旋转Timoshenko梁的动力学分析

针对旋转Timoshenko梁结构,在梁的纵向、横向变形中均考虑横向弯曲以及轴向伸缩的耦合作用,同时在横向弯曲中考虑剪切变形的影响,在柔性梁的2个变形方向上均考虑了变形的二次耦合项,并充分考虑轴向离心力、横向惯性力的作用,利用有限元方法进行离散并利用Hamilton原理建立非线性变形模式下的一种新的Timoshenko梁动力学方程。对一平面旋转梁进行仿真计算,通过分析不同情况下的频率与端点变形位移,说明耦合作用的"软化"效果,以及轴向离心力、横向惯性力对模型的影响。

Dynamic Analysis of Rotating Timoshenko Beams

In this paper, a rotating Timoshenko beam is investigated. The effect of shear deformation is included into flexural deflection. Then, considering the coupling effects of deformations in the extensional and flexural deflection, the second-order coupling terms of deformations in two displacement fields are developed. At the same time, the axial inertial force and transverse distributed force are considered. The new governing differential equations of the beam in the geometrically non-linear kinematics of deformation are derived using finite element technique and Hamilton’s principle. Numerical examples of a rotating Timoshenko beam are studied to analysis the frequency and tip deflection of the proposed methods, and to investigate the effect of axial inertial force and transverse distributed force and the 'softer effects’ resulting form the coupling effect, with different angular velocities and high-length ratios.