Abstract: A nonlinear dynamic model of thin rectangular plate rotating around its symmetrical axis with two opposite simply-supported edges and two opposite free edges is established using general Hamilton's Variational Principle. Three lower modes and the critical bifurcation values of the plate are analyzed approximately by employing assumed modes method. The results show that the overall motions can result in dynamic softening in the flexible multi-body system. Furthermore, the same method is also used to investigate the post-buckling behaviour of the plate. The symmetrical stable post-buckling solutions which are developed from the trivial solution through first bifurcation, the asymmetrical stable post-buckling solutions which are developed from the symmetrical post-buckling solutions through the second bifurcation and the antisymmetry unstable post-buckling solutions which are developed from the trivial solution through its second bifurcation are obtained.

Key words: flexible multi-body system, assumed modes method, dynamic softening, bifurcation, buckling

摘要： 应用Hamilton原理建立了轴对称匀速转动状态下对边简支对边自由矩形薄板的非线性动力学方程，采用假设模态法解析分析了板的前3阶近似振动频率、临界分岔值，表明整体运动可使柔性多体系统中的柔性构件产生动力软化效应；进一步采用假设模态法分析了板的后屈曲近似解，分别得到了从稳定平凡解失稳分岔形成的稳定的对称后屈曲解及其二次分岔产生的非对称后屈曲解，以及从不稳定平凡解分岔产生的不稳定的反对称后屈曲解。

关键词: 柔性多体系统, 假设模态法, 动力软化效应, 分岔, 屈曲