Classifications of surface waves in magneto-electro-elastic materials

Abstract

The present study investigates the classifications of surface waves in magneto-electro-elastic materials. First, the standard eigenrelation, relating to the generalized displacement and the generalized tractions, is derived from the governing equations and constitutive relations. The number of distinct eigenvalues and the number of independent eigenvectors of the matrix N(v), which appears in the standard eigenrelation, play a crucial role in determining the surface wave solutions. However, this issue is often overlooked by most researchers. Therefore, our focus in this paper is to address this oversight by providing expressions for the solutions in various scenarios, considering the number of distinct eigenvalues and independent eigenvectors of the matrix N(v). Subsequently, we classify the surface waves in magneto-electro-elastic materials based on the aforementioned eigenvalue and eigenvector quantities of the 10 × 10 real matrix N(v). By considering the simple and semisimple properties, as well as the ten types of degenerate cases of the real matrix N(v), we identify a total of fifteen distinct types of surface waves within this classification.