Computation of Acoustic Shape Design Sensitivity Using a Boundary Element Method

Numerical acoustic radiation prediction schemes have developed to the point where they can be used to reliably predict the acoustic response of a vibrating structure. However, the objective of many of the applications of these techniques is the design of a best structural/acoustic configuration for a given application. Thus, the acoustic radiation prediction scheme must be incorporated into a design methodology. Traditionally, the most difficult design variables to incorporate into numerical prediction schemes have been those which define the geometry of the configuration, normally referred to as shape variables. In this investigation, a technique for computing the design sensitivity of the radiated pressure solution to shape variables is formulated and verified. The method uses a boundary element implementation of the Helmholtz integral equation. The potential problems at the characteristic nonuniqueness frequencies of the Helmholtz integral equation are also addressed. The technique is verified for several pulsating sphere examples where analytical solutions are available.