约束阻尼板的渐进法结构减振拓扑动力学优化

摘要

Structure topological optimization for vibration reduction of constraint damping plates was studied. The dynamic equations for the constraint damping plates were established, and a modal loss factor model for the plates was obtained. A topological optimization model to maximize the modal loss factor with lest viscoelastic damping materials consumption and minimum modal frequency variation as the constraints, was established for the constraint damping plates. The evolutionary structural optimization method was employed to solve the optimization model, and the modal loss factor sensitivity formula was deduced. Independent mesh filter method was introduced to avoid checkerboard appearance. An optimization program was accomplished for damping plate optimizing simulation. Results of simulation show that compared with the non-optimized method, the evolutionary structural optimization was more advantageous for realizing the viscoelastic material optimal layout, and the modal frequency variation was more stable. Harmonic response analysis was carried out for the damping plate to verify the topological optimization method, and the modal loss factor density index was introduced to evaluate the optimization performance. The results of the study show that the constraint damping plates can obtain better vibration suppression effects while the damping materials layout can maximize the modal loss factor. This method has strong practicability and high stability for the optimization design of damping structures.%旨在为结构减振设计奠定一定基础，研究约束阻尼板减振优化问题。建立约束阻尼板动力学平衡方程，推导模态损耗因子计算模型。构建以模态损耗因子最大为目标，黏弹性材料用量及模态频率变动最小为约束的阻尼板拓扑优化数学模型，推导模态损耗因子灵敏度算式。引入渐进结构优化方法对约束阻尼板动力学优化模型进行求解，采用独立网格滤波技术，解决优化迭代中出现的棋盘格问题。编制阻尼板拓扑优化程序，实现约束阻尼板减振优化。仿真显示，与非优化删除方法相比，采用渐进拓扑动力学优化，更有利于实现黏弹材料优化布局，且模态频率变化比较稳定。对阻尼结构进行谐响应分析，以验证拓扑优化方法有效性，引入模态损耗因子体积密度指标以评价阻尼板减振拓扑优化性能。研究表明，若能实现结构模态损耗因子最大化，约束阻尼板减振效果明显。该方法对于约束阻尼板设计具有较强实用性，拥有较高的稳定性。