Abstract:

For the beam with simple and flexible supports, a nonlinear dynamic model is established by applying the flexible multi-body dynamic theory. The model can describe both the global rotation and the relative deformation of the beam. The modal and axial-compressive stability of the system are investigated by using analytical and numerical method, and the effect of the movable support stiffness are obtained. The results show that there is great influence on the lower-order frequencies, vibration shape and the buckling mode of the system while the movable support stiffness is smaller than the beam. In this case, they behave to the global rotation characteristic and the lower-order vibration shape in the floating coordinate system is also different to the classical beam, which is affected by the global rotation. However, when the movable support is very stiff, the influence on the lowerorder frequencies, vibration shape and the buckling mode of the system are extremely slight and the uncertainty of the movable support stiffness only lightly affects the higher-order frequencies and vibration shape of the system. The results are important to the constraint boundary design of the beam and the application of the flexible multibody dynamic theory.

Key words: flexible multi-body systems, simply-supported beam, boundary flexibility, modal analysis, stability

摘要：

针对可移动简支具有挠性/不确定性的简支梁系统, 采用柔性多体系统动力学相对描述方式, 建立可描述其整体转动和相对变形的非线性动力学模型, 解析结合数值分析了可移动简支刚度对系统模态和轴向压缩稳定性的影响。研究表明, 简支梁可移动简支刚度相对梁刚度偏小时, 对系统低阶频率、低阶振型和失稳模式影响显著, 主要体现在梁的整体转动特性上, 且相对描述方式中的低阶振型也与经典梁的模态不同, 体现了整体运动对相对变形模态的影响特性; 简支梁可移动简支刚度相对梁刚度偏大时, 主要对系统高阶频率和振型有一定影响, 而对低阶频率、振型和失稳模式的影响很小。此研究成果和认识对于梁构件约束边界设计与柔性多体动力学理论的应用具有重要意义。

关键词: 柔性多体系统, 简支梁, 边界挠性, 模态分析, 稳定性