中文摘要：

基于Euler—Bernoulli梁理论，采用样条有限点法建立旋转变截面梁弯曲振动分析新模型．通过沿梁轴线均匀布置一定数量的样条节点对变截面梁样条离散化，采用三次B样条函数对变截面梁的位移场进行插值．考虑截面尺寸变化和旋转离心刚化效应的影响，基于Hamilton原理推导出旋转变截面梁计算模型的总刚度和总质量矩阵表达式，编制程序对旋转变截面梁动力特性进行分析，并建立ANSYS有限元模型进行比较验证．结果表明：本文解答与文献和有限元解答吻合良好，本文模型具有计算精度好、建模效率高、边界条件简单和程序编制方便的优点，可适用于不同边界约束、截面变化率、截面变化类型、旋转角速度和轮毂半径条件下的旋转变截面梁的弯曲自由振动问题．参数分析表明截面变化率和旋转角速度对旋转变截面梁动力特性有重要影响．

英文摘要：

Based on the Euler-Bernoulli beam theory （EBT）, a new model for free bending vibration problems of rotating tapered beams using spline finite point method （SFPM） was investigated. The beam was discretized by a set of uniformly scattered spline nodes along the beam axis direction instead of me-shes, and the displacement field was approximated by the cubic B-spline interpolation functions. Both of the variations of cross-sectional dimension and the rotating centrifugally stiffened effect were considered in the proposed model, and the global stiffness and mass matrices of the structures were deduced based on the Hamilton principle. Computer programs were compiled to Study the dynamic properties of rotating tapered beams. The finite element model （FEM） for the rotating tapered beams by using ANSYS was also built for validating the proposed model. The results show that the present results agree very well with the results of other reported literatures and the FEM, and the proposed model has the advantages of good computational accuracy, high modeling efficiency, simple boundary conditions, and convenience for compiling computer program. It is capable of studying the free bending vibration of rotating tapered beams with the variation of boundary conditions, taper ratios, cross-sectional types, rotating speeds, and hub radius. Both the taper ratios and rotating speeds have important roles on the dynamic properties of rotating tapered beams through parameter analysis.