约束阻尼结构拓扑优化设计的进化算法

约束阻尼结构的阻尼材料优化布局是约束阻尼结构振动控制设计中的关键问题,它直接影响到振动能量耗散与全局能量流分布。在约束阻尼结构设计中引入拓扑优化渐进优化算法,以约束阻尼胞单元为设计变量,建立以模态阻尼比为目标函数,约束阻尼材料用量为约束条件的拓扑优化模型。分析结构模态阻尼比相对于阻尼胞单元位置的敏度,导出灵敏度计算表达式。提出基于渐进优化算法的优化准则,通过逐步删除利用率低的材料,使目标模态阻尼比达到最大化,给出了数值计算的例子,理论计算结果验证了拓扑优化方法的正确性和有效性。

Topology optimization for constrained layerdamping material in structures using ESO method

Topology optimization for constrained damping material in structures is investigated in order to suppress structural vibration through the optimal placement of constrained damping material in structure. A mathematical model to describe the topology optimization problem is established. In the topology optimization approach, structural modal damping ratio is designed as objection function, while constrained damping material consumption is considered as constraint condition. The sensitivity of modal damping ratio to the place is analyzed. An evolutionary criterion for placement of constrained damping material in a structure is presented. The formula of sensitivity is derived and used to determine the optimized placement of constrained damping material in structure. The topology optimization problem is further solved by evolutionary structural optimization (ESO) method. The numerical examples are given. The results show that a stable and dramatic increase of the modal damping ratio during the course of iterations can be observed. Therefore, an optimal layout of constrained damping material in structure is obtained. The comparison of amplitude frequency characteristics with the optimal and fully covered layout validates the effectiveness of proposed topology optimized approach.