Regular articleAnomalies of the A0leaky lamb mode of a fluid-loaded, elastic plate
Review articleOpen access

AbstractFor the fundamental, antisymmetric, leaky Lamb mode, A0, 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 A0locus 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 ρf/ρp,cf/csandcd/cs, whereρfandρpare the fluid and plate densities,cfis the wave speed in the fluid, andcdandcsare the speeds of dilatational and shear waves in the plate material. Computations covering a wide range ofρf/ρpand a limited range ofcd/csindicate that the value ofcf/csis the dominant factor in the creation of anomalous behaviour, the splitting occurring ifcf/csis 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 A0and antisymmetric Stoneley waves is suggested for the transition from normal to anomalous behaviour. Areas needing further investigation are exposed.

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