基于优化准则法的自由阻尼材料拓扑优化

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振动与冲击 ›› 2013, Vol. 32 ›› Issue (14) : 98-102.

论文

基于优化准则法的自由阻尼材料拓扑优化

张志飞1，2，倪新帅2，徐中明1，2，贺岩松1，2，袁琼2，李耀光2

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Topology Optimization of Free Damping Material Based on Optimality Criteria Method

ZHANG Zhifei1, 2, NI Xinshuai2, XU Zhongming1, 2, HE Yansong1, 2, Yuan Qiong 2&Li Yaoguang 2

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摘要

基于各向正交惩罚材料密度法法，建立了以自由阻尼结构模态阻尼比最大化为目标，以阻尼材料体积为约束条件，以阻尼材料单元相对密度为设计变量的拓扑优化数学模型。推导了模态阻尼比对阻尼单元相对密度的灵敏度和设计变量的更新准则，基于优化准则算法用MSC.Nastran的Direct Matrix Abstraction Program语言编制了通用的阻尼材料拓扑优化程序。以一铝板-声腔耦合系统为对象，以结构一阶弯曲模态阻尼比最大为目标，利用该拓扑优化程序和有限元分析方法对铝板上的阻尼材料进行优化布置，并用试验进行了验证。把铝板全阻尼处理和拓扑优化后部分阻尼处理的降噪效果进行对比，在仿真环境中，参考点处声压分别下降了110.6Pa和107.7Pa，在实验条件下，参考点处声压分别下降了22.47Pa和20.91Pa，从而验证了优化方法的有效性。

Abstract

Based on SIMP, a topology optimal model was established with maximum modal damping ratio as goal, damping material volume as restriction and densities of damping cell as design variables. The sensitivity of modal damping ratio to density of damping cell was analyzed, and the updating criterion was derived. Then, the topology optimization program based on optimization criteria algorithm was written using Direct Matrix Abstraction Program of MSC.Nastran. The structure-acoustic coupling model, consisting of aluminum plate and the acoustic cavity, was selected as an example. With this program, the arrangement of the damping material on the aluminum plate was optimized to maximize the damping ratio of the first bending mode by finite element method, which is validated by experiments. These two separate damping treatments: fully damped and partly damped after optimized, was compared with no damp material. After treated, the peak pressure at the reference point was respectively reduced 110.6Pa and 107.7Pa in simulation, while 22.47Pa and 20.91Pa in experiments. The comparison of them indicated the topology optimization program was valid.

导出引用

张志飞;倪新帅;徐中明;贺岩松;袁琼;李耀光. 基于优化准则法的自由阻尼材料拓扑优化[J]. 振动与冲击, 2013, 32(14): 98-102

ZHANG Zhifei;;NI Xinshuai;XU Zhongming;;HE Yansong;;Yuan Qiong &Li Yaoguang . Topology Optimization of Free Damping Material Based on Optimality Criteria Method[J]. Journal of Vibration and Shock, 2013, 32(14): 98-102