基于全局基的滑动梁模型降阶：公式与评估
Model Order Reduction of a Sliding Beam using a Global Basis: Formulation and Evaluation
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中文总结 AI 辅助
针对伸缩结构中滑动梁模型降阶难题，本文构建全局降阶基，由模态矩阵快照经适当正交分解压缩而成，在约束多体形式体系中应用，经验证可减少约90%计算时间，且均方根位移误差低于2%。
中文摘要 AI 辅助
模型降阶通过引入保留重要动态特性的模态坐标来降低机械系统的维度。伸缩结构中的滑动梁带来了根本挑战，固定模态坐标无法捕捉系统特性的演变，模拟过程中更新模态基会使模态坐标含义改变。本文通过为滑动梁构建全局降阶基来应对这一挑战。全局基由模态矩阵形式的快照构建，并使用适当正交分解进行压缩。在具有代数强制约束以允许滑块连续移动的约束多体形式体系中应用降阶。该方法针对具有滑动关节的滑动梁的绝对节点坐标公式进行了验证。研究了快照数量和每个快照的特征模式的不同组合，并展示了误差图。一个具有挑战性的测试案例表明，全局降阶基在将全局降阶引入的均方根位移误差保持在2%以下的同时，将计算时间减少了约90%。
英文摘要
Model order reduction decreases the dimension of a mechanical system by introducing modal coordinates that retain important dynamic characteristics. Sliding beams, as found in telescopic structures, pose a fundamental challenge. Fixed modal coordinates fail to capture evolving system properties, and updating the modal basis during simulation causes modal coordinates to change meaning. The present work addresses this challenge by constructing a global reduction basis for a sliding beam. The global basis is constructed from snapshots in the form of modal matrices and compressed using proper orthogonal decomposition. Reduction is applied within a constraint multibody formalism with algebraically enforced constraints that permit continuous slider movement. The method is validated against an absolute nodal coordinate formulation of a sliding beam with a sliding joint. Different combinations of snapshot quantity and eigenmodes per snapshot are investigated and an error map is shown. A challenging test case involving a highly flexible beam subjected to time-dependent loading and slider movement demonstrates that the global reduction basis reduces computation time by approximately 90% while keeping the root-mean-square displacement error, introduced by the global reduction, below 2%.
