Dynamic stiffness of three-dimensional anisotropic multi-layered media based on the continued-fraction method

Abstract

Summary Solving the dynamic response of three-dimensional anisotropic media has always been rather challenging. Although many researchers have found solutions to homogeneous anisotropic half-spaces, there is little research into anisotropic layered media. In this paper, for the three-dimensional anisotropic layered media, the modified scaled boundary finite element method (SBFEM) is used to solve the dynamic impedance matrix of the anisotropic layered media after introducing a high-order transmitting boundary based on the continued-fraction method. The algorithm in this paper can solve not only isotropic and cross-anisotropic layered media, but also general anisotropic layered media. First, the algorithm is degraded to obtain the dynamic impedance matrix of cross-anisotropic layered media; the result is compared with that in the previous studies to verify the accuracy of our algorithm. Then, the solutions of our algorithm are given for general anisotropic media.