Active Control of Both Vibration and Sound in Free Space

Abstract

Orthogonal contributors in terms of both structural kinetic energy and radiated acoustic power are derived for the purpose of simultaneous attenuation of both vibration and sound. The orthogonal contributors are referred to as “vibroacoustic modes”. The vibroacoustic modes have eigenvalues and eigenvectors along with structural modes and radiation modes. The eigenvalues of the vibroacoustic modes indicate the vibroacoustic modes' contributions to the sum of the structural kinetic energy and radiated acoustic power. The eigenvectors of the vibroacoustic modes indicate the modal shapes of the vibroacoustic modes. The complex modal amplitudes of the vibroacoustic modes can be measured by filtering error signals from discrete structural sensors attached on a structure. It is found that the sum of the structural kinetic energy and radiated acoustic power can be estimated by the sum of the squared complex modal amplitudes of few of the vibroacoustic modes which have higher contributions (higher eigenvalues). This allows one to get a reduced order controller. To verify the validity of vibroacoustic modal control, numerical results relating to an isotropic plate in an infinite baffle are presented.