基于本征正交分解的网格加筋筒壳模型降阶方法

针对网格加筋筒壳结构动力响应分析效率低的问题，本文提出了一种基于本征正交分解技术的模型降阶方法。基本思路是通过静力分析获得原模型的节点位移场并组装成快照矩阵，利用本征正交分解技术提取快照矩阵的主成分作为转换矩阵，实现模型降阶。通过算例对比验证了本文提出的降阶模型具有较高的计算精度及效率，降阶模型的低阶频率计算结果与全阶模型十分吻合，高阶频率误差仅为1.01%，而计算时间为全阶模型的0.03%。最后以自由-固支的网格加筋筒为例，采用降阶模型计算其在不同激励下的振动响应，计算结果与全阶模型非常吻合，降阶模型的单个频响分析的计算效率有显著提升。

A model reduction method based on proper orthogonal decomposition for stiffened shells

Stiffened shells have been widely utilized in the fuel tank and in launch vehicles due to high specific stiffness and strength. Since these structures are subjected to complex dynamic loads, reliable prediction of natural vibration characteristics is essential in preventing excessive vibration levels, which may result in failure or very high noise levels. The natural frequency of a system is calculated via high fidelity model, such as using the finite element (FE) method, however, the detailed FE model has a very high computational cost. In order to obtain frequency of these complex structures accurately and efficiently, reduced order models (ROMs) are used as substitution to decrease the computational expense. This paper presents a model reduction method based on proper orthogonal decomposition technique (POD). The basis idea is to extract the principal component as the transformation matrix from the correlation matrix assembled by nodal displacement field of full order models (FOMs) subjected to different cross-section loads. The relationship between the ability of ROMs to predict mode shapes of interest and cross-section loads is investigated by a clamped-clamped stiffened shell, and the accuracy and efficiency of the proposed model reduction method are also validated by this example. Numerical results show that the maximum frequency error is about 1.01% and the computational time is only 0.03% of the associated FOM. Finally, a free-clamp stiffened shell subjected to harmonic external force is studied and the frequency response function is calculated through FOM and associated ROM. The number of degrees of freedom reduces from 48960 to 480 and average calculation time at each frequency point is only 0.04s for ROM and 4.65s for the associated FOM. And the displacement response in frequency range shows good agreement between the FOM and ROM.