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| 受简谐基础激励作用的结构频响拓扑优化 |
| Structural topology optimization considering frequency response subject to harmonic base excitations |
| 投稿时间：2024-01-17 修订日期：2024-03-01 |
| DOI： |
| 中文关键词: 简谐基础激励 拓扑优化 频响振幅 灵敏度分析 广义模态截断扩增法（GMTAM） |
| 英文关键词:harmonic base excitation topology optimization frequency response amplitude sensitivity analysis Generalized Modal Truncation Augmentation Method(GMTAM) |
| 基金项目:国家重点研发计划,国家自然科学基金项目（面上项目，重点项目，重大项目）,中国华能集团科技项目 |
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| 中文摘要: |
| 本文研究了在简谐基础激励作用下的频响拓扑优化问题。首先，推导了结构在简谐基础激励作用下的动力学控制方程；其次，在人工变密度法的框架下基于伴随法推导了结构指定位置的频响振幅的灵敏度列式，并应用RAMP模型以抑制局部模态问题。在结构响应分析和灵敏度计算环节使用广义模态截断扩增法（GMTAM）以兼顾计算成本与精度。通过典型数值算例中验证了本文灵敏度列式的正确性，并进一步考虑了一致与非一致两类基础激励情况下的拓扑优化问题，并对拓扑优化模型进行了讨论，优化结果验证了所提出方法的有效性。 |
| 英文摘要: |
| This study investigated dynamic topology optimization under harmonic base excitations. The dynamic control equation under harmonic base excitations was derived. Within the framework of the artificial variable density method, the sensitivity analysis of the steady-state frequency response amplitude at a designated position in the structure was formulated using the adjoint method. The RAMP model was adopted to suppress localized mode issues. For the purpose of reducing computational costs without compromising result accuracy, the Generalized Modal Truncation Augmentation Method(GMTAM) was introduced in the analysis process of structure responses and sensitivities. Numerical examples first validated the correctness of the derived sensitivity analysis formulation. Topology optimization problems under both uniform and non-uniform base excitations were then considered, where the topology optimization model was also discussed. The optimization results verified the effectiveness of the proposed method. |
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