轴向运动功能梯度悬臂梁动力学分析

针对轴向运动悬臂梁振动会影响系统的安全性、稳定性问题，对功能梯度悬臂梁振动特性进行分析，利用广义哈密尔顿原理及假设模态法导出系统动力学方程。结果表明，功能梯度悬臂梁的横向位移与轴向位移耦合，功能梯度材料在厚度方向按体积分数函数呈指数变化，且梁自由端有集中质量块。并讨论材料指数及末端集中质量大小对振动影响，分析梁在伸展、收缩时的运动特性。所得结论可为类似结构的动力学分析、设计提供依据。

Dynamic analysis of an axially translating functionally graded cantilevered beam

The axially translating cantilevered beams are widely used in engineering. The vibration of the beams will exert great effect on the safety and reliability of the system. Dynamic analysis of an axially translating functionally graded (FG) cantilevered beam is investigated. The equations of the system are derived by the Hamilton’s principle with the assumed mode method. And the coupled equations of motion are gotten. The properties of FG materials are functionally graded in the thickness direction according to the volume fraction power-law distribution. A tip mass is considered to be concentrated at the free end of the beam. The effects of the power-law exponent and tip mass on the vibration are discussed. Moreover, the movement characteristics of the FG beam during the extension mode and the retraction mode are analyzed. The conclusions of this paper give a basis for dynamic analysis and design of similar structures.