Topology optimization of composite macrostructures comprising multi-phase viscoelastic composite microstructures for enhanced structural damping

Structural damping is the most important characteristic for evaluating the vibration suppression performance of engineering structures. This paper proposes a dynamic topology optimization method for designing a composite macrostructure containing a multiphase viscoelastic composite material microstructure layer. The method optimizes the macrostructure damping performance, which is indicated by the modal loss factor, in the multiphase microstructural configuration design process. The damping layer is assumed to be constructed from a viscoelastic composite material, and viscoelastic composite material microstructures are composed of a high-stiffness material and a high-damping material. The effective properties of the viscoelastic composites were homogenized and integrated into the macrostructure analysis. Design variables were assigned for each microstructure to implement topology optimization on each viscoelastic material microstructure. Sensitivity analysis was performed to compute the derivatives of structural damping with respect to each design variable. Several numerical examples were conducted to demonstrate the effectiveness of the proposed approach. Various optimized structures were obtained using varying objectives and volume fractions. The numerical example results show that the proposed method is effective for designing a composite structure with multiphase viscoelastic composite materials for maximizing the modal loss factor. The structural vibration performance of the optimal composite structure was significantly improved.