Sub-critical vibrating structures: on algorithm to speed up calculation of the acoustic radiated field

The Boundary Element Method (BEM) allows the calculation of the acoustic field emitted by a structure from its wall / panel surface velocity. This method requires a surface mesh whose number of nodes N increases with the maximum analytical frequency. Due to its complexity and O(N?) storage requirements, the BEM does not perform well enough in terms of calculation time. The aim of this work is to reduce this calculation time by applying to 3D acoustic problems a method widely used in the field of electromagnetism named the Fast Multipole Method (FMM). The FMM makes the BEM faster by reducing the complexity and the memory cost up to O(N logN). The FMM, which does not take the vibratory properties of the radiating surface into account, has been digitally and experimentally applied to cases of sub-critical vibration. Vibrations are termed sub-critical when their wavelength is lower than the acoustic wavelength. Although the FMM is not theoretically adapted to this type of field, it yields satisfactory results for slightly sub-critical fields.