旋转柔性梁的动力学建模及分析

基于一次近似理论，采用弧坐标分量和Cartesian坐标分量共同描述柔性梁的变形场，并采用Green应变张量描述应变能，用Hamilton原理建立系统动力学方程。揭示产生动力刚化现象的力学本质。采用有限元方法进行离散，基于数值实验系统地研究旋转柔性梁的动力刚化现象。计算表明，旋转柔性梁的横向固有频率随旋转角速度和中心刚体半径的增大而增大．从而只存在一阶临界转速，且当中心刚体半径超过临界半径时．不存在临界转速。

Dynamic modelling and analysis of a rotating flexible beam

Based on the first-order approximation method(FAM),a non-Cartesian variables and a Cartesian variable s and a Cartesian u_2,which denote the arc-length stretch and the transverse displacement respectively,are employed to describe the deformation of the beam.The equation of the strain energy is then derived by adopting Green strain theory.The governing partial differential equations deduced from Hamilton's principle are discretized via two-node beam elements.Then,the dynamic stiffening effects are investigated for the variations of rotating speed and hub radius.It is shown that the bending natural frequencies increase as the angular speed increases,and the increasing rates become larger as the hub radius become larger.It is demonstrated that there exists only the first order critical rotating speed and a critical hub radius,above which no first order critical rotating speed exists.