Reflection/transmission of plane waves at the interface of an ideal fluid and nonlocal piezothermoelastic medium

Abstract

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.

The effect of memory and stiffness on energy ratios at the interface of distinct media

“…is the memory-dependent derivative for delay time τ and a limiting case when time delay tends to zero, MDD becomes a common derivative and D τ → v vt in the absence of memory effect. In general, from the standpoint of applications, the kernel function κðt À ξÞ should satisfy the inequality 0 ≤ κðt À ξÞ < 1 for ξ ∈ ½t À τ; t. Following Gupta et al (2023), we can choose a suitable kernel function as Yu et al (2014) analyzed that when MDD is used in the heat conduction law, the heat transport equation is changed. As a result, the constitutive equations are also changed, as well as the new memory-dependent model, which might be better than fractional ones for many reasons: first, the new model has a unique shape, while different authors' fractional order theories have different pictures; and second, the physical meaning of the former is clearer when readers look at what MDD is all about.…”

“…In general, from the standpoint of applications, the kernel function κ(t-ξ) should satisfy the inequality 0≤κ(t-ξ)<1 for ξ∈[t-τ,t]. Following Gupta et al . (2023), we can choose a suitable kernel function as…”

Energy analysis at the interface of piezo/thermoelastic half spaces

“…The ability to freely choose the delay time factor, as well as the kernel function, which is outlined in equations (1.1) and (1.2), are the two most important advantages of this MDD model, making it flexible in applications. Following Gupta et al (2023), Ashida et al (1994), Dube et al (1996), Kumar and Chawla (2013a) and Kumar and Sarthi (2006), the cadmium selenide and magnesium material constants have been considered, as shown in Table 1.…”

“…Following Roy Choudhuri (2007), Eringen and Edelen (1972), Gupta et al (2023) and Kaur et al (2020b), the governing field equations for a nonlocal anisotropic piezothermoelastic medium in a HTT, three-phase lag with MDD and without considering heat source and body forces are: …”

“…Using the three-phase lag theory, Tiwari and Kumar (2021) discussed a thermoelastic problem in a piezoelastic medium with MDD. Gupta et al (2023) studied the impact of two-temperature and MDD on the interface of elastic/piezothermoealstic with dual-phase lag theory.…”