Vibro-acoustic design of plate using bi-material microstructural topology optimization

This study presents a microstructural topology optimization-based method for dealing with the problem of minimizing the sound power flow that radiates from a vibrating composite plate. The plate is assumed to be constructed with periodic microstructures that are uniformly distributed over the macrostructural domain. The design variable in this case is the relative material volume density of the unit cell of the microstructure. The equivalent macromaterial properties of the microstructure are calculated using the homogenization method, and the bi-material solid isotropic material with penalization model is employed to achieve a zero-one design at a microscale. The high frequency approximation formulation and the weak coupling assumption are adopted to achieve an efficient overall analysis and sensitivity analysis of the coupling system. The proposed method is validated by several numerical examples. Results show that effective vibroacoustic isolation may be implemented by the topology design of periodical microstructures.