Design optimization of mid-frequency vibro-acoustic systems using a statistical modal energy distribution analysis model

In the past decades, many researches have been done on the design optimization of low- and high-frequency vibro-acoustic systems. However, the work of mid-frequency vibro-acoustic systems was rarely reported. As an improved statistical energy analysis (SEA), statistical modal energy distribution analysis (SmEdA) is based on the power balance between modes in different subsystems and extends SEA to mid-frequency range. In this article, an optimization procedure for mid-frequency vibro-acoustic systems based on SmEdA is presented. First, a vibro-acoustic system can be decoupled by using the dual-modal formulation (DMF) into a structural subsystem and an acoustic subsystem. Then, the optimization model is built by designating the total energy of the acoustic subsystem as objective function and the structural thicknesses as design variables. Finally, the optimal solution is obtained by using the method of moving asymptotes (MMA) which need to be provided with the gradient information of the objective and constraint functions in each iteration. Therefore, a sensitivity analysis about the total energy of the acoustic subsystem with respect to the thicknesses of the structures surrounding the interior acoustic cavity is performed by adopting a semi-analytical method. Moreover, a coefficient condensation technique is introduced in the sensitivity analysis to avoid the dimensional inconformity of the coefficient matrices in SmEdA due to the variation of the number of modes with the perturbation of structural sizes. Numerical examples are given to validate the effectiveness of the optimization procedure.