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.

本文提出了一种扩展的高级边界积分方程方法 (BIEM)，用于模拟具有条状裂纹或电极的层状压电声子晶体中的弹性波激发和传播。该方法基于整个压电层压板的格林矩阵傅里叶变换的积分表示。提出了一种用于构造格林矩阵的新算法，该算法允许考虑结构的周期性。使用Bubnov-Galerkin 方法对裂纹和电极的第一类和第二类切比雪夫多项式分别对所获得的边界积分方程进行数值求解。本方法与标准有限元方法（FEM）进行比较，并且通过几个有代表性的数值例子证明了本方法的效率和收敛性。当前扩展和先进的 BIEM 的主要优点在于它具有强大的模拟具有大量层（周期性或非周期性排列）的无界压电层压板的能力以及与 FEM 相比的高精度和高效率。后者允许我们将该方法应用于综合参数分析和多个裂纹和/或电极的复杂情况以及裂纹和/或电极的周期性阵列。当前扩展和先进的 BIEM 的主要优点在于它具有强大的模拟具有大量层（周期性或非周期性排列）的无界压电层压板的能力，以及与 FEM 相比的高精度和高效率。后者允许我们将该方法应用于综合参数分析和多个裂纹和/或电极的复杂情况以及裂纹和/或电极的周期性阵列。当前扩展和先进的 BIEM 的主要优点在于它具有强大的模拟具有大量层（周期性或非周期性排列）的无界压电层压板的能力以及与 FEM 相比的高精度和高效率。后者允许我们将该方法应用于综合参数分析和多个裂纹和/或电极的复杂情况以及裂纹和/或电极的周期性阵列。