Finite element prediction of wave motion in structural waveguides

A method is presented by which the wavenumbers for a one-dimensional waveguide can be predicted from a finite element (FE) model. The method involves postprocessing a conventional, but low order, FE model, the mass and stiffness matrices of which are typically found using a conventional FE package. This is in contrast to the most popular previous waveguide/FE approach, sometimes termed the spectral finite element approach, which requires new spectral element matrices to be developed. In the approach described here, a section of the waveguide is modeled using conventional FE software and the dynamic stiffness matrix formed. A periodicity condition is applied, the wavenumbers following from the eigensolution of the resulting transfer matrix. The method is described, estimation of wavenumbers, energy, and group velocity discussed, and numerical examples presented. These concern wave propagation in a beam and a simply supported plate strip, for which analytical solutions exist, and the more complex case of a viscoelastic laminate, which involves postprocessing an ANSYS FE model. The method is seen to yield accurate results for the wavenumbers and group velocities of both propagating and evanescent waves.