Cluster Control of a Distributed-Parameter Planar Structure. On the Suppression of Structural Acoustic Power.

Abstract

This paper considers the cluster control of a distributed-parameter planar structure with particular emphasis on the suppression of the total acoustic power radiated from a vibrating structure. This paper begins by discussing the power matrix of a planar structure, clarifying that the power matrix is expressed in a form of a block diagonal matrix by reordering the columns and rows of the matrix. That enables one to introduce a notion of vector space for understanding the concept of the cluster control. From this viewpoint, the acoustic power space is found to be consisting of four subspaces;odd/odd modal cluster, odd/even modal cluster, even/odd modal cluster and even/even modal cluster. Then, it is shown that the modal matrix derived from the acoustic power matrix has exactly the same form as the power matrix described in a block diagonal matrix. Moreover, a total acoustic power of a vibrating planar structure is found to be written as a sum of acoustic powers radiated from each cluster. Finally, the experiment is conducted, demonstrating the validity of the cluster control for suppressing the radiated power.