Multiscale optimisation of resonant frequencies for lattice-based additive manufactured structures
Multiscale optimisation of resonant frequencies for lattice-based additive manufactured structures
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DOI：
10.1007/s00158-020-02752-8
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发表时间：
2020-12
影响因子：
3.9
通讯作者：
Morgan Nightingale;R. Hewson;M. Santer
中科院分区：
文献类型：
--
作者：
Morgan Nightingale;R. Hewson;M. Santer
本文介绍了一种新的方法，优化的谐振频率在三维晶格结构。该方法使用多尺度方法，其中晶格晶胞的均匀化材料性质由空间变化的晶格参数定义。从小尺度晶格的预先计算的模拟得到的材料特性被投影到响应表面上，从而将大尺度超材料特性描述为小尺度参数的多项式函数。通过对大型有限元模型的特征值分析，得到了结构的共振频率和振型，为推导频率灵敏度提供了依据。通过对谐振频率施加约束以实现顺应性最小化优化来实现频率定制。基于模态保证准则的排序方法允许优化特定的模态振型，同时减少局部模态对优化的影响。三种情况下的频率约束进行了研究，并与无约束优化证明算法的适用性。结果表明，优化是能够处理严格的频率约束，并与使用的模态跟踪，甚至可以改变原来的顺序的谐振模式的形状。频率定制允许通过避免谐振频率和动态应力来改进顺应性最小化的航空航天部件的功能。
This paper introduces a novel methodology for the optimisation of resonant frequencies in three-dimensional lattice structures. The method uses a multiscale approach in which the homogenised material properties of the lattice unit cell are defined by the spatially varying lattice parameters. Material properties derived from precomputed simulations of the small scale lattice are projected onto response surfaces, thereby describing the large-scale metamaterial properties as polynomial functions of the small-scale parameters. Resonant frequencies and mode shapes are obtained through the eigenvalue analysis of the large-scale finite element model which provides the basis for deriving the frequency sensitivities. Frequency tailoring is achieved by imposing constraints on the resonant frequency for a compliance minimisation optimisation. A sorting method based on the Modal Assurance Criterion allows for specific mode shapes to be optimised whilst simultaneously reducing the impact of localised modes on the optimisation. Three cases of frequency constraints are investigated and compared with an unconstrained optimisation to demonstrate the algorithms applicability. The results show that the optimisation is capable of handling strict frequency constraints and with the use of the modal tracking can even alter the original ordering of the resonant mode shapes. Frequency tailoring allows for improved functionality of compliance-minimised aerospace components by avoiding resonant frequencies and hence dynamic stresses.