约束阻尼板双线性材料插值法拓扑动力学优化

为减小阻尼板质量并提高减振性能，研究了结构动力学优化技术。构建了以移动常数与模态损耗因子差值为目标、阻尼层单元密度为拓扑变量、阻尼层体积用量及振动模态频率为约束的阻尼板优化模型。利用序列凸规划法构造目标函数的凸性逼近式，采用拉格朗日乘子法解算逼近函数，以获取全局优化的阻尼层布局。利用模态损耗因子与模态应变能的本构关系推导目标函数关于拓扑设计变量的灵敏度，基于K-T条件构造拓扑变量迭代式。引入双线性插值函数惩罚拓扑变量并使其值聚集于0或1，编写并实现了悬臂阻尼板优化程序。当阻尼层体积用量控制在50%时，1阶模态损耗因子增大52.29%，灰度单元占比1.78%。阻尼板谐响应分析表明优化构形具良好减振特性。双线性插值优化既能充分发挥阻尼层的耗能效力又可大幅减少灰度阻尼单元数。

Topological Dynamics Optimization of Constrained Damping Plates Based on Bilinear Material Interpolation Model

Aimed to reduce vibrations and weights， a dynamics optimization method of damping plates was proposed. An optimization model of damping plates was presented taking the difference between a moving constant and the modal loss factor as objective function， density of damping layers elements as design variables， the volume usage of damping materials and the modal frequencies as constraints. A convex approximation function for objective function was provided with sequential convex programming method， and the Lagrange multiplier method was employed to solve the function so that a globally optimized damping layer layout was obtained. The sensitivity of objective function to design variables was derived using the relation of the modal loss factor and modal strain energy， and the iterative formulas of these variables were derived from K-T condition. The bilinear interpolation functions were used to punish the variables to make them converge to 0 or 1. The optimization programs were programmed and implemented for a cantilever damping plate. It is shown that the 1st order modal loss factor increases 52.29% and the proportion of gray element is as 1.78%， when the volume usage of damping materials is limited to 50%. Better vibration suppression property of the optimized plates is demonstrated by harmonic response analysis. The optimized damping layout from bilinear interpolation may make full use of the energy dissipation of damping materials and reduce the number of gray damping elements largely.