Abstract:

The dynamic stiffness method is imposed to analyse the vibration problem for rotating tapered beams. Based on Euler-Bernoulli beam theory, the governing equation of free vibration of a rotating tapered beam is derived. Then the dynamic stiffness matrix is developed by using the dynamic stiffness method. Finally, the natural frequencies and corresponding mode shapes of the beam are obtained by using fzero function of MATLAB. The accuracy and effectiveness of the proposed method are verified by numerical calculations. Furthermore, the effect of the hub radius, rotating speed and taper ratio on natural frequency are discussed in detail.

摘要：

通过引入动态刚度法分析旋转变截面梁的振动特性。首先基于欧拉-伯努利梁理论给出旋转变截面梁自由振动方程，然后通过动态刚度法推导该旋转梁的动态刚度矩阵，最后运用MATLAB中的fzero函数求解特征值方程得到旋转梁横向振动的固有频率和模态振型。数值计算结果证明了动态刚度法的精度和有效性，同时分析了轮毂半径、转速以及渐变系数对固有频率的影响。

关键词: 振动与波, 旋转变截面梁, 欧拉-伯努利梁, 固有频率, 弯曲振动