Reflection phenomena of thermoelastic plane waves on a rigid surface within a size-dependent elastic media

Abstract

The current investigation aims to comprehend the spread of time-harmonic thermoelastic plane waves in an isotropic and homogeneous nonlocal elastic material without bounds, within the framework of the Lord–Shulman model and Eringen’s nonlocal stress model. Our analysis reveals two sets of coupled longitudinal waves and one independent shear-type wave. The coupled longitudinal waves experience dispersion and damping over time due to the dissipative nature of the L-S model. In contrast, the vertically shear-type waves exhibit dispersion characteristics due to the presence of nonlocality in the medium. Furthermore, we observe that the shear-type wave encounters a critical frequency, while the coupled longitudinal waves may face critical frequency conditions under certain circumstances. We explore the reflection of thermoelastic waves at a rigid, thermally insulated, and isothermal boundary of a thermoelastic half-space, particularly in the case of an incident coupled longitudinal thermoelastic wave. We determine the amplitude ratios of the reflected waves to the incident wave through analytical methods. For a specific model, we generate various graphs to analyze the behavior of phase speeds, attenuation coefficients, and reflection coefficients. To assess the impact of the elastic nonlocal parameter on the variations of phase speeds, attenuation coefficients, and amplitude ratios of the reflected waves, we present graphical representations. Notably, our observations indicate that all waves are influenced by the nonlocality of the medium. Longitudinal waves exhibit sensitivity to thermal parameters, whereas the shear-type wave remains independent of thermal effects. Furthermore, the presence of elastic nonlocality results in a reduction in the classical shear-type wave speed.