Propagation and reflection of thermoelastic waves in the framework of nonlocal elasticity and dual-phase-lag heat conduction: Modeling and investigation

Abstract

Small-scale effects become important at short-wavelength regions of wave propagation. When the wavelength is on the same order as the small-scale parameter, its effects become significant, leading to deviations from classical behavior of elastic solids. The wave characteristics are noticeably influenced by the nonlocal interactions in this situation. This study presents a theoretical framework based on the generalized thermoelasticity theory with dual-phase-lag (DPL) heat conduction, incorporating Eringen’s nonlocal elasticity theory to investigate the propagation and reflection of thermoelastic plane waves in a linear, homogeneous, isotropic, heat-conducting elastic medium. The governing equations are solved to show the existence of three plane waves, namely, two coupled P- and (thermal) T-waves along with an uncoupled vertically shear (SV-) wave. Unlike the classical SV-wave, this SV-wave is both weakly dispersive and suffer attenuation due to the presence of the small-scale (nonlocal) effect but remain unaffected by the thermal field like the classical case. Moreover, it is noteworthy that the SV-wave propagates at a slower speed compared to the classical shear wave speed. On the other hand, the coupled P- and T-waves are dispersive and experience attenuation over space. The reflection problems of the incident P- and SV-waves from a rigidly fixed thermally insulated or isothermal surface are presented in detail to obtain the amplitude ratios of the reflected waves in closed form and the corresponding energy ratios. An analytical and visual investigation is carried out on the wave characteristics of propagating plane waves, considering the effects of angular frequency, small-scale parameter (nonlocal) thermal boundaries, and incident wave properties. Finally, energy conservation within the studied medium is verified, and some validations with existing literature are noted. This work presents the unified nonlocal–dual-phase-lag thermoelastic model and the first reflection analysis under this formulation, leading to new dispersion, attenuation, and mode-conversion behaviors absent in earlier studies.