摘要
根据哈密尔顿原理建立旋转梁的弯曲振动方程,运用有限差分方法对旋转梁的动力方程进行离散处理,得到旋转梁的质量和刚度矩阵。借助MATLAB振动工具箱对系统的弯曲振动进行模态分析,得到圆形、矩形和叶片类型三种变截面旋转梁的固有频率,并与相关文献进行比较。在差分离散矩阵的基础上,建立旋转梁的线性定常状态空间方程。运用MATLAB振动工具箱对旋转梁的自治系统和非自治系统进行仿真,分别求得旋转梁的时间位移曲线和相轨迹。最后对非自治系统的旋转梁进行频域分析,得到幅频特性和相频特性曲线。
The bending vibration equations of rotating tapered beams are established based on Hamilton’s principle. The equations are then discretized by using finite difference method and the mass and stiffness matrices are gotten. The natural frequencies for circular, rectangular and blade cross-section beams are obtained by using MATLAB vibration toolbox. The results of computation are analyzed and compared with those in relevant references. The linearized stationary state spaces of autonomous and non- autonomous systems are built based on the mass and stiffness matrices. Then the displacement curves and phase tracks of the rotating tapered beams are drawn with MATLAB vibration toolbox. Finally the amplitude-frequency and phase-frequency characteristic curves for the non-autonomous rotating tapered beams are plotted based on the frequency-domain analysis.
出处
《噪声与振动控制》
CSCD
2014年第3期6-10,14,共6页
Noise and Vibration Control
关键词
振动与波
变截面
旋转梁
有限差分
固有频率
状态空间
vibration and wave
taper
rotating beams
finite difference
natural frequency
state space
