Normalizations in acoustic optimization with Rayleigh integral

The numerical difficulties of the acoustic optimization subject to an acoustic constraint, when structural boundary conditions are imposed on the velocity profiles with the finite element solution, have been discussed in this paper. A structural constraint is proposed for the acoustic optimization. This constraint leads to a radiation efficiency index, which is the ratio of the acoustic energy radiated by the structure to its potential energy. The structural constraint allows for the boundary conditions to be satisfied prior to the optimization, leading to velocity profiles physically feasible to elastic structures.