The purpose of this paper is to extend and generalize the precise integration method (PIM) and the Wittrick–Williams (W–W) algorithm to analyze the dispersion of guided waves in multilayered anisotropic piezoelectric structures. The analysis shows that the W–W algorithm cannot be directly applied to piezoelectric materials. This is due to the fact that a submatrix of the Hamiltonian matrix is not positive definite for piezoelectric materials such that the eigenvalue count of sublayers is not zero when the divided sublayers are sufficiently small. The reason for this issue is explored by a theoretical analysis, and then, a symplectic transformation is introduced to ensure that the W–W algorithm can conveniently be applied to solve wave propagation problems in multilayered anisotropic piezoelectric structures. The present method not only guarantees that the computation is accurate and stable, but also finds all eigenfrequencies without being missed. Three numerical examples are provided to illustrate the performance of the method, and the results obtained by the method are compared with the published results and the results obtained by the semi-analytical finite element method. The effects of boundary conditions, wave propagation direction, thickness ratios and stacking sequences on the dispersion behavior of guided waves are discussed.

中文翻译：

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多层各向异性压电结构中导波传播的精确方法

本文的目的是扩展和推广精确积分法 (PIM) 和 Wittrick-Williams (W-W) 算法，以分析多层各向异性压电结构中导波的色散。分析表明 W-W 算法不能直接应用于压电材料。这是因为哈密顿矩阵的子矩阵对于压电材料不是正定的，因此当划分的子层足够小时，子层的特征值计数不为零。通过理论分析探讨了这个问题的原因，然后引入了辛变换，以确保 W-W 算法可以方便地应用于解决多层各向异性压电结构中的波传播问题。本方法不仅保证了计算的准确和稳定，而且能找到所有的特征频率而不会遗漏。提供了三个数值例子来说明该方法的性能，并将该方法获得的结果与已发表的结果和半解析有限元方法获得的结果进行了比较。讨论了边界条件、波传播方向、厚度比和叠加序列对导波色散行为的影响。并将该方法得到的结果与已发表的结果和半解析有限元法得到的结果进行比较。讨论了边界条件、波传播方向、厚度比和叠加序列对导波色散行为的影响。并将该方法得到的结果与已发表的结果和半解析有限元法得到的结果进行比较。讨论了边界条件、波传播方向、厚度比和叠加序列对导波色散行为的影响。