Multi-scale optimization design of viscoelastic damping sandwich plate

Aiming at the optimization design problem of viscoelastic damping sandwich plate under the background of lightweight, a multi-scale optimization design method is proposed to realize the collaborative optimization design of viscoelastic damping sandwich plate in both macro and micro scales. It is assumed that the viscoelastic damping material is microscopically composed of 3D periodic unit cells. The effective constitutive matrix of the unit cell is derived using the homogenization method. The topology optimization model is established, and sensitivity analysis is conducted. The iteration of the design variables is realized by the Optimization Criterion (OC) method. Several numerical examples are presented to demonstrate the effectiveness of the proposed multi-scale optimization method. In-depth discussions are given for the impact of optimization objectives and volume fractions on the design results. The results show that the optimized configuration on both scales are dependent on the objective mode. The macroscopic optimal layout is affected by the microscopic volume fraction, while the change in macroscopic volume fraction has little effect on the microscopic optimal configuration. The dynamic characteristics of the viscoelastic damping sandwich plate are improved significantly through multi-scale optimization design.