Sound scattering from an internally loaded cylindrical shell

Abstract

Sound scattering from a cylindrical shell with a mass-spring system diametrically attached inside it is examined analytically. Explicit solutions for both the shell motions and the scattered acoustic field are derived. It is shown that the attachment of the simple mass-spring loading causes significant changes in the acoustic behavior of the shell. The scattering from the internally loaded shell is shown to be dominated by the interactions between structural waves in the shell and the attachment, which have an overall resonant effect, manifested by a series of scalloplike variations in the scattering form function in the low- and intermediate-frequency domain. In the low-frequency region, it is shown that in contrast to the case of an empty shell where scattering is essentially controlled by the total mass of the scatterer, the acoustic behavior of the internally loaded shell is basically determined by waves in the shell, and, hence, is elasticity controlled. It is found that the shell deformation is dominated by short-wavelength structural waves. This is shown to be the case even for very long-wavelength incident sound. In the high-frequency region, the two subsystems are essentially decoupled from each other in this mass-spring model, because the coupling forces (or impedances) reduce rapidly to zero and become out of phase with the shell velocities at the attachment points as frequency increases. Effects of dissipation in both the internal system and the shell are examined, which shows that the scattering is largely unaffected by dissipation in the internal system. However, damping in the shell dissipates the structural waves, and, hence, affects the scattering that is dominated by the interactions of these waves with the loading.