Design Sensitivity Analysis of Steady-State Acoustic Problems using Boundary Integral Equation Formulation

Abstract

This paper presents an integral equation formulation for design sensitivity coefficients of frequency responses in acoustic problems. The implicit differentiation approach is applied in the derivation of the sensitivity formula. The integral equation relating the pressure at an internal point to the boundary pressures and velocities is regularized and differentiated directly with respect to a design variable such as shape design parameter, frequency, mass density and impedance. The resulting integral equation for the design sensitivity coefficients has no Cauchy principal value integrals and can be applied continuously across the boundary of the acoustic field. The effectiveness of the present formulation is illustrated through some numerical examples for three-dimensional problems.