Abstract:
The modal-style approach for representing the exterior radiation characteristics of structures generally seeks to find a set of orthogonal functions, or acoustic modes, that diagonalize a radiation operator in the exterior domain of the structure. The choice of basis functions, whether global or local, is arbitrary. The acoustic modes are found through an eigenanalysis of the radiation operator, with corresponding eigenvalues which are proportional to the radiation efficiencies. The analytical acoustic modes of a finite sphere radiating into free space are represented by the orthogonal set of spherical harmonics. The spherical harmonics and the modes of arbitrary structures exhibit a grouping among their respective radiation efficiencies at long wavelength conditions. The analytical basis for the grouping within the spherical harmonics provides an avenue for describing the grouping within the acoustic modes of an arbitrary structure. Further, the spherical harmonics provide insight into the shapes of the acoustic modes for arbitrary structures. Here, the acoustic modes of a free-space sphere are compared to those of an arbitrary free-space object, half space object, baffled panel, and baffled beam. [Work supported by NASA GSRP program, NGT-51115.]