A multiple multipole expansion approach for predicting the sound power of vibrating structures

A multiple multipole expansion algorithm to evaluate the sound field from a collection of volume or surface sources is presented. The algorithm combines the proper assembly of the different multipole expansion terms together with the proper choice of the spatial extent of each expansion to yield rapid and accurate evaluation of the far-field pressure. Integration of this field over a hemisphere surrounding the sources leads to the radiated power. A special emphasis is put on discussing error scares and developing, for the truncated multipole expansion (monopole + dipole + quadrupole), a non dimensional convergence criterion in terms of the source spatial extent. This convergence criterion allows for an optimized numerical implementation of the algorithm. The algorithm is applied to the evaluation of the radiation efficiency of a baffled rectangular plate. It is verified by comparison with classical computational techniques. Numerical results show good agreement with other techniques for problems with both low and high modal densities. For the plate's problem, the use of the first three terms in the expansion (= monopole, dipole and quadrupole), together with a novel numerical implementation in a multiple multipole expansion scheme, is seen to be more efficient than classical computational techniques.