A multi-domain boundary element formulation for acoustic frequency sensitivity analysis

The determination of acoustic sensitivity characteristics for vibrating structures with respect to the design parameters is a necessary and an important step of the acoustic design and optimization process. Acoustic frequency sensitivity analysis, as one kind of the sensitivity analysis, is extremely useful for large models in which only a few discrete frequencies can be analyzed due to high computational cost. Through frequency sensitivity analysis, the acoustic performance can be obtained near the initial frequency for less cost than a second full analysis. However, based on single-domain boundary element method (BEM), acoustic sensitivity analysis also has low computation efficiency. When many forces, with the same frequency, act on one vibrating structure, it is hard to decide which one should be improved. On the contrary, by using multi-domain BEM, the sensitivity figure can clearly show which exciting frequency has the greatest influence on acoustic characteristics with lower computational cost. Adopting multi-domain BEM, the expressions of the change of acoustical characteristic with respect to the change of the frequency are presented for exterior problems. The sensitivities of coefficient matrix are computed by analytical differentiation of the discrete Helmholtz integral equation. Finally, several examples are given to demonstrate the validation and availability of the presented method.