RAY SYNTHESIS OF LAMB WAVE CONTRIBUTIONS TO THE TOTAL SCATTERING CROSS-SECTION FOR AN ELASTIC SPHERICAL-SHELL

The optical theorem relates the extinction cross section cre(ka) to the forward-scattering amplitude f (9 = 0, ka). Here, 0 denotes the scattering angle, k is the wavenumber of the incident sound, and a is the radius of the scattered If the absorption by the scatterer is negligible so that the scatterer is elastic, creis equal to the total scattering cross section σrBy applying this theorem to the partial wave series for f (0, ka), an expression can be obtained for σtfor an elastic spherical shell in water. However, the series representation of σtdoes not facilitate a direct understanding of the rich structure caused by the shell's elastic response. In particular, the elastic response is attributable to leaky Lamb waves. A generalization of the geometrical theory of diffraction [P. L. Marston, J. Acoust. Soc. Am. 83, 25–37 (1988)] is employed to synthesize f (0, ka). This simple ray acoustic synthesis contains a component for ordinary diffraction by the shell and distinct contributions for the individual Lamb waves that can be excited on the shell. A comparison of numerical computations for crtutilizing the exact partial wave series and the ray synthesis shows good agreement in the description of the resonance structure. The relevant range of ka for this comparison is 7 < ka < 100. The elastic material of the shell is 440c stainless steel and the inner-to-outer radius ratio is b /a = 0.838. Dispersion curves and radiation damping for Lamb waves were calculated by Watson transform methods. The structure in σt(ka) due to Lamb waves may also be depicted as a manifestation of forward glory scattering and experimental evidence for the forward glory is noted. © 1990, Acoustical Society of America. All rights reserved.