Design Sensitivity Analysis of Structure-Induced Noise and Vibration

Abstract

A continuum design sensitivity analysis (DSA) method for dynamic frequency responses of structural-acoustic systems is developed using the adjoint variable and direct differentiation methods. A variational approach with a non-self-adjoint operator for complex variables is used to retain the continuum elasticity formulation throughout derivation of design sensitivity results. It is shown that the adjoint variable method is applicable to the variational equation with the non-self-adjoint operator. Sizing design variables such as the thickness and cross-sectional area of structural components are considered for the design sensitivity analysis. A numerical implementation method of continuum DSA results is developed by postprocessing analysis results from established finite element analysis (FEA) codes to obtain the design sensitivity of noise and vibration performance measures of the structural-acoustic systems. The numerical DSA method presented in this paper is limited to FEA and boundary element analysis (BEA) is not considered. A numerical method is developed to compute design sensitivity of direct and modal frequency FEA results. For the modal frequency FEA method, the numerical DSA method provides design sensitivity very efficiently without requiring design sensitivities of eigenvectors. The numerical method has been tested using passenger vehicle problems. Accurate design sensitivity results are obtained for analysis results obtained from established FEA codes.