Topology Optimization Design of Resonant Structures Based on Antiresonance Eigenfrequency Matching Informed by Harmonic Analysis
Topology Optimization Design of Resonant Structures Based on Antiresonance Eigenfrequency Matching Informed by Harmonic Analysis
复制标题
基于谐波分析的反谐振特征频率匹配的谐振结构拓扑优化设计
DOI：
10.1115/1.4062882
复制
发表时间：
2023
影响因子：
3.3
通讯作者：
Frecker, Mary
中科院分区：
文献类型：
--
作者：
Giraldo Guzman, Daniel;Lissenden, Clifford;Shokouhi, Parisa;Frecker, Mary
在本文中，我们提出了一种结合本征频率匹配方法和基于谐波分析的本征模式识别策略来设计具有特殊动力响应的共振结构的方法。这种基于拓扑优化的系统设计方法，为在特定谐波载荷作用下需要在特定目标频率处产生反共振的三维动力学问题提供了一种新的计算高效的方法。优化的目标函数使目标反共振频率和实际结构的反共振特征频率之间的误差最小化，而基于谐波分析的识别策略使用模态保证准则将简谐位移响应与特征向量进行比较，从而确保准确识别和选择在优化过程中使用的适当的反共振特征模式。同时，该方法有效地防止了本征模在低密度区的局域化、本征模的切换顺序、重复本征频等本征频率拓扑优化中的常见问题。此外，我们提出的局域本征模识别方法通过分析低密度区与高密度区的特征向量的响应，完全消除了优化问题中的虚假本征模。拓扑优化问题采用基于密度的参数化方法，并采用基于梯度的序列线性规划方法进行求解，其中包括材料内插模型和拓扑过滤器。两个实例研究表明，在不同的简谐载荷、设计区域尺寸、网格离散化或材料特性的作用下，所提出的设计方法成功地在期望的目标频率处产生反共振。
In this article, we present a design methodology for resonant structures exhibiting particular dynamic responses by combining an eigenfrequency matching approach and a harmonic analysis-informed eigenmode identification strategy. This systematic design methodology, based on topology optimization, introduces a novel computationally efficient approach for 3D dynamic problems requiring antiresonances at specific target frequencies subject to specific harmonic loads. The optimization’s objective function minimizes the error between target antiresonance frequencies and the actual structure’s antiresonance eigenfrequencies, while the harmonic analysis-informed identification strategy compares harmonic displacement responses against eigenvectors using a modal assurance criterion, therefore ensuring an accurate recognition and selection of appropriate antiresonance eigenmodes used during the optimization process. At the same time, this method effectively prevents well-known problems in topology optimization of eigenfrequencies such as localized eigenmodes in low-density regions, eigenmodes switching order, and repeated eigenfrequencies. Additionally, our proposed localized eigenmode identification approach completely removes the spurious eigenmodes from the optimization problem by analyzing the eigenvectors’ response in low-density regions compared to high-density regions. The topology optimization problem is formulated with a density-based parametrization and solved with a gradient-based sequential linear programming method, including material interpolation models and topological filters. Two case studies demonstrate that the proposed design methodology successfully generates antiresonances at the desired target frequency subject to different harmonic loads, design domain dimensions, mesh discretization, or material properties.