弹性薄板绕轴转动时刚-柔耦合动力学非线性分析

从连续介质力学中关于弹性薄板的变形理论出发,讨论绕轴作大范围运动的弹性薄板的动力学性质.由于在无大范围运动的情况下,弹性薄板的变形对系统的动力学性质影响很小而被忽略,而其一旦与大范围运动耦合,对系统的动力学性质产生明显的影响.根据弹性薄板的应变-位移几何非线性关系,建立了作大范围运动弹性薄板的几何非线性动力学方程,然后利用Garlerkin模态截断方法建立了该系统的离散动力学方程,仿真计算验证了理论分析的正确性,从而表明了系统的横向振动是稳定的.

Nonlinear analysis on coupling dynamical of axial rotation of elastic thin plate

With the deformation theory on elastic thin plate in continuum mechanics,this paper investigated the dynamic properties of elastic thin plate rotating around an axis with large overall motions.In the absence of large overall motion,the effects of the deformation of elastic thin plate on the dynamic properties of the system are small and can be neglected.But if the deformation is coupled with large overall motion,its effects on the dynamic properties are significant.This paper established a geometrically nonlinear dynamic equation for elastic thin plate in the case of large overall motion with the strain-deformation geometrically nonlinear relation,and established a dynamic discrete equation of the system with Garlerkin's mode shapes method.Numerical simulation was given to verify the correctness of the theoretical analysis,which showed that the transverse vibration of the system was stable.