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This article is aimed at studying the propagation of surface waves in a homogeneous, isotropic, thermally conducting elastic solid bordered with layers or half spaces of inviscid liquid in the context of generalized theories of thermoelasticity. After developing formal solutions, secular equations for the solid in closed form and isolated mathematical conditions for leaky Rayleigh waves, leaky Lamb waves, and nonleaky Lamb waves in completely separate terms are derived. The thin-plate wave results for leaky Lamb waves have also been derived. The amplitude ratios of displacement in liquid layers and half spaces are also obtained and computed analytically. The results have been deduced and compared with the relevant publications available in the literature at the appropriate stages of the work. Finally, the numerical solution is carried out for an aluminum-epoxy composite material solid (half space) or plate bordered with water layers of finite and infinite thickness. The dispersion curves, attenuation profiles, and amplitude ratio of displacement in liquid layers and half spaces for symmetric and antisymmetric thermoelastic leaky Lamb waves, leaky Rayleigh waves, and nonleaky Lamb waves are presented and illustrated graphically in order to illustrate and compare the theoretical results. The theory and numerical computations are found to be in close agreement.The study of the interaction of elastic waves with fluid-loaded solids has been recognized as a viable means for nondestructive evaluation of solid structures. The reflected acoustic field from a fluid-solid interface has a wealth of information, which, if exploited, reveals details of many characteristics of solid. These include its properties, the possible existence of internal defects, and also the quality of interface, to name a few. Specifically, the reflected field of a finite-width incident acoustic beam shows unusual behavior in that it is nonspecular, it displaces (shifts) along the interface, and it contains a trailing edge that attenuates away from the center of reflection. This behavior is widely known as the leaky wave phenomenon. These

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.

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