Active control of sound radiation from a fluid-loaded rectangular uniform plate

Abstract

Active control of sound radiation from a simply supported rectangular fluid-loaded plate is analytically studied. The plate is assumed to be excited by a point force at subsonic frequencies. The solution to the plate motion is based on the admissible functions for an in vacuo homogeneous plate, which is also the basis for Fourier decomposition of the fluid loading [B. E. Sandman, J. Acoust. Soc. Am. 61, 1502–1510 (1977)]. Feed-forward control is carried out by using point forces applied to the plate. The amplitudes of the control forces are determined by the optimal solution of a quadratic cost function that integrates the far-field radiated acoustic pressure over a hemisphere in the radiation half-space. The results show that for subsonic disturbances, a high global reduction in radiated pressure is possible. For on-resonant excitations, a reasonable sound reduction can be achieved with up to two properly located active control forces, and for off-resonant excitations, up to four control forces may be necessary. The results thus indicate that the active structural acoustic control approach will provide large attenuations in radiated sound when edge mode coupling induced by heavy fluid loading is present. The number and location of the control forces are determined so as to suppress the efficiently radiating modes. The far-field directivity pattern, the plate velocity autospectrum in the two-dimensional wave number domain, and the near-field pressure distribution are studied.