Mid-frequency enhancement of the backscattering of tone bursts from thin elastic shells: Fourier synthesis and ray model.

Abstract

A broad enhancement of the form function for these shells is known to be present in the mid-frequency range. A ray model of the form function in this region was previously demonstrated for cylinders and spheres [N. H. Sun and P. L. Marston, J. Acoust. Soc. Am. 89, 1949 (1991)] and the enhancement was found to be associated with contributions to the scattering from the subsonic surface guided wave frequently designated as A<lu>0<bu>−<lux>. The consequences of this enhancement were investigated for spherical shells by synthesizing the response to tone bursts from an evaluation of the exact partial wave series over the sampled spectrum of the burst [L. Zhang, M. S. dissertation, Washington State University, 1991]. This was compared with a ray approximation for the earliest contribution for this wave, which circumnavigates only the backside of the shell. The amplitude from the ray model is ‖f0,l‖ ≊ 8πβl(c/cl)exp(−πβl), where the surface wave parameters cl and βl are found from the exact elastic equation for the roots of Dν(ka)=0. Both the Fourier synthesis and ray models show a broad enhancement which for a 2.5% stainless steel shell peaks at ka≊46 where ‖f0,l‖ ≊ 3.1 and the exact results differ by only 3%. Neglecting dispersion the peak occurs where βl=π−1. [Work supported by ONR.]