A three-dimensional formulation for deriving the acoustic shape sensitivity using the boundary element method.

摘要

The improvement of the acoustic behavior of complex systems has acquired great importance in the last decades. In various fields, there is a continuous need to reduce the level of radiated sound. Sensitivity information on how the radiated noise will be modified when a shape parameter of the system is modified can be utilized in determining design changes for noise reduction. The change of the sound level due to changes in the shape and geometry of the radiating object comprises the acoustic shape sensitivity and its analytical development and computational implementation are the main objectives of this Dissertation. The analytical development of the shape sensitivity equations may guide a shape optimization process without the requirement of remeshing the object as necessary in finite difference procedures.; The major contributions of this Dissertation are the analytical formulation, the numerical implementation and the validation of the shape sensitivity equations through analytical differentiation of the Helmholtz equation. The developments are validated by comparing numerical results to analytical solutions for both exterior and interior acoustic analyses.; The new developments are based on a three-dimensional direct boundary element formulation for solving and evaluating numerically the Helmholtz integral equation. The direct boundary element method is a two step process. First, the primary acoustic variables are computed on the surface of the boundary element model. Then, the acoustic response at any field point is evaluated. The computation of the acoustic shape sensitivity is also a two step process. First, the primary system of equations on the surface of the boundary element model is differentiated with respect to the shape design variables and is evaluated. Then, the Helmholtz integral equation for the acoustic response at a field point is differentiated with respect to the shape design variables. Validation of the developments is performed by comparing the numerical results with the analytical solutions for the noise radiated from a pulsating sphere and for a planar wave propagating inside a duct. Good agreement is observed in all validation analyses.