Radiation clusters and the active control of sound transmission through symmetric structures into free space

The purpose of this paper is attenuating harmonic sound transmission through symmetric structures into free space using error signals derived from structural vibration sensors. It is well known that structural modal functions of symmetric structures are clustered to an even function or an odd function and each of the clusters uncouples with the other cluster in the radiated acoustic field. This indicates that the clusters are orthogonal contributors, i.e., independent contributors, with respect to the radiated acoustic field. In this paper, the clusters are referred to as “radiation clusters” in contrast with radiation modes, which are conventional orthogonal contributors with respect to the radiated acoustic power. The active control of harmonic sound transmission through symmetric structures into free space based upon independently measuring and controlling the individual radiation clusters, termed “radiation cluster control”, is proposed. The approach falls into a category of middle authority control (MAC), which is between low authority control (LAC): structural modal control and high authority control (HAC): radiation modal control, possessing the benefit of practicality similar to LAC, while providing high control performance and some flexibility of control gain assignment similar to HAC. Specific examples relating to radiation cluster control of a simply supported rectangular plate in an infinite baffle are given.