A faster scheme to generate multimodal dispersion plots for Rayleigh wave propagation

摘要

A faster computational scheme is proposed to determine multimodal dispersion plots using the stiffness matrix method (SMM) for Rayleigh wave propagation in horizontally layered ground media. The scheme decomposes the governing stiffness matrix (K) into a product of unit lower triangular matrix (L) and the upper triangular matrix (U). Accordingly, the determinant of K, which is needed for obtaining the required solution, becomes the product of all the diagonal terms in U. An algorithm is introduced to write all the diagonal terms in U. By considering the special structure of the stiffness matrix, the determinant of K is evaluated directly in a single step avoiding all the computationally expensive loops. The solution is then obtained by using the root search method (RSM). No approximation is involved in this scheme which involves hyperbolic and transcendental functions, and there is no need to discretize different strata further into a number of thin layers. The efficacy of the proposed scheme is demonstrated by using different examples both for regular and irregular dispersive layered media. The proposed computational scheme is found to be highly time efficient in obtaining multimodal dispersion plots.