最优阻尼复合结构应该是阻尼材料自身的材料性能和阻尼材料在板壳结构上的分布形态均是最优的。针对板壳阻尼复合结构的多尺度设计问题，建立了基于非比例阻尼模型的复合结构多尺度拓扑优化方法，实现了阻尼材料在宏微观两尺度上的协同设计，同时获得最优的阻尼材料宏观分布形态和微观构型。以结构模态阻尼比为目标，分别研究了复合结构的单目标和多目标多尺度设计问题。结果表明，在单目标设计中，当最大化结构的某一阶模态阻尼比时，优化后结构的该阶模态阻尼比最大，同时结构在该阶处的频率响应最小；在多目标设计中，以结构前3阶模态阻尼比之和为目标，虽然在每一阶处的性能劣于单目标设计结果，但是结构前3阶模态阻尼比的总体性能更优。同时，从微结构的构型可得，最优的微结构构型中低刚度高阻尼材料的分布相互连接，其损失模量（微结构复弹性矩阵的虚部）和阻尼因子（微结构复弹性矩阵的虚部与实部之比）都相对较高，且呈现负泊松比现象。优化后复合结构的动力学性能显著提高。
For the purpose of reducing vibration of thin-walled structures, the use of damping material is one of the most effective and robust approaches. Damping performance of the thin-walled damping composite structures mainly depends on the damping material layout and its material physical properties. This paper proposes a concurrent topology optimization method for the design of the thin-walled damping composite structures based on non-proportional damping model. In this method, both the microstructural configurations and their macroscopic distribution are optimized in an integrated manner. In order to maximize the structural damping performance, the single-objective and multi-objective concurrent topology optimization problem are studied. The results show that, for the single objective design, when the k-th modal loss factor is set to be the objective function, the damping at k-th Eigen mode is maximum and the amplitude of frequency response function at the k-th natural frequency is minimum. However, the multi objective design obtains a better equilibrium in the lowest 3 modes and shows good vibration performance in the 1-3 modes. From the microstructure layout, it can be found that the optimal microstructure has relatively great loss moduli and high material loss factor, and it also presents a negative Poisson’s ratio. The structural vibration performance of the optimal composite structure is significantly improved.
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