Active control of sound power using acoustic basis functions as surface velocity filters

Abstract

An improved method of active structural acoustics control is presented that is based on the minimization of the total power radiated from any structure expressed in terms of a truncated series sum. Each term of this sum is related to the coupling between the orthogonal eigenvectors of the radiation impedance matrix (referred to as ‘‘basis functions’’ in this paper) and the structural surface velocity vector. The basis functions act as surface velocity filters. These acoustic basis functions are found to be weak functions of frequency but their corresponding weighting coefficients increase monotonically with frequency. The minimization of the radiated power is shown to result in a structural surface velocity vector that couples poorly to those acoustic basis functions that account for high-efficiency sound radiation. This strategy is demonstrated numerically for a clamped–clamped baffled beam in air. Point force primary and control actuators (shakers) are used to explore the control mechanisms. As expected, the minimization of the radiated power results in a controlled beam response that contains much lower supersonic wave-number content than that of the uncontrolled beam response. Finally, an unexpected benefit of the control strategy described is that it provides a rational procedure for selecting the number and placement of actuators and sensors on a structure for effective control. This development is significant since this procedure does not require a priori knowledge of the dynamics of the structure.