An accurate method for dispersion characteristics of surface waves in layered anisotropic semi-infinite spaces. (February 2023) - Gao, Q.; Yan, B.W.; Zhang, Y.H.
Highlights: A method is proposed to solve surface waves in layered anisotropic half-spaces. The radiation condition is derived from the properties of the Hamiltonian matrix. The concept of mixed energy matrix is used to improve the accuracy. The Wittrick-Williams algorithm is used to ensure that all surface waves are found. The accuracy and efficiency of the method is validated with numerical examples. Abstract: In this paper, we develop a novel method for the dispersion characteristics of surface waves in layered anisotropic semi-infinite spaces. Compared to solving the algebraic transcendental eigenequations directly, this method can find all surface waves accurately. For solving accurately, the first-order state equation is formed by introducing the dual variable. Some properties of the complex Hamiltonian matrix are presented and proved, then based on these properties, the radiation condition for the homogeneous anisotropic half-space is given. And, based on the scaling and squaring algorithm and mixed energy matrix, the precise integration method (PIM) is presented for solving accurately the eigenvalue problem of ordinary differential equations (ODEs) corresponding to surface waves. All eigenfrequencies can be found with certainty by using the concept of the eigenvalue count in the Wittrick-Williams (W-W) algorithm. Numerical examples show that the proposed method is highly accurate and efficient for solving dispersion relations of surface waves in layered anisotropic semi-infinite spaces, which involves the comparison of other previously published methods.