Analysis of SH Wave Reflection and Refraction at a Viscoelastic Membrane Interface

This study investigates the behavior of shear-horizontal (SH) waves in viscoelastic substrates, with a particular focus on wave reflection and refraction phenomena. The interaction between SH waves and common interfaces of viscoelastic media reveals complex dynamics, largely due to the inherent ability of viscoelastic materials to absorb some of the wave energy. Mathematical formulations and graphical illustrations are employed to show how viscoelastic properties influence the amplitude and phase angles of both reflected and refracted waves. The study also introduces a strain-gradient membrane into the mathematical model, which significantly affects wave behavior by modifying amplitudes, phase angles, and energy transmission. This inclusion of strain-gradient membranes at the interface of viscoelastic media offers new insights into wave-membrane interactions. Numerical results indicate considerable variation in reflection coefficients and phase shifts due to the presence of strain-gradient membranes, highlighting their potential for use in wave-filtering and vibration-damping technologies. Overall, the research contributes to a deeper understanding of wave propagation phenomena in complex media, with potential applications in material science and engineering fields where wave interactions with viscoelastic interfaces are critical.