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.
PurposeThis paper aims to study the energy ratios of plane waves on an imperfect interface of elastic half-space (EHS) and orthotropic piezothermoelastic half-space (OPHS).Design/methodology/approachThe dual-phase lag (DPL) theory with memory-dependent derivatives is employed to study the variation of energy ratios at the imperfect interface.FindingsA plane longitudinal wave (P) or transversal wave (SV) propagates through EHS and strikes at the interface. As a result, two waves are reflected, and four waves are transmitted, as shown in Figure 2. The amplitude ratios are determined by imperfect boundaries having normal stiffness and transverse stiffness. The variation of energy ratios is computed numerically for a particular model of graphite (EHS)/cadmium selenide (OPHS) and depicted graphically against the angle of incidence to consider the effect of stiffness parameters, memory and kernel functions.Research limitations/implicationsThe energy distribution of incident P or SV waves among various reflected and transmitted waves, as well as the interaction of waves for imperfect interface (IIF), normal stiffness interface (NSIF), transverse stiffness interface (TSIF), and welded contact interface (WCIF), are important factors to consider when studying seismic wave behavior.Practical implicationsThe present model may be used in various disciplines, such as high-energy particle physics, earthquake engineering, nuclear fusion, aeronautics, soil dynamics and other areas where memory-dependent derivative and phase delays are significant.Originality/valueIn a variety of technical and geophysical scenarios, wave propagation in an elastic/piezothermoelastic medium with varying magnetic fields, initial stress, temperature, porosity, etc., gives important information regarding the presence of new and modified waves.
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