Calculation of acoustic radiation using equivalent-sphere methods

Among the methods generally used to solve a problem in the domain of acoust ic radiation, the equivalent sources method offers an interesting alternati ve. It consists in replacing the vibrating surface with a distribution of a coustic sources placed inside the structure. The contribution of each sourc e is determined in such a way that the acoustic field radiated by these sou rces verifies the same boundary conditions on the structure. The number of unknowns in the problem is no longer directly linked to the number of mesh points on the structure, as with boundary elements methods, but to the numb er of equivalent sources employed in the model. The equivalent source metho d is therefore of major interest if the acoustic radiation of the structure can be approximated with a sufficiently low number of sources. This paper proposes its application when the equivalent source is a sphere. In this ca se, the number of unknowns is equal to the number of modes. In contrast to the one-point multipole, the sphere has a surface surrounding a closed volu me to express the boundary conditions. Although sphere/multipole equivalenc e has been demonstrated, the surface of the sphere allows normalization of the functions used, leading to stabilization of the system to be resolved. First, the main acoustic radiation characteristics of a sphere and of the l inear system verified by the modal coefficients of an equivalent sphere are presented. The different parameters of the model are then studied: positio n and radius of the equivalent sphere, truncation of the series, and influe nce of the spatial sampling (mesh). In the same vein, a second approach is presented. It consists of making each point of the structure correspond to a point of the sphere, and the vibrating field at the surface of the sphere is deduced from that of the structure by simple geometric projection. Resu lts can be obtained very quickly as no matrix inversion is required. The ac curacy of the results depends on the distance between the sphere and the st ructure. Finally, an experimental validation that uses both methods is pres ented and shows interesting results when the structure is closed, and when its shape is not too far removed from a sphere. (C) 2000 Acoustical Society of America. [S0001-4966(00)01805-1].