非侵入式频谱子流形模型降阶用于几何非线性旋转结构的科里奥利力和离心力
Non-intrusive spectral submanifold model reduction for geometrically nonlinear rotating structures with Coriolis and centrifugal forces
AI总结：
本文提出一种非侵入式频谱子流形模型降阶方法，用于高效准确捕捉旋转结构的非线性振动特性，通过实例验证了该方法在处理科里奥利力和离心力耦合非线性动力学中的有效性。
摘要：
旋转结构在工程应用中广泛存在，如涡轮机械和风力涡轮机。这些旋转结构，特别是由轻质材料制成的叶片，在操作中可能产生大变形，并在几何非线性、科里奥利效应和离心力的耦合作用下表现出复杂的非线性动力学。有限元（FE）方法为捕捉真实旋转结构的复杂非线性动力学提供了强大而准确的建模方法，但其高维性对非线性振动的高效预测构成显著挑战。本文提出了一种非侵入式频谱子流形（SSM）模型降阶方法，用于这些旋转结构的有限元模型。我们使用COMSOL建立有限元模型并模拟这些有限元模型以验证SSM降阶方法的准确性。我们首先计算由离心力引起的非平凡静态平衡，然后非侵入式地构建基于子流形的降阶模型（ROM），并以平衡点为锚点。这些基于SSM的ROM能够高效且准确地提取主路径和强迫响应曲线。我们使用一系列复杂度递增的示例来演示SSM降阶方法的有效性，包括旋转梁、扭曲板、带有两个盘的转子以及具有三个叶片的内部共振风扇。所获得的结果还突显了科里奥利力对旋转结构非线性振动的显著影响。
英文摘要：
Rotating structures are widely observed in engineering applications such as turbomachinary and wind turbine. These rotating structures, particularly for blades made by lightweight materials, can undergo large deformation in operations and display complex nonlinear dynamics under the coupling interaction of geometric nonlinearity, Coriolis effect and centrifugal force. Finite element (FE) methods provide a powerful and accurate modeling approach for capturing the complex nonlinear dynamics for realistic rotating structures, yet its high-dimensionality causes significant challenge to efficient prediction for the nonlinear vibration. Here, we present a non-intrusive spectral submanifold (SSM) model reduction for these FE models of rotating structures. We use COMSOL to establish FE models and simulate these FE models to verify the accuracy of SSM-based reduction. We first compute nontrivial static equilibrium induced by the centrifugal force and then construct non-intrusively SSM based reduced-order model (ROM) anchored at the equilibrium. These SSM-based ROMs enable efficient and accurate extraction of backbone and forced response curves. We use a suite of examples with increasing complexity to demonstrate the effectiveness of the SSM reduction, including a rotating beam, a twisted plate, a rotor with two disks, and an internally resonant fan with three blades. The obtained results also highlight the significant effects of Coriolis force on the nonlinear vibration of rotating structures.
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