受初应力作用的轴向运动功能梯度梁的动力学分析

基于Euler梁模型研究了初始应力作用下轴向运动功能梯度材料梁的横向振动问题。假设材料性质沿梁的厚度方向按幂指数形式连续变化,利用Hamilton原理建立了系统的控制方程,应用复模态法求得了其固有频率和模态函数,接着分析了轴向运动速度、梯度指数、初应力大小等因素对梁的动力响应的影响。结果表明：梯度指数和轴向速度的增大都会导致固有频率降低,轴向初应力的增大则使得固有频率升高。

DYNAMIC ANALYSIS OF AXIALLY MOVING FUNCTIONALLY GRADED BEAMS SUBJECTED TO INITIAL STRESS

Based on Euler beam theory, the transverse vibration of an axially moving, initially tensioned beam made of functionally graded materials is investigated. The material properties are assumed to vary continuously through the thickness of the beam according to a power law distribution. The Hamilton’s principle is employed to derive the governing equation and the complex mode approach is performed to obtain the transverse vibration modes and natural frequencies, respectively. The effects of some parameters including axially moving speed, the power-law exponent and the initial stress on the dynamic responses are examined and revealed in detail. The results show that an increase in the power-law exponent or the axial speed results in a lower natural frequency, while the axial initial stress tends to increase the natural frequency.