ANOMALIES OF THE A(0) LEAKY LAMB MODE OF A FLUID-LOADED, ELASTIC PLATE

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 rho(f)/rho(p), c(f)/c(s) and c(d)/c(s), where rho(f) and rho(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 rho(f)/rho(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.