Topology optimization of viscoelastic materials on damping and frequency of macrostructures

Damping and natural frequency are the most important characteristics for evaluating the performance of dynamic structures. This paper proposes a topology optimization algorithm based on the bi-directional evolutionary structural optimization (BESO) method to designing viscoelastic materials. This algorithm optimizes damping and natural frequency of macrostructures by tailoring microstructures of viscoelastic materials. The material microstructures are assumed to be composed of periodic unit cells (PUCs) and the effective properties of the PUC are extracted by the homogenization theory and further integrated into the analysis of the macroscopic structure. To improve the performance of dynamic structures, the inverse homogenization is conducted to seek the best distribution of the base materials within the PUC. Numerical examples are presented to demonstrate the effectiveness of the proposed algorithm, which optimizes the microstructures of viscoelastic cellular or composite materials for 2D and 3D structures.