Midfrequency Structural/Acoustic Optimization with a Complex Variable Sensitivity Analysis Method

Abstract

In this paper, a design optimization procedure for midfrequency structural/acoustic systems is proposed, based on the statistical modal energy distribution analysis model. In the optimization model, the total energy of the acoustic subsystem is designated as the optimization objective, and the structural mass serves as a constraint condition. The structural thicknesses at different areas are set to be design variables. The optimization model is solved by the globally convergent method of moving asymptotes that need to be provided with the sensitivities of the objective and constraint functions in each iteration. In the sensitivity analysis process, the derivatives of the modal energies of the acoustic subsystem with respect to the structural modal information are deduced in an analytical form. Next, the complex variable method is integrated into the analytical sensitivity formulation in order to calculate the derivatives of the structural modal information with respect to structural thicknesses. Numerical examples are given to demonstrate that the sensitivities of the acoustic subsystem energies obtained by employing the complex variable method are more accurate than by using the traditional semianalytical method and the overall finite difference method. The significant energy reduction of the acoustic subsystem further validates the effectiveness of the proposed optimization procedure.