Midfrequency enhancement of the backscattering of tone bursts by thin spherical shells

Abstract

A broad enhancement of the form function f(ka) for steady-state backscattering by thin spherical shells in the midfrequency range has been noted by several investigators. Consequences of this enhancement on the backscattering of tone bursts are investigated with a Fourier synthesis of the temporal response from the exact f(ka). The emphasis is on incident bursts that are sufficiently short so that scattering consists primarily of distinct echoes associated with the specular reflection and different circumnavigations of a dominant surface guided wave. That wave lies on the subsonic branch of the lowest antisymmetric Lamb mode for a fluid-loaded shell designated as a0− by some authors. A ray method, previously verified for echo amplitudes from leaky (or supersonic) Lamb waves on thick shells [S. Kargl and P. Marston, J. Acoust. Soc. Am. 85, 1014–1028 (1989)], is generalized to subsonic waves. The ray method well approximates echo amplitudes from the Fourier synthesis provided the incident burst is sufficiently long that effects of dispersion are weak. Over a broad frequency range, the amplitude of the earliest a0− echo is enhanced relative to the specular echo. For the 2.5% thick stainless steel shell in water considered, the enhancement factor peaks near ka≊46 where the amplitude ratio ≊3.1. The ray theory suggests that the peak ratio depends only weakly on shell thickness and material parameters provided certain conditions hold. The a0− wave is also found to contribute a prominent wave packet to the far-field impulse response of the shell. The radiation damping and velocity of relevant surface waves were computed from the complete elastic equations and those results may be helpful for testing thin shell approximations near the coincidence frequency.