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The purpose of this paper is to investigate propagation characteristics of seismic waves at the welded interface of an elastic solid and unsaturated poro-thermoelastic solid.

A theoretical formulation of partially saturated poro-thermoelastic solid is used in this study established by Zhou et al. (2019). The incidence of two primary waves (P and SV) is taken. The incident wave from the elastic solid induces two reflected waves and five refracted waves. Due to viscous pore fluids, partially saturated poro-thermoelastic solid behave dissipative, whereas elastic solid behaves non-dissipative. As a result, both reflected and incident waves are homogeneous. However, all the refracted waves are inhomogeneous. A non-singular system of linear equations is formed by the coefficients of reflection and refraction for a specified incident wave. The energy shares of various reflected and refracted waves are determined by using these reflection and refraction factors. Finally, a sensitivity analysis is performed, and the effect of critical variables on energy partitioning at the interface is observed. The numerical example shows that throughout the process of reflection/refraction, the energy of incidence is conserved at all angles of incidences.

This study demonstrated two refracted (homogeneous) and five refracted (inhomogeneous) waves due to the incident wave from elastic solid. The reflection and refraction coefficients and partitioning of incident energy are acquired as a part of diverse physical parameters of the partially saturated poro-thermoelastic media. The interference energies between unlike pairs of refracted waves have been discovered due to the dissipative behavior of unsaturated poro-thermoelastic solid.

The sensitivity of different energy shares to various aspects of the considered model is graphically analyzed for a specific numerical model. The energy balance is maintained by combining interaction energy and bulk wave energy shares.

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..

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.

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.

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.

This paper aims to study the variation of energy ratios of different reflected and transmitted waves by calculating the amplitude ratios.

This investigation studied the reflection and transmission of plane waves on an interface of nonlocal orthotropic piezothermoelastic space (NOPHS) and fluid half-space (FHS) in reference to dual-phase-lag theory under three different temperature models, namely, without-two-temperature, classical-two-temperature, and hyperbolic-two-temperature with memory-dependent derivatives (MDDs).

The primary (P) plane waves propagate through FHS and strike at the interface x₃ = 0. The results are one wave reflected in FHS and four waves transmitted in NOPHS. It is noticed that these ratios are observed under the impact of nonlocal, dual-phase-lag (DPL), two-temperature and memory-dependent parameters and are displayed graphically. Some particular cases are also deduced, and the law of conservation of energy across the interface is justified.

According to the available literature, there is no substantial research on the considered model incorporating NOPHS and FHS with hyperbolic two-temperature, DPL and memory.

The current model may be used in various fields, including earthquake engineering, nuclear reactors, high particle accelerators, aeronautics, soil dynamics and so on, where MDDs and conductive temperature play a significant role. Wave propagation in a fluid-piezothermoelastic media with different characteristics such as initial stress, magnetic field, porosity, temperature, etc., provides crucial information about the presence of new and modified waves, which is helpful in a variety of technical and geophysical situations. Experimental seismologists, new material designers and researchers may find this model valuable in revising earthquake estimates.

The researchers may classify the material using the two-temperature parameter and the time-delay operator, where the parameter is a new indication of its capacity to transmit heat in interaction with various materials.

The submitted manuscript is original work done by the team of said authors and each author contributed equally to preparing this manuscript.

The purpose of the present paper is to investigate the thermo-mechanical interactions in an initially stressed nonlocal micropolar thermoelastic half-space having void pores under Lord–Shulman model. A moving thermal shock is applied to the formulation.

The normal mode technique is adopted to obtain the exact expressions of the physical quantities.

Numerical computations for stresses, displacement components, temperature field and change in the volume fraction field are performed for suitable material and are depicted graphically. Some comparisons have been shown in figures to estimate the effects of micropolarity, initial stress, voids, nonlocal parameter and time on the resulting quantities.

The exact expressions for the displacement components, stresses, temperature and change in the volume fraction field are obtained in the physical domain. Although numerous investigations do exist to observe the disturbances in a homogeneous, isotropic, initially stressed, micropolar thermoelastic half-space, the work in its current form has not been established by any scholar till now. The originality of the present work lies in the formulation of a fresh research problem to investigate the dependence of different physical fields on nonlocality parameters, micropolarity, initial stress, porosity and time due to the application of a moving thermal shock.

