The radiation efficiency grouping of free-space acoustic radiation modes

Abstract

The use of a modal representation for the exterior acoustic field of a structure has received increasing attention in recent years. This modal approach generally seeks a set of orthogonal functions, representing independent surface velocity distributions, termed acoustic radiation modes, which diagonalize a radiation operator in the exterior domain of the structure. These orthogonal acoustic radiation modes may be found, among other methods, through an eigenvalue analysis of a radiation operator and possess a corresponding set of eigenvalues that are proportional to the radiation efficiencies of the acoustic radiation modes. In free space, the acoustic radiation modes of a sphere display a grouping characteristic in their radiation efficiencies, where each acoustic radiation mode’s radiation efficiency within a group has the same frequency dependency. This is a consequence of the fact that the acoustic radiation modes of a sphere are the spherical harmonics. Further, the acoustic radiation modes of an arbitrary three-dimensional structure exhibit the same frequency grouping as those for the sphere. The basis for the arbitrary structure’s grouping follows from the sphere’s grouping. The observation that the acoustic radiation modes of an arbitrary body are dominated by spherical harmonics provides insight on the behavior of such modes. These results have significance for various applications of acoustic radiation modes, including active noise control design, radiation modeling, etc.