On the effect of damping on dispersion curves in plates

This paper presents a study on quantitative prediction and understanding of time-harmonic wave characteristics in damped plates. Material dissipation is modelled by using complex-valued velocities of free dilatation and shear waves in an unbounded volume. A Wave Finite Element (WFE) method is used to solve the Rayleigh-Lamb problem for a viscoelastic plate in plain strain, and results are validated using a Finite Product (FP) method. A numerical example concerning a viscoelastic panel is then presented in order to illustrate and discuss the role of dissipation in the cut-off phenomenon and in the phenomenon of veering for dispersion curves. These phenomena are explained in more detail considering a simple model, which allows accurate asymptotic analysis of the perturbation of dispersion curves in the regions of cut-off and veering.