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.

The radiation efficiency grouping of free-space acoustic radiation modes

“…Johnson and Elliott 12 extended their earlier work by showing that a substantial reduction in the radiated power on planar structures was obtained at long wavelengths by volume velocity cancellation, clearly demonstrating a close relationship between volume velocity control and control of the dominant acoustic radiation mode. Naghshineh and Koopmann 13,14 applied the technique to structural active noise control, with the objective of forcing the structure to respond in a forced mode of vibration that coincided with an inefficient acoustic radiation mode ͑termed a ''weak radiator''͒. Naghshineh et al 15 demonstrated a design optimization technique such that a subject structure would naturally respond in a structural mode of vibration coinciding with a weak radiation mode, representing an application of the acoustic modal technique to passive control.…”

Optimization Design for Minimization of Sound Radiation from Thin Plate Based on Acoustic Design Sensitivity Analysis

“…Since then the sound radiation efficiency and active control of thin plate had been studied [6,7]. Based on the acoustic radiation modes and further study about acoustic radiation, ADS (Acoustic Design Sensitivity) analysis [8,9,10] was presented to guide Low Noise Design of structures.…”

Sensor scheme design for active structural acoustic control

“…Sensing strategies using velocity information can also be based on so-called radiation modes, 6 which are the vibration patterns of a structure that radiate sound independently in free space [7][8][9][10][11][12][13] or in enclosed spaces. 14,15 The resulting control strategy is optimal with respect to the number of error signals for the controller.…”