目的 为得到抗振性能良好的板壳结构，保证设备的正常工作，文中提出一种板壳阻尼复合结构多尺度优化设计方法。方法 以动柔度为目标，建立频域激励下和固定频率点激励下板壳阻尼复合结构中阻尼材料宏观分布和微结构协同设计的多尺度问题的数学模型，推导目标函数和约束条件对设计变量的灵敏度，并基于移动渐近线法求解优化数学模型。结果 所提多尺度设计方法可以有效获得板壳结构最优阻尼材料宏观布局和最优阻尼复合材料微结构构型，提高了结构的动力学性能，同时结果也表明涂敷阻尼复合材料结构的振动响应相较于仅涂敷单一阻尼材料的振动响应大幅减小。结论 研究表明，不同激励频率下阻尼材料的宏观分布形态不同，阻尼材料主要分布于结构模态振型位移的最大处和支撑端，通过加强结构的刚度，抑制了结构变形，减小了振动响应。微结构构型基本类似，其基本形态都是低刚度、高阻尼材料呈条状分布，条状分布的阻尼复合材料微结构在受弯方向上的刚度较大，可以有效抵制结构的弯曲变形。

The work aims to propose a multi-scale optimization design method of plate and shell damping composite structure to obtain a plate and shell structure with good anti vibration performance and ensure the normal operation of the equipment. Aiming at dynamic flexibility, a mathematical model of multi-scale problem was established under frequency domain excitation and fixed frequency point excitation. Macro distribution of damping materials and microstructure of plate and shell damping composite structure were collaboratively designed. The sensitivity of objective function and constraint conditions to design variables was derived, and the optimization mathematical model was solved based on the moving asymptote method. The proposed multi-scale design method can effectively obtain the optimal macro layout of damping materials and the optimal microstructure configuration of damping composites for plate and shell structures. It improved the structural dynamic performance. At the same time, the results also showed that the vibration response of the structure coated with damping composites was significantly reduced compared with that coated with only a single damping material. The research shows that the macro distribution of damping materials is different under different excitation frequencies. The damping materials are mainly distributed at the maximum displacement of the structural modal shape and the support end. By strengthening the structural stiffness, the structural deformation is restrained and the vibration response is reduced. The microstructure configuration is basically similar. Its basic morphology is that the distribution of low stiffness and high damping materials is strip-shaped. The strip-shaped damping composite microstructure has a large stiffness in the bending direction of the structure, which can effectively resist the bending deformation of the structure.