Abstract In this paper, a novel reduction method for planar flexible mechanisms based on global flexible modes is proposed. Using the framework provided by the finite-element floating frame of reference formulation (FE-FFRF), the global flexible modes of a planar mechanism are derived from the linearized modal equations of motion at a given linearization point. The global flexible modes are consistent with the reference conditions necessary to prevent rigid body motions of the finite elements inside their floating frames of reference. Furthermore, the global flexible modes satisfy the multibody joints constraints of the mechanism. These features make the global flexible modes eligible to be used as local normal modes for the reduction of single components. In this first use, referred to as the GNMC, the global modes are employed to substitute the normal modes obtained using the conventional normal mode approach. In the second use, referred to as the GNMS, the global flexible modes impose global shapes to the whole mechanism allowing for a global reduction of the flexible coordinates. Two benchmark problems are reported to show the feasible applications of the proposed method. The numerical results of the global method are compared to those coming from the models without reduction and from the models reduced through the normal mode approach and the Craig-Bampton method.

中文翻译：

---

使用参考公式的有限元浮动框架的平面机构模型简化的全局灵活模式

摘要 本文提出了一种基于全局柔性模态的平面柔性机构约简方法。使用有限元浮动参考框架 (FE-FFRF) 提供的框架，平面机构的全局柔性模式是从给定线性化点的线性化模态运动方程导出的。全局柔性模式与防止有限元在其浮动参考系内发生刚体运动所需的参考条件一致。此外，全局柔性模式满足机构的多体关节约束。这些特性使全局灵活模式有资格用作减少单个组件的局部正常模式。在第一次使用中，称为 GNMC，使用全局模式来替代使用常规正常模式方法获得的正常模式。在称为 GNMS 的第二种用途中，全局灵活模式将全局形状强加给整个机制，从而允许全局减少灵活坐标。报告了两个基准问题以显示所提出方法的可行应用。将全局方法的数值结果与来自未经简化的模型以及通过正常模式方法和 Craig-Bampton 方法简化的模型的结果进行比较。报告了两个基准问题以显示所提出方法的可行应用。将全局方法的数值结果与来自未经简化的模型以及通过正常模式方法和 Craig-Bampton 方法简化的模型的结果进行比较。报告了两个基准问题以显示所提出方法的可行应用。将全局方法的数值结果与来自未经简化的模型以及通过正常模式方法和 Craig-Bampton 方法简化的模型的结果进行比较。