Modeling of wave dispersion along cylindrical structures using the spectral method

Abstract

Algorithm and code are presented that solve dispersion equations for cylindrically layered mediaconsisting of an arbitrary number of elastic and fluid layers. The algorithm is based on the spectralmethod which discretizes the underlying wave equations with the help of spectral differentiationmatrices and solves the corresponding equations as a generalized eigenvalue problem. For a givenfrequency the eigenvalues correspond to the wave numbers of different modes. The advantage ofthis technique is that it is easy to implement, especially for cases where traditional root-findingmethods are strongly limited or hard to realize, i.e., for attenuative, anisotropic, and poroelasticmedia. The application of the new approach is illustrated using models of an elastic cylinder and afluid-filled tube. The dispersion curves so produced are in good agreement with analytical results,which confirms the accuracy of the method. Particle displacement profiles of the fundamental mode in a free solid cylinder are computed for a range of frequencies.