Dispersion curves of fluid filled elastic pipes by standard FE models and eigenpath analysis

This paper presents the application of an alternative waveguide finite element method (WFE) using standard FE-code for the computation of dispersion curves in fluid filled elastic pipes. Only one element is needed in longitudinal direction of the pipe in the FE model, which includes structural–acoustic interaction by a full coupling interface. After rearranging the dynamic stiffness matrix of the segment model in transfer matrix form, a periodicity condition is applied leading to an eigenvalue problem. Here, eigenvectors correspond to wave modes and eigenvalues are a function of the complex wavenumber. From the eigenpairs, phase velocities and group velocities of branches are computed as well as sound power transmission. Instead of solving the eigenvalue problem for each frequency separately, an eigenpath analysis is presented in order to track dispersion curves through the frequency band of interest. The numerical results are compared to results from an analytical model of a thin walled fluid-filled shell. The method allows periodic wave guides with any cross section to be analyzed while employing standard FE discretization.