平动柔性矩形薄板的动力学特性与屈曲分析

应用Hamilton变分原理建立了平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，分别应用假设模态法和康特洛维奇法分析了板的前4阶近似振动频率、临界分岔值及板的前3阶后屈曲近似解，并比较了取不同阶数假设模态对分析结果的影响．分析表明整体平动可使柔性多体系统中的柔性构件产生动力刚化和动力软化效应，且软化效应还可使系统平衡位置发生分岔而失稳；在动力刚化和动力软化情况下，柔性构件模态出现的顺序均可能发生改变，此性质在柔性多体系统动力学简化建模特别是模态截断时应引起足够的重视．

DYNAMIC AND BUCKLING ANAYSIS OF A FLEXIBLE TRANSLATING RECTANGULAR PLATE

The present work establishes a nonlinear dynamic model of a thin translating rectangular plate with two opposite simply supported edges and two opposite free edges by employing Hamilton's variational principle. Four lower vibration frequencies and critical bifurcation values and three former post buckling solutions of the plate are analyzed by employing the assumed modes method and Kantorovich method respectively. The dependence of frequencies and the critical bifurcation values on the numbers of assumed modes is also discussed. The results show that the overall translating motions can result in dynamic stiffening and dynamic softening in the flexible multi body system, and dynamic softening can make the equilibrium of flexible components lose its stability through bifurcation. Furthermore, sequences of modes of flexible components can be changed by dynamic softening and dynamic stiffening. This phenomenon should be noted enough when simplifying models of the flexible multi body systems, especially when truncating the modes.