旋转复合材料薄壁轴的自由振动与稳定性

Free vibration and stability of a rotating thin-walled composite shaft

提出了一个匀速旋转复合材料薄壁轴的动力学模型,研究了轴的自由振动特性与稳定性。从基于变分渐进法(VAM)的复合材料薄壁梁理论出发,在引入横向剪切变形的情况下,采用Hamilton原理推导出旋转坐标系下轴的自由振动控制方程,采用Galerkin法进行模型离散化并编制了近似数值计算程序。揭示了铺层角、旋转速度、长径比、径厚比以及横向剪切对复合材料传动轴振动固有频率和临界转速的影响。计算结果表明:建立的模型能够用于计算旋转复合材料传动轴的动力学特性,通过对模型结果的收敛性验证以及与相关文献的计算结果进行比较,说明了模型的正确性。

A dynamical model of the rotating composite shaft with constant angular speed is presented in this paper.The free vibration and stability of the shaft is studied.A composite thin-walled beam theory based on variational asymptotically approach（VAM）is employed to describe the relationship between the displacement and strain,where the transverse shear deformation effects are considered.The Hamilton principle is used to derive the continuous equations of motion of the shaft.The governing equations are discretized and solved by Galerkin′s method.On the basis of the computing programs complied in Matlab,the effects of fiber orientation,rotating speed and ratios of length over radius,ratios of radius over thickness and the effects of shear deformation on the natural frequency and the critical speeds are investigated.The numerical results show that the model presented in this paper can be used to calculate the dynamic characteristics of the rotating composite shaft.The validity of the model is proved by comparing the results with those in other related literatures and the verification of its convergence.