This study presents a robust method towards the computation of dispersion curves of surface waves in an anisotropic semi-infinite periodically layered structure (PLS) coated by a stack of layers. Using the properties of the symplectic transfer matrix to analyze the relationship between the eigenequations of surface waves in a semi-infinite PLS and of its corresponding finite PLS, the eigenfrequencies within the stopbands for surface waves in a semi-infinite PLS are solved by a finite PLS consisting of a sufficient number of unit cells. The eigenvalues of a finite PLS are calculated by combining the precise integration method with the Wittrick–Williams (W-W) algorithm, which makes the present method accurate, efficient and numerically stable. On this basis, using the concept of the eigenvalue count in the W-W algorithm, the eigenfrequencies of surface waves in a semi-infinite PLS coated by a stack of layers are accurately computed for any given wavenumber. Unlike most existing approaches that determine dispersion curves by directly seeking roots from the transcendental eigenequation, the present method takes full advantages of the eigenvalue count to find all eigenfrequencies without the possibility of any being missed. The method can be applicable for surface wave problems in an arbitrarily anisotropic semi-infinite PLS and does not restrict layer number, layer thickness and material properties.

这项研究提出了一种鲁棒的方法，用于计算由层堆叠覆盖的各向异性半无限周期性分层结构（PLS）中的表面波色散曲线。利用辛传递矩阵的性质分析半无限PLS中的表面波本征方程及其对应的有限PLS之间的关系，通过有限元求解半无限PLS中的表面波阻带内的本征频率。 PLS由足够数量的单位单元组成。通过将精确积分方法与Wittrick-Williams（WW）算法相结合，可以计算出有限PLS的特征值，从而使本方法准确，高效且数值稳定。在此基础上，使用WW算法中特征值计数的概念，对于任何给定的波数，都可以精确计算出由一叠层覆盖的半无限PLS中的表面波的本征频率。与大多数通过直接从先验本征方程求根来确定弥散曲线的现有方法不同，本方法利用本征值计数的全部优势来查找所有本征频率，而不会遗漏任何本征频率。该方法可以应用于任意各向异性的半无限PLS中的表面波问题，并且不限制层数，层厚度和材料特性。本方法充分利用了特征值计数的优势，可以找到所有特征频率，而不会遗漏任何特征频率。该方法可以应用于任意各向异性的半无限PLS中的表面波问题，并且不限制层数，层厚度和材料特性。本方法充分利用了特征值计数的优势，可以找到所有特征频率，而不会遗漏任何特征频率。该方法可以应用于任意各向异性的半无限PLS中的表面波问题，并且不限制层数，层厚度和材料特性。