The purpose of this study is to investigate the reflection of plane waves in a double-porosity (DP) thermoelastic medium.

To derive the theoretical formulas for elastic wave propagation velocities through the potential decomposition of wave-governing equations. The boundary conditions have been designed to incorporate the unique characteristics of the surface pores, whether they are open or sealed. This approach provides a more accurate and realistic mathematical interpretation of the situation that would be encountered in the field. The reflection coefficients are obtained through a linear system of equations, which is solved using the Gauss elimination method.

The solutions obtained from the governing equations reveal the presence of five inhomogeneous plane waves, consisting of four coupled longitudinal waves and a single transverse wave. The energy ratios of reflected waves are determined for both open and sealed pores on the stress-free, the thermally insulated surface of DP thermoelastic medium. In addition, the energy ratios are compared for the cases of a DP medium and a DP thermoelastic medium.

A numerical example is considered to investigate the effect of fluid type in inclusions, temperature and inhomogeneity on phase velocities and attenuation coefficients as a function of frequency. Finally, a sensitivity analysis is performed graphically to observe the effect of the various parameters on propagation characteristics, such as propagation/attenuation directions, phase shifts and energy ratios as a function of incident direction in double-porosity thermoelasticity medium.

The purpose of this study is to analyze the thermo-diffusion process in a semi-infinite nonlocal fiber-reinforced double porous thermoelastic diffusive material with voids (FRDPTDMWV) in light of the fractional-order Lord–Shulman thermo-elasto-diffusion (LSTED) model. By virtue of Eringen’s nonlocal elasticity theory, the governing equations for the considered material are developed. The free surface of the substrate is governed by the inclined mechanical load and thermal and chemical shocks.

With the aid of the normal mode technique, the solutions of the nondimensional coupled governing equations have been obtained.

The expressions of field variables are obtained analytically. By using MATHEMATICA software, various graphical implementations are presented to describe the impacts of angle of inclination, fractional-order and nonlocality parameters. The present model is also validated on the basis of some comparative studies with some preestablished cases.

As observed from the literature survey, many different studies have been carried out by taking into account the deformation analysis in nonlocal double porous thermoelastic material structures and thermo-mechanical interaction in fiber-reinforced medium under fractional-order thermoelasticity theories. However, to the best of the authors’ knowledge, no research emphasizing the thermo-elasto-diffusive interactions in a nonlocal FRDPTDMWV has been carried out. Moreover, the effect of fractional-order LSTED theory on fiber-reinforced thermoelastic diffusive half-space with double porosity has not been illuminated till now, which significantly defines the novelty of the conducted research.

This paper aims to study photothermal excitation process in an initially stressed semi-infinite double porous thermoelastic semiconductor with voids subjected to Eringen’s nonlocal elasticity theory under the fractional order triple-phase-lag thermoelasticity theory. The considered substrate is governed by the mechanical and thermal loads at the free surface.

The normal mode technique is used to carry out the investigation of photothermal transportation. By virtue of the MATHEMATICA software, each distribution is exhibited graphically.

The expressions of the displacements, temperature, volume fractions of both kinds of voids, carrier density and stresses are determined analytically. With the help of the numerical data for silicon (Si) material, graphical implementations are presented on the basis of initial stress, fractional order, nonlocality and thermoelectric coupling parameters.

The present study fabricates the association of Eringen’s nonlocal theory and the stress analysis in a semiconducting double porous thermoelastic material with voids, which significantly implies the originality of the conducted work.

The purpose of this paper is to study the wave propagation in a porous medium through the porothermoelastic process using the finite element method (FEM).

One-dimensional (1D) application for a poroelastic half-space is considered. Due to the complex governing equation, the finite element approach has been adopted to solve these problems.

The effect of porosity and thermal relaxation times in a porothermoelastic material was investigated.

The numerical results for stresses, displacements and temperatures for the solid and the fluid are represented graphically. This work will enable future investigators to have the insight of nonsimple porothermoelasticity with different phases in detail.