Mathematical modelling of rayleigh wave fields incorporating microstructural and resonator effects

Abstract

Applied mathematics plays a crucial role in investigating Rayleigh waves, a fundamental class of surface waves, by enabling analysis and modelling of their propagation in complex media. This necessitates the application of sophisticated mathematical frameworks, which mainly involves the rigorous study of wave propagation theory, the formulation of the problem using partial di!erential equations, and the application of diverse mathematical tools to derive the solution. Specifically, this research focuses on the mathematical modelling of Rayleigh wave generation, propagation and control, emphasizing the development and application of analytical, asymptotic and numerical techniques to solve complex mathematical problems arising from these geophysical phenomena. This approach allows for a purely mathematical investigation of wave behavior, together with a mechanical interpretation to some extent, and contributes to the advancement of mathematical methodologies applicable to a range of wave-based problems.