Acoustic resonances of thin cylindrical shells and the resonance scattering theory

Abstract

An experimental and theoretical study is presented of the properties of circumferential waves on thin-walled elastic, air-filled cylindrical shells immersed in water, and of their excitation by normally incident acoustic pulses of short duration. A spectral decomposition of the multiple echo pulses using the Numrich–de Billy method, and subsequent analysis by the resonance scattering theory (RST), reveal for an aluminum shell the presence of an ℓ=2 wave that can be identified with the S0 Lamb wave on a plate, and of an ℓ=0 wave that at low frequencies corresponds to a water-borne circumferential wave, not given by the Lamb theory of free-plate vibrations but by its extension to a plate with one-sided fluid loading. Calculations of complex pole resonances on aluminum and steel shells, as well as of the corresponding circumferential wave speeds and attenuations, serve to clarify the physical situation.