Anomalies of the A0leaky lamb mode of a fluid-loaded, elastic plate

Abstract

Abstract For the fundamental, antisymmetric, leaky Lamb mode, A 0 , of an elastic plate immersed in a fluid, an investigation has been made of a form of anomalous behaviour in the subsonic region which occurs for some combinations of plate material and loading fluid. This behaviour consists of splitting of the modal locus to form a loop along which the modal wavenumber is lossless. At a point on the A 0 locus in the subsonic region which is not on a loop, the mode consists of a highly damped and, hence, (effectively) non-propagating wave, whereas, at a point on a loop, the mode corresponds to a wave propagating without loss along the plate. The relevant parameters for the locus are ρ f /ρ p , c f /c s and c d /c s , where ρ f and ρ p are the fluid and plate densities, c f is the wave speed in the fluid, and c d and c s are the speeds of dilatational and shear waves in the plate material. Computations covering a wide range of ρ f /ρ p and a limited range of c d /c s indicate that the value of c f /c s is the dominant factor in the creation of anomalous behaviour, the splitting occurring if c f /c s is greater than some value between 0.5 and 0.6. At the entry to and exit from a loop, the two arms of the loop are shown to meet without discontinuity of slope at a point at which the group velocity is zero. This provides an understanding of how a loop can occur and leads to the establishment of a rather complicated criterion for the formation of a loop. A structure of nesting of loops within one another has been observed, indicating a sequence of loop formation. An, as yet unverified, physical explanation involving interaction of the A 0 and antisymmetric Stoneley waves is suggested for the transition from normal to anomalous behaviour. Areas needing further investigation are exposed.