Condensing structural finite element meshes into coarser acoustic element meshes

The sound power radiated by a vibrating structure (with negligible fluid loading) is typically computed in two steps. First, a finite element mesh of the structure is constructed, and the structural vibrations are computed. The finite element mesh is then converted to a surface mesh, and the sound power output is computed using the boundary element method. In many cases, the acoustic analysis is computationally inefficient because the structural finite element mesh is much denser than required for the acoustic calculations, leading to the solution of a large, fully populated, matrix equation. It is shown that the efficiency of the acoustic analysis can be significantly increased by condensing the structural finite element mesh into a much coarser acoustic element mesh, where the surface meshes of several structural elements are combined to form a single acoustic element. This condensation becomes possible when the boundary condition for the acoustic analysis is written in terms of elemental volume velocities instead of nodal velocities. An example is given in which sample computation times are tabulated, and the accuracy of the numerical calculations are assessed.