Modal properties of elastic surface waves in the presence of material anisotropy and prestress

Abstract

Elastic surface waves have been widely applied across many disciplines such as crystallography, seismology, non-destructive evaluation (NDE) and microfluidics. Thorough understanding and accurate prediction of modal properties of surface waves is essential for successful practical applications. However, computations of surface waves could be challenging due to two frequently encountered complications: material anisotropy and acoustoelasticity induced by prestress. Although a lot of approaches, such as solving secular equations, matrix method and perturbation method, have been developed to deal with these complications, some of them may suffer from mathematically algebraic complexity, tedious numerical coding and limited applicability. A method, combining the semi-analytical finite element (SAFE) method and perfectly matched layers (PMLs), is proposed in this paper for computation of the modal properties of surface waves. As the governing equations of the model are formulated based on acoustoelasticity, the model can simulate surface waves in materials with anisotropic properties and prestress. The governing equations of the model are reorganized in a standard finite element eigenvalue formalism which can be implemented into a commercial software, enabling easy access of the method. Therefore, the method provides a powerful forward modelling to understand the response of surface waves to material anisotropy and prestress. The method is firstly validated by analytical solutions as well as perturbation solutions available in the literature and then applied to two challenging cases to demonstrate its capability.