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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： |
| 中文关键词: 旋转板减振 二次指标 拓扑优化 Lyapunov第二方法 |
| 英文关键词:Vibration reduction of rotating plate Quadratic index Topology optimization Lyapunov second method |
| 基金项目:国家自然科学基金项目（面上项目，重点项目，重大项目） |
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| 中文摘要: |
| 本文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。论文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的增加的变化，边界条件、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 rotating plate around the fixed axis under given material volume to reduce the vibration under impact load. A quadratic performance index in integral form is used as the objective and the artificial density of element is 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 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 rotating plate and the topology configuration is different from that of maximum frequency. Material distribution and fundamental frequency of topological configuration change with the increase of rotational speed. Boundary conditions, location of impact or observation point and plate size have influence on optimal solution. |
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