Acoustic scattering from spherical shells and its active control

Abstract

The scattering of sound by a thin spherical shell is considered using an analytic formulation involving spherical harmonics. The integral of the far field scattered intensity, termed the scattered power, can then be expressed in a simple form. At low frequencies the scattered power can be minimised by an appropriate choice of material properties and shell thickness, which is illustrated for both a steel shell and for one in which the mass and stiffness of the shell are equal to those of the displaced fluid. Simulations of feedforward active control are then used to investigate the best possible performance in attenuating the scattered power, although this approach requires knowledge of the incident and scattered sound fields. Feedback control of the shell vibration using structural actuators and sensors is a more practical control strategy since it does not involve the need to separate the incident and scattered contributions. Direct velocity feedback control is considered using collocated and distributed actuators and sensors that spread the applied force and sensed velocity over spherical caps on the surface of the shell. This approach shows effective suppression of the structural shell modes that give rise to significant scattering at their resonant frequencies.