Abstract:
A previous formulation of two-dimensional high-frequency scattering by smooth elastic objects is based on a one-dimensional convolution of a one-sided spatial response function with the local pressure of the incident wave evaluated at the surface of the object [P. L. Marston, J. Acoust. Soc. Am. 91, 34--41 (1995)]. That result is shown to follow from a more general three-dimensional formulation as an embedded special case. The new formulation expresses the local outgoing leaky wave amplitude as a surface convolution of the pressure of the incident wave with a two-dimensional response function. The formulation makes use of the local surface mechanics and wave properties but does not directly use thin-shell assumptions. Previous results are recovered for the leaky wave coupling coefficient and limiting phase for broadside illumination of a circular cylinder, the dimensions of elliptical coupling patches, and (from stationary phase) the coupling conditions for tilted cylinders. The formulation is useful for obtaining quick and simple backscattering strength estimates for objects with truncations where there are dominant leaky wave scattering contributions. It also describes the size of coupling regions on general smooth surfaces. [Work supported by the Office of Naval Research.]