The radiation modes of baffled finite plates

Abstract

The modal-style approach for representing the exterior radiation characteristics of structures generally seeks to find a set of orthogonal functions, or radiation modes, that diagonalize a discretized radiation operator in the exterior domain of the structure. The choice of basis functions for the modal representation is arbitrary, though use of the structural modes of vibration tends to provide some physical insight. The radiation modes are found through an eigenanalysis or singular-value decomposition analysis of the radiation operator. The eigenvalue or singular value associated with a given radiation mode is directly proportional to the radiation efficiency of that radiation mode. In this paper, the dependency of the radiation efficiencies and radiation mode shapes on the number of degrees of freedom permitted in the derivation of the radiation operator is investigated for a baffled finite rectangular plate. The accuracy of the acoustic modal representation depends on the number of degrees of freedom in the radiation operator, with the least efficient radiation modes converging slowest. Further, the rate of convergence is dependent on the particular basis function selection. The convergence behavior has significant impact on those applications of the exterior acoustic modal approach that seek to exploit the least efficient radiation modes.