An advanced boundary integral equation method for wave propagation analysis in a layered piezoelectric phononic crystal with a crack or an electrode

Abstract

The paper presents an extended and advanced boundary integral equation method (BIEM) for simulating the elastic wave excitation and propagation in a layered piezoelectric phononic crystal with a strip-like crack or electrode. The method is based on the integral representation in terms of the Fourier transform of the Green's matrix for the whole piezoelectric laminate. A novel algorithm for constructing the Green's matrix, which allows taking into account the periodicity of the structure, is proposed. The obtained boundary integral equations are solved numerically using the Bubnov-Galerkin method with Chebyshev polynomials of the first and the second kind for a crack and an electrode respectively. The present method is compared with the standard finite element method (FEM), and the efficiency and convergence of the present method are also demonstrated by several representative numerical examples. The main advantages of the present extended and advanced BIEM lie in its strong capability of simulating unbounded piezoelectric laminates with a large number of layers (periodically or non-periodically arranged) as well as its high accuracy and efficiency compared with the FEM. The latter allows us to apply the method for a comprehensive parametric analysis and for the complex cases of multiple cracks and/or electrodes as well as for periodic arrays of cracks and/or electrodes.