Revisiting the edge resonance for Lamb waves in a semi-infinite plate

The resonance for the elastic plate with a free edge is studied from the point of view of complex resonance. The variations of the real part and of the imaginary part of the complex resonance frequency as a function of the Poisson ratio ν are determined numerically. The results confirm the real resonance frequency theoretically predicted in I. Roitberg et al., Q. J. Mech. Appl. Math. 51, 1–13 (1998) for a zero Poisson ratio ν1=0, and a real resonance frequency that corresponds to a Lamé mode is discovered for a Poisson ratio ν2=0.2248. It is shown that both real resonance frequencies may exist, at these two particular values of ν, because of the decoupling between the propagating Lamb mode and the set of evanescent Lamb modes.