Observations and modeling of the backscattering of short tone bursts from a spherical shell: Lamb wave echoes, glory, and axial reverberations

Tone bursts having durations of 3 or 4 cycles were incident on an air‐filled stainless steel shell in water. The resulting sequence of echoes included a specular reflection and echoes radiated by Lamb waves on the shell. Echo structure was studied for ka of 24 to 75, where a denotes the outer radius; b/a=0.838, where b denotes the inner radius. The amplitudes of Lamb wave echoes were modeled using an elastic generalization of the geometrical theory of diffraction (GTD) [P. L. Marston, J. Acoust. Soc. Am. 83, 25–37 (1988)]. The required Lamb wave parameters (the phase velocity cl and damping βl ) were found by the Sommerfeld–Watson method; an efficient numerical method for the computation of the required complex root νl is described. The echoes were identified by comparing arrival times with predictions; bursts reflected from a solid tungsten carbide sphere were used for a reference amplitude. Measurements with ka=24 of the largest Lamb wave echo (which was due to a flexural wave) were made at various back...