Acoustic shape sensitivity analysis using the boundary integral equation

Boundary integral equations are formulated for the shape sensitivity analysis of the acoustic problems. The concept of the material derivative is employed in deriving the sensitivity equations. Since the equation is derived by the direct differentiation of the boundary integrals containing the field values, it is expected that the sensitivity would be computed more effectively and accurately than the conventional finite difference method. In addition, the equation has the potential to be applied to many complex acoustic problems, because the derived equation is regularized by using the integral identity that incorporates the one-dimensional propagating wave and its material derivative. The validity of the formulations is demonstrated through examples having regular shapes such as the three-dimensional pulsating sphere and the one-dimensional duct, for which the analytical solutions are available. As an example for an irregular domain, the two-dimensional model of an automotive interior cavity is dealt with in the view point of the noise level at the passenger's ear position. The results show that the present method can be an effective tool for the shape optimization in designing the desired sound field. It is noted that the present method permits accurate sensitivities of the acoustic pressure on the boundary as well as at the field points. The present method is thought to be an alternative to the previous finite difference techniques for computing the shape sensitivity using the boundary element method and the formal derivative method using the finite element method. (C) 1998 Acoustical Society of America. [S0001-4966(98)02111-0]