匀速旋转刚环-内接柔性梁系统的共振分析

Resonance analysis of internal flexible beam system on steadily rotating ring

研究了旋转刚环-内接柔性梁系统的动力学建模与振动特性。基于浮动坐标系方法,考虑柔性梁由于弯曲变形产生的轴向缩短量,利用有限元法对柔性梁位移场进行插值,推导出柔性梁的动能、应变能和重力做功的表达式,运用第二类拉格朗日原理,建立旋转刚环-内接柔性梁系统的动力学模型。基于该模型分析系统的临界失稳转速,其仿真结果与现有数据以及商业软件ANSYS数值结果相吻合,可验证该模型的正确性。研究表明:系统存在比临界失稳转速小的共振转速,在共振转速时,重力周期性变化频率接近系统的固有频率,梁的振幅随时间的增大而增大;径长比越大,共振转速越小;系统在径长比为1时,无量纲共振转速区间为2.20至2.36,若转速接近共振转速区间,则柔性梁的振幅时而变大,时而变小,产生拍振现象。

In this paper,the dynamic modeling and vibration characteristics of an internal flexible beam system on a steadily rotating ring are studied.The floating frame reference method is adopted,in which the axial shortening of flexible beams due to bending deformation is considered.The displacement field of the flexible beam is interpolated by finite element method,and then the expressions of the kinetic energy,strain energy and work done by gravity can be derived.Using the second kind Lagrange’s equations,the dynamic model of the internal flexible beam system on a steadily rotating ring is established.Based on this model,the critical instability speed of the system is analyzed.The simulation results are consistent with the data in the existing literature and the numerical results obtained from commercial software ANSYS,which can validate this model.Several findings observed clearly in the numerical results are as follows:There is resonance speed of the system which is smaller than the critical instability speed.In the case of the resonance speed,the frequency of gravity periodic change is close to the natural frequency of the system,and then the vibration amplitude of the beam increases with time.The larger ratio of diameter to length will be result in the smaller resonance speed.When the ratio of diameter to length is 1,the resonance speed region is approximately from 2.20 to 2.36.If the speed is close to the resonance speed region,the vibration amplitude of the flexible beam will become larger or smaller from time to time,resulting in beat vibration phenomenon.