Modification of Lamb wave spectrum in fluid coupled plate

Abstract

It has been accepted previously that for most practical eases when a plate is immersed in a liquid the Lamb wave spectrum is only slightly perturbed due to energy loss related to leakage of the wave from the plate to the liquid. In contrast it was recently discovered by D. E. Chimenti and A. H. Nayfeh [Appl. Phys. Lett. 49 (9) (1986)] that for leaky Lamb waves in a graphite epoxy composite plate in water a strong anomaly appears in the topology of the S0 mode as a function of frequency. Although it was caused by the fluid, the reason for this anomaly was still not clear. The nature of the anomalous behavior of leaky Lamb waves is discussed in this paper. It is shown that for an understanding of the spectrum topology, the full complex spectrum of propagating and nonpropagating modes should be considered. It is demonstrated that the topological changes in the S0 mode are related to its nearness to the first complex branch of the spectrum. Increasing liquid density leads to interaction between these modes and mutual interchange between their branches in the complex plane. It is shown that, in general, as the density of the immersion liquid increases from zero to infinity the complex spectrum of plate modes gradually transforms from a spectrum of Lamb waves in a free plate to a spectrum of waves in a plate clamped on its surfaces with slip (boundary conditions σxy = 0, Uy = 0).