Evaluation of modal density and group velocity by a finite element method

A finite element method (FEM), the waveguide-FEM, is used to calculate wave propagation characteristics for built-up thin-walled structures. Such characteristics are determined from a dispersion relation in the form of an eigenvalue problem established from the FE formulation. In particular, vital characteristics such as the modal density, the group velocity and the waveform are evaluated. A description of the evaluation of a dispersion relation for a channel beam, from data given by the FE formulation, is presented. Subsequently, the method for determining the modal density and group velocity from FE input data is shown in detail for the beam structure. To show the versatility of the method a second example considers a statistical energy analysis (SEA), made to establish the degree to which vibrations in a wind tunnel are transmitted to a thin-walled plate mounted into its wall. The critical input datum to the SEA model is the wind tunnelʹs modal density, which is calculated by the method presented.