have been exhibited in the form of an energy matrix. Originality/value The sensitivity of propagation characteristics (velocity, attenuation, phase shift, loci of vertical slowness, energy) to numerous aspects of the physical model is analyzed graphically through a particular numerical example. The balance of energy is substantiated by virtue of the interaction energies at the thermally insulated stress-free surface (opened/sealed pores) of unsaturated poro-thermoelastic media through the bulk waves energy shares and interaction energy.

Wave propagation at the welded interface of an elastic solid and unsaturated poro-thermoelastic solid

“…The velocities and attenuations of inhomogeneous P1,P2,P3,Tp and SV waves were presented in Figure 2 of Kumar et al (2021a). In Figure 1, we will be analyzing the impact of thermal expansion coefficient β T with incident direction ( θ 0 ) on the partitioning of incident energy among distinct reflected and refracted waves.…”

“…In the scarcity of heat source and body force, the wave equations in spans of displacement vectors boldul, boldus, boldug and temperature T of unsaturated poro-thermoelastic media are given as follows [Kumar et al (2021a)]. …”

“…As a result, all of the waves are attenuating and dispersing. The corresponding compressional wave potentials are coupled, and different couplings coefficients are given in Kumar et al (2021a).…”

“…Expressions of the general components of the k –phase displacement in the x - and z -directions in an unsaturated thermoplastic medium are given by Kumar et al (2021a): where, …”

“…They used a generalized non-Fourier heat conduction law with two relaxation times, resulting in implicit temperature field extrapolations during the computation. Most recently, Kumar et al (2021aKumar et al ( , 2021b investigated the propagation attributes of inhomogeneous waves at the surface of unsaturated poro-thermoelastic solid. They used the formalism conceived by Zhou et al (2019) to reach that goal.…”