Microstructural topology optimization of structural-acoustic coupled systems for minimizing sound pressure level

The aim of this paper is to present a microstructural topology optimization methodology for the structural-acoustic coupled system. In the structural-acoustic system, the structure is considered to be a thin composite plate composed of periodic uniform microstructures. The discrete design variables are used in the microstructural topology optimization, and the constitutive matrix is interpolated by the power-law scheme at the micro scale. The equivalent macro material properties of the microstructure are computed through the homogenization method. The design objective is to minimize the sound pressure level (SPL) in an interior acoustic medium. The sensitivities of the SPL with respect to design variables are derived. The bi-directional evolutionary structural optimization (BESO) method is extended to solve the structural-acoustic coupled optimization problem to find the optimal material distribution of the microstructure. Numerical examples of a hexahedral box and an automobile passenger compartment are given to demonstrate the efficiency of the presented microstructural topology optimization method.