旋转运动柔性梁的假设模态方法研究

ASSUMED MODE METHOD OF A ROTATING FLEXIBLE BEAM

采用假设模态法对旋转运动柔性梁的动力特性进行研究，给出简化的控制模型．首先采用 Hamilton 原理和假设模态离散化方法，在计入柔性梁由于横向变形而引起的轴向变形的二阶耦合量的条件下，推导出基于柔性梁变形位移场一阶完备的一次近似耦合模型，然后对该模型进行简化，忽略柔性梁纵向变形的影响，给出一次近似简化模型，最后将采用假设模态离散化方法的结果与采用有限元离散化方法的结果进行了对比研究．研究中考虑了两种情况：非惯性系下的动力特性研究和系统大范围运动为未知豹动力特性研究．研究结果显示，当系统大范运动为高速时，在假设模态离散化方法中应增加模态数目，较少的模态数目将导致较大误差．一次近似简化模型能够较好地反映出系统的动力学行为，可用于主动控制设计的研究．

In this paper,dynamics of a rotating flexible beam is investigated by the assumed mode method.The simplified control model is presented as well.Based on the Hamilton theory and the assumed mode method(AMM),the first-order approximation coupling(FOAC)model is presented,taking the second-order couplingquantity of axial displacement caused by transverse displacement of the beam into account.The simplifiedfirst-order approximation coupling(SFOAC)model which neglects the effect of axial deformation of a beamis studied.Then,numerical comparisons are made between the results by AMM and FEM.Two cases areconsidered in the simulations.One is the dynamics study in non-inerita system which the large motion of asystem is known,another one is that the large motion of a system is unknown.Simulation demonstrates,thatmore modes are needed in the AMM when the large motion of a beam is high,and less modes may result ina greater error.The SFOAC model is valid for the description of dynamic behavior of a rotating beam,whichcan be used as control model in active control design.