约束阻尼结构的改进准则法拓扑减振动力学优化

旨在为减振设计提供理论基础,研究约束阻尼结构拓扑动力学优化。以阻尼材料用量、振动特征方程、模态频率为约束,以多模态损耗因子倒数的加权和最小为目标,建立了约束阻尼结构拓扑优化模型,引入MAC因子控制结构的振型跃阶。在引入质量阵惩罚因子基础上推导出优化目标灵敏度。考虑到优化目标函数的非凸性,采用常规准则法(OC)寻优可能会使拓扑变量出现负值或陷入局部优化,故引入数学规划移动渐近技术对OC法进行改进,从而将全体拓扑变量纳入改进算法的优化迭代全过程。编程实现了约束阻尼板改进OC法拓扑动力学优化并对改进法性能进行了仿真。结果显示,改进算法可得到更合理的约束阻尼层构形,可使结构取得更佳减振效果。研究表明,改进算法迭代稳定性更好、寻优效率更高、更具全域最优性。

Topology optimization of plates with constrained damping based on improved optimal criteria

A dynamic topology optimization for plates with constrained damping was conducted to provide a theoretical basis for vibration reduction design.Taking maximizing plate’s multi-modal loss factor as an objective,and taking amount of damping material,frequency equation and frequency region,and MAC factor as constraints,a topology optimization model was developed.The penalty factors for mass matrix were introduced,and the multi-modal loss factor sensitivity was deduced.Considering optimal objective function being non-convex,using a common optimal criterion might lead to the topological variables to be negative,or the optimization calculation to fall into a local optimization.So a moving asymptotic technique of mathematical programming was adopted to improve the common optimal criterion.With the improved criterion,all topological variables were brought into the optimization process so as to avoid the occurrence of local optimization.Dynamic optimization for the plates based on improved optimal criterion method were simulated.The results showed that a more reasonable constrained damping layer’s configuration is obtained with the improved method and algorithm,the plates with constrained damping achieve a better vibration reduction effect; the improved method has a better iteration stability and a faster optimization speed,and can more effectively provide a global optimal solution.