The dynamic characteristics of a hub-functionally graded material beam undergoing large overall motions are studied. The deformation field of the flexible beam is described by using the assumed mode method (AMM), the finite element method (FEM) and the point interpolation method (PIM). Assuming that the physical parameters of functionally graded materials follow certain kind of power law gradient distribution and vary along the thickness direction. The longitudinal deformation and transversal deformation of the beam are both considered, and the nonlinear coupling term which is known as the longitudinal shortening caused by transversal deformation is also taken into account. The rigid-flexible coupling dynamics equations of the system described by three different discrete methods which have a uniform form are derived via employing Lagrange’s equations of the second kind. The validity of the point interpolation method established in this paper is verified by comparing with the numerical simulation results of the assumed mode method and the finite element method. On this basis, the influence of the functional gradient distribution rules on the dynamic characteristics of flexible beams undergoing large overall motions is discussed. The results show that the assumed mode method cannot deal with large deformation problem. Remaining other physical parameters of functionally graded materials beam unchanged, the maximum displacement of the beam increases with the increase of functionally graded materials index. The natural frequency of transverse bending of beam increases with the increase of rotational speed, when rotational speed is constant, the natural frequency will decrease with the increase of functional gradient index.

研究了轮毂功能梯度材料梁在进行大整体运动时的动力学特性。采用假设模态法(AMM)、有限元法(FEM)和点插值法(PIM)描述柔性梁的变形场。假设功能梯度材料的物理参数遵循某种幂律梯度分布，沿厚度方向变化。考虑了梁的纵向变形和横向变形，还考虑了横向变形引起的纵向缩短非线性耦合项。利用第二类拉格朗日方程，推导出了由三种不同离散方法描述的具有统一形式的系统刚柔耦合动力学方程。通过与假设模态法和有限元法的数值模拟结果对比，验证了本文建立的点插值法的有效性。在此基础上，讨论了函数梯度分布规律对大整体运动柔性梁动态特性的影响。结果表明，假设模态法不能处理大变形问题。在功能梯度材料梁的其他物理参数不变的情况下，梁的最大位移随着功能梯度材料指数的增加而增加。