Maximizing the Power Output of Air-Acoustic Actuator Arrays

Abstract

The maximization of radiated sound power from baffled vibrating structures is studied as a means of examining the structural-acoustic control authority of point force and distributed moment actuators. The relationship between the structural vibration and radiated sound power is expressed as a quadratic function of the modal velocities and the structural mode shapes. The sound power model is nondimensionalized through geometric transformations. The problem of computing the maximum radiated acoustic power using an array of actuators is shown to reduce to a generalized eigenvalue analysis. A term denoting the power efficiency, which is defined as the ratio of maximum radiated power normalized with respect to the maximum achievable radiated power, is stated and a series of numerical simulations are performed. The numerical simulations examine the physical mechanisms of maximizing the sound power output of structures. The expressions for the modal coefficients of point force and distributed moment actuators are used to determine actuator locations that influence only the efficient radiator modes. Power efficiency studies illustrate the relationship between the modal velocities and the direction of the maximizing force input. The numerical studies indicate that a group of properly placed point force actuators can achieve broadband power efficiency over the frequency range studied, whereas distributed moment actuation exhibits lower power efficiency at high frequencies. This difference is attributed to the magnitude and phasing of the array modal velocities. The simulations also demonstrate the utility of the eigenvalue technique for determining optimal placement and sizing of a multiple transducer air-acoustic actuator array.