Reflection–transmission coefficients of SH waves across thin-walled spring-membrane strain gradient interface

Abstract

The current investigation focuses on the reflection and refraction phenomena of SH waves as they encounter two distinct non-ideal interfaces positioned between two half-spaces. The initial interface consists of a spring layer positioned between two membranes, while the second interface is comprised of a thin membrane based on strain gradient principles. Notably, the investigation is done for two cases, namely, the Spring Membrane Strain Gradient (SMSG) and the Spring Membrane Surface Elasticity (SMSE). Analytical derivations have been performed for the reflection and transmission coefficients, as well as the phase shifts associated with both interfaces in the context of reflection and refraction phenomena. The case SMSE and SMSG have the potential to transition into alternative interface models when specific limits of the interface parameters are applied, which has been discussed in detail as particular cases. Moreover, to enhance the understanding of the diverse parameters, we have graphically represented the amplitude ratios and phase shifts mentioned above. When examining the behavior of reflection and refraction coefficients at different angles of incidence, the presence of one versus two interfaces introduces additional complexity. As the angle of incidence increases the interaction between the wave and the material interfaces changes. This complex interplay is crucial for designing materials and structures in applications like acoustic insulation, optical devices, and advanced engineering materials.