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张君茹,程耿东.基于二次型性能指标定轴转动板减振拓扑优化[J].计算力学学报,2022,39(2):135~141
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基于二次型性能指标定轴转动板减振拓扑优化
Topology optimization of vibration reduction of in-plane rotating plate around a fixed hub based on quadratic performance index
投稿时间:2021-01-16  修订日期:2021-02-18
DOI:10.7511/jslx20210116003
中文关键词:  旋转板  残余振动减振  二次指标  拓扑优化  Lyapunov 第二方法
英文关键词:residual vibration reduction  rotating plate  quadratic index  topology optimization  lyapunov second method
基金项目:国家自然科学基金(11821202)资助项目.
作者单位E-mail
张君茹 大连理工大学 工程力学系, 大连 116024  
程耿东 大连理工大学 工程力学系, 大连 116024 chenggd@dlut.edu.cn 
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中文摘要:
      研究在给定材料体积的条件下绕定轴旋转的平板结构的拓扑优化设计,以使受到冲击荷载后平板结构的振动最小,采用积分形式的二次型性能指标为目标函数,以单元人工密度为设计变量建立拓扑优化列式。假定板结构在面内以常速旋转并考虑小应变假设,采用多体动力学理论和有限元方法建立运动微分方程。使用李亚普洛夫第二方法将积分形式的二次型性能指标简化,使用伴随法求解敏度并结合振型叠加法提高分析和优化的效率。数值结果表明,所提出的拓扑优化方法可实现旋转板减振设计,得到与频率拓扑优化有区别的拓扑构型。展示了基于二次型指标的优化解、其拓扑构型的材料分布和基频随转速增加的变化以及边界条件和冲击点或者观察点的位置及板尺寸对优化解的影响。
英文摘要:
      This paper studies topology optimization of a rotating plate around a fixed axis under given material volume to reduce vibration under impact load.A quadratic performance index in integral form is used as the objective function and the artificial densities of finite elements are used as design variables.Considering that the plate structure rotates at a constant speed in the plane and the assumption of small strain,the differential equations of motion are established by using multi-body dynamics theory and the finite element method.Lyapunov’s second method is applied to simplify the objective.Adjoint variable method for sensitivity analysis and mode superposition method are used to improve efficiency.Numerical results show the proposed topology optimization method can reduce the vibration of the rotating plate and the topology configuration is different from that of maximum frequency.Material distribution and the fundamental frequency of the topological configuration change with the increase of the rotational speed.Boundary conditions,location of impact or observation point and plate size have influences on the optimal solution.
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