Reflection of plane waves from the stress-free isothermal and insulated boundaries of a nonlocal thermoelastic solid

Abstract

• Harmonic plane waves are studied in an infinite nonlocal thermoelastic solid of type II. • Two sets of coupled longitudinal waves and one shear type wave may travel in the medium. • All these waves are dispersive in nature and influenced by the elastic nonlocality. • Reflection of these waves from a stress-free isothermal or thermally insulated surface has been studied. • The reflection coefficients and energy ratios are determined analytically and presented graphically. The generalized thermoelasticity theory based upon the Green and Naghdi model II of thermoelasticity as well as the Eringen’s nonlocal elasticity model is used to study the propagation of harmonic plane waves in a nonlocal thermoelastic medium. We found two sets of coupled longitudinal waves which are dispersive in nature and associated with attenuation. In addition to the coupled waves, there also exists one independent vertically shear type wave which is dispersive but without any attenuation. All these waves are found to be influenced by the elastic nonlocality parameter. Furthermore, the shear type wave is found to to be associated with a critical frequency, while the coupled longitudinal waves may have critical frequencies under constraints. The problem of reflection of the thermoelastic waves at the stress-free insulated and isothermal boundary of a homogeneous, isotropic nonlocal thermoelastic half-space has also been investigated. The formulae for various reflection coefficients and their respective energy ratios are determined in various cases. For a particular material, the effects of the angular frequency and the elastic nonlocal parameter have been shown on the phase speeds and the attenuation coefficients of the propagating waves . The effect of the elastic nonlocality on the reflection coefficients as well as the energy ratios has been observed and depicted graphically. Finally, analysis of the various results has been interpreted.