A microstructural topology optimization approach for vibro-acoustic interaction systems based on the piecewise constant level set method

Microstructural topology optimization of bi-material for minimizing the responses of exterior vibro-acoustic interaction systems is investigated. The finite element method for structural modeling and the boundary element method for acoustic field modeling are combined to analyze the response of vibro-acoustic systems. The macrostructure is assumed to be composed of periodic microstructures, and the equivalent material properties of the macrostructure are calculated by the homogenization method. A topology optimization approach is developed based on the piecewise constant level set method, and the coupling interface between the structure and the acoustic domain is assumed to be unchanged during the design process. Considering the higher computational efficiency in complex optimization problems with multiple variables compared to the direct differentiation method, adjoint variable method is derived to obtain the sensitivity of the objective function. A new updating formula for the penalty coefficient based on sensitivity information is proposed to overcome its dependence on the observation variables. Numerical results show that the response of the coupled systems can be reduced significantly, indicating the effectiveness of the optimization algorithm. The volume constraints are satisfied under the same optimization parameters in different cases, showing the advantages of the proposed optimization parameter formula.