Focused backscattering from hollow spherical shells in water: Lamb waves and the acoustical glory

Abstract

When a short tone burst is incident on a spherical shell in water, the first backscattered echo is the specular reflection. This is followed by radiation from the Lamb waves on the shell [R. Hickling, J. Acoust. Soc. Am. 36, 1124–1137 (1964)]. The angular dependence of the largest Lamb wave echo has been modeled and measured as the receiver is shifted an angle γ away from the backscattering axis. The sphere was made of stainless steel with an inner‐to‐outer radius ratio b/a = 0.84. For the frequencies used, 50 < ka < 65 and the largest Lamb echo is predicted to be the lowest flexural mode. Previous SWT results (for solid spheres) were applied to calculate the surface wave's phase velocity csw and angular damping parameter β and were extended to include a subtle effect of β on the Lamb echo amplitude psw. It is found that psw ≈ ps A0|J0(u) − iβγJ1(u)|, where ps is the specular ampliture at γ = 0, u≈kaγc/cw, A0 = |G|exp[− 2β(π − θsw)], sin θsw = c/csw, and G is a coupling coefficient. Measured psw near the central peak at γ = 0 generally agree, but near the γ where psw is minimized, dispersion (not included in the model) becomes significant. [Work supported by ONR.]