Acoustic Design Sensitivity Analysis and Optimization for Reduced Exterior Noise

Abstract

A program, global acoustic design sensitivity analyzer, is developed that can perform a global acoustic design sensitivity analysis of exterior noise with respect to structural sizing design variables. A system for global acoustic design sensitivity is introduced and implemented numerically by employing the continuum sensitivity analysis. A half-scale automobile cavity model is considered as a numerical example. By using a continuum method, we obtained accurate and efe cient sensitivities when the number of design variables was large. Also, the tendency plotsof element sensitivities and energy contribution for global acousticsensitivities areavailable. Finally, a design optimization was performed to simultaneously reduce the weight and sound pressure level at interesting points and frequencies. I. Introduction T HE range of engineering problems that can be solved through numericalanalyses hasbeen greatlybroadened with the advent of high-speed digital computers. In addition, the development of the e nite element method (FEM)and the boundary element method (BEM) has also been important to engineering analysis. These two typesofanalysesareassociatedwithanalyticalstructure-bornenoise prediction. FEM is commonly used to compute the vibration of the structure emitting noise, and BEM can be used to predict the generated noise. Other methods for acoustic prediction, such as statistical energy analysis, are also available. In this paper, the focus is on FEM and BEM. In a gradient-based optimization scheme, it is important to have accurate gradients (sensitivities ) of the objective function and constraints with respect to the design variables. Formulation of global acoustic sensitivity through chain-ruled derivatives using FEM and BEM has been studied and implemented by many researchers. Coyette et al. 1 have previously investigated the computation and utilizationofacousticsensitivitieswith respecttosizingdesignvariables. Two types of sensitivities were considered. One was acoustic sensitivity with respect to the normal velocity ofvibratingstructure, and the other was structural sensitivity of structural velocities with respect to physical sizing design variables such as thickness. The acoustic sensitivities and structural sensitivities were calculated using BEM and FEM, respectively, and then these sensitivities were combined to obtain a globalacousticsensitivity.In addition,this approach was implemented to the commercial code, SYSNOISE. The same approach was presented in the articles by Cunefare et al., 2;3 who focused on e nding the best optimization formulation by comparing the relative performance and results obtained through the use of several different objective functions and constraints. They obtained acoustic sensitivities and structural sensitivities from the commercial codes NASTRAN and COMET. They also developed COMIN to combine the acoustic and structural sensitivities. Most researchers who studied global acoustic design sensitivity analysis (DSA) and acoustic optimization have used the structural sensitivity analysis module supported by commercial codes and have thus faced limitations in the accuracy and number of design variables. There are several reasons for the limitations of the semianalytical method. First, when the semianalytical method is used forstructural sensitivity analysis, a slight error could occur due to the amount of perturbation. For this paper, we used a continuum approach 4i6 to calculate the structural sensitivity combined with acoustic sensitiv