A modal approach to acoustic scattering and its active control

Abstract

An elegant theory of acoustic scattering has been formulated by Bobrovnitskii in terms of three separate impedance matrices, corresponding to the structural response of the scattering body, the internal acoustic response of the space of the scattering body if filled with fluid, and the external sound radiation from the scattering body into the surrounding fluid. The original formulation assumes that the surface of the scattering object is divided into a large number of discrete elements, but an analogous formulation for acoustic scattering can be derived using a modal expansion of the velocity and pressure distribution on the surface of the scattering body. For the particular case of scattering from a thin spherical shell, all of these modes correspond to spherical harmonic components and the formulation for the scattered sound field takes a particularly simple form, since all of the impedance matrices become diagonal. The normalised scattered power from various examples of thin, empty spherical shells is considered, together with the active control of this scattered power. A feedforward control approach can be used to investigate the best possible performance of various configurations of secondary actuators, including point force actuators acting on the shell, in attenuating the scattered sound field. Feedback control of the shell vibration, from surface velocities to forces acting on the shell, is a more practical control strategy and will change the shell’s dynamics so that its modal impedance matrix is generally no longer diagonal, although the general matrix formulation can still be used to calculate the scattering. The change in the scattered power is illustrated for de-centralised velocity feedback control.

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Identifiers

ORCID for Mihai Orita: orcid.org/0000-0001-7307-0497

ORCID for Jordan Cheer: orcid.org/0000-0002-0552-5506

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