ACOUSTIC SHAPE SENSITIVITY ANALYSIS USING THE BOUNDARY INTEGRAL-EQUATION

Boundary integral equations are formulated for the shape sensitivity a nalysis of the acoustic problems. The concept of the material derivati ve is employed in deriving the sensitivity equations. Since the equati on 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 fin ite difference method. In addition, the equation has the potential to be applied to many complex acoustic problems, because the derived equa tion is regularized by using the integral identity that incorporates t he one-dimensional propagating wave and its material derivative. The v alidity of the formulations is demonstrated through examples having re gular shapes such as the three-dimensional pulsating sphere and the on e-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 noi se level at the passenger's ear position. The results show that the pr esent method can be an effective tool for the shape optimization in de signing the desired sound field. It is noted that the present method p ermits accurate sensitivities of the acoustic pressure on the boundary as well as at the field points. The present method is thought to be a n alternative to the previous finite difference techniques for computi ng the shape sensitivity using the boundary element method and the for mal derivative method using the finite element method. (C) 1998 Acoust ical Society of America. [S0001-4966(98)02111-0]