论文标题
通过光谱亚策略的约束机械系统的模型降低
Model reduction for constrained mechanical systems via spectral submanifolds
论文作者
论文摘要
动态系统通常与其管理的普通微分方程相结合的代数约束。特别是，多体系统通常受到构型约束的约束，这些结构定义了不同物体运动之间的运动学兼容性。对这种约束问题的全面数值模拟是具有挑战性的，这使最重要的是减少订购模型（ROM）。在这项工作中，我们展示了如何使用频谱子策略（SSM）来构建具有配置约束的机械系统的严格ROM。这些基于SSM的ROM可以直接提取主链曲线和强制响应曲线，并促进有效的分叉分析。我们在几个不同复杂性的示例中演示了这种基于SSM的还原程序的有效性，包括多体系统的非线性有限元模型。我们还提供了所提出方法的开源实现，其中还包含我们数值示例的所有细节。
Dynamical systems are often subject to algebraic constraints in conjunction to their governing ordinary differential equations. In particular, multibody systems are commonly subject to configuration constraints that define kinematic compatibility between the motion of different bodies. A full-scale numerical simulation of such constrained problems is challenging, making reduced-order models (ROMs) of paramount importance. In this work, we show how to use spectral submanifolds (SSMs) to construct rigorous ROMs for mechanical systems with configuration constraints. These SSM-based ROMs enable the direct extraction of backbone curves and forced response curves, and facilitate efficient bifurcation analysis. We demonstrate the effectiveness of this SSM-based reduction procedure on several examples of varying complexity, including nonlinear finite-element models of multi-body systems. We also provide an open-source implementation of the proposed method that also contains all details of our numerical examples.
