Purpose This paper aims to study the variation of energy ratios of different reflected and transmitted waves by calculating the amplitude ratios. Design/methodology/approach 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). Findings 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. Research limitations/implications 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. Practical implications 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. Social implications 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. Originality/value The submitted manuscript is original work done by the team of said authors and each author contributed equally to preparing this manuscript.
Purpose This paper aims to study the energy ratios of plane waves on an interface of nonlocal thermoelastic halfspace (NTS) and nonlocal orthotropic piezothermoelastic half-space (NOPS). Design/methodology/approach The memory-dependent derivatives (MDDs) approach with a hyperbolic two-temperature (HTT), three-phase lag theory is used here to study how the energy ratios change at the interface with the angle of incidence. Findings Plane waves that travel through NTS and hit the interface as a longitudinal wave, a thermal wave, or a transversal wave send four waves into the NOPS medium and three waves back into the NTS medium. The amplitude ratios of the different waves that are reflected and transmitted are used to calculate the energy ratios of the waves. It is observed that these ratios are affected by the HTT, nonlocal and MDD parameters. Research limitations/implications The energy ratios correspond to four distinct models; nonlocal HTT with memory, nonlocal HTT without memory, local HTT with memory and nonlocal classical-two-temperature with memory concerning the angle of incidence from 0 degree to 90 degree. Practical implications This model applies to several fields, including earthquake engineering, soil dynamics, high-energy particle physics, nuclear fusion, aeronautics and other fields where nonlocality, MDD and conductive temperature play an important role. Originality/value The authors produced the submitted document entirely on their initiative, with equal contributions from all of them.
Phenomena of reflection and refraction of plane harmonic waves at a plane interface between an elastic solid and doubleporosity dual-permeability material are investigated. The elastic solid behaves non-dissipatively, while double-porosity dual-permeability materials behave dissipatively to wave propagation due to the presence of viscosity in pore fluids. All the waves (i.e., incident and reflected) in an elastic medium are considered as homogeneous (i.e., having the same directions of propagation and attenuation), while all the refracted waves in double-porosity dual-permeability materials are inhomogeneous (i.e., having different directions of propagation and attenuation). The coefficients of reflection and refraction for a given incident wave are obtained as a non-singular system of linear equations. The energy shares of reflected and refracted waves are obtained in the form of an energy matrix. A numerical example is considered to calculate the partition of incident energy among various reflected and refracted waves. The effect of incident direction on the partition of the incident energy is analyzed with a change in wave frequency, wave-induced fluid-flow, pore-fluid viscosity and double-porosity structure. It has been confirmed from numerical interpretation that during the reflection/refraction process, conservation of incident energy is obtained at each angle of incidence.
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