On the exterior acoustic radiation modes of structures

Abstract

The use of a modal-style approach for the analysis of the exterior radiation characteristics of structures has recently received increasing attention. This approach generally seeks to find a set of orthogonal functions, or acoustic modes, that diagonalizes a radiation operator. These acoustic modes are found through an eigenfunction or singular value decomposition of the radiation operator. The eigenvalue or singular value associated with a given acoustic mode is directly proportional to the radiation efficiency of that acoustic mode. The acoustic mode represents a particular velocity pattern on the surface of the radiator. As with the analogous problem of finding structural natural frequencies and mode shapes, the accuracy of the acoustic modal representation depends on the number of degrees of freedom in the radiation operator. The radiation efficiency of the most efficient acoustic mode has a finite upper bound, and converges fastest with increasing degrees of freedom. Each additional degree of freedom in a model introduces a new least efficient acoustic mode. In fact, the radiation efficiency of the least efficient acoustic mode may be forced arbitrarily close to zero by introducing sufficient degrees of freedom. The most efficient acoustic modes are least sensitive to perturbations in their velocity patterns, while the least efficient acoustic modes are most sensitive. These characteristics of the exterior modal acoustic representation have significant implications for the use of the modal representation in design, optimization, and active noise control. This paper explores these issues using the example of a finite baffled beam.