Polynomial eigenvalue solution for elastic wave prediction of piezoelectric shunting arrays

Abstract

This paper presents a polynomial eigenvalue solution to predict the propagation behaviors of elastic wave in piezoelectric shunting arrays. Based on the Bloch theorem, one independent unit cell is selected to conduct the dynamic characteristic analysis instead of infinity. The reduced form of the discretized governing equations is first derived by the standard finite element procedures. To facilitate the subsequent acquisition of dispersion relationship, the dynamic stiffness matrix is then partitioned into a block matrix. Through applying the periodic boundary conditions, a polynomial eigenvalue equation concerning complex propagation constant is finally obtained. The wave propagation and attenuation characteristics in arbitrary directions are investigated using the above methodology. The results demonstrate that the present method can provide very accurate and reliable solutions for wave propagation prediction of piezoelectric shunting arrays.