Modeling and analysis of an axially acceleration beam based on a higher order beam theory
Modeling and analysis of an axially acceleration beam based on a higher order beam theory
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DOI：
10.1007/s11012-018-0840-4
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发表时间：
2018-03
期刊：
影响因子：
2.7
通讯作者：
Yuanbin Wang;H. Ding;Liqun Chen
中科院分区：
文献类型：
--
作者：
Yuanbin Wang;H. Ding;Liqun Chen
本文提出了轴向加速光束的高阶模型方程。 基于一种新的梁的运动学坐标系和连续介质力学理论，借助广义汉密尔顿原理，得到了轴向加速梁的非线性振动耦合控制方程。控制方程考虑了材料特性、剪切应变、转动应变以及轴向加速度引起的纵向变化张力的影响。当横向非线性振动较小时，方程组解耦为非线性偏积分微分方程组。对于主参数共振，用多尺度法得到了稳态频率响应。分析了平凡和非平凡稳态响应的稳定和不稳定区间。研究了系统参数对振幅的影响。结果表明，材料参数（面内泊松比）对非线性振动的振幅和行为类型有显著影响。振幅随面内泊松比的增大而减小。模态分析表明，总势能在确定频率响应幅值方面起着非常重要的作用。最后，将解析解和数值解进行了比较，发现两者在振幅上有很好的一致性。
In this paper, a higher order model equation is presented for an axially accelerating beam. Based on a new kinematic frame of the beam and continuum mechanics theory, the coupled governing equations of nonlinear vibration for axially accelerating beam are obtained with the aid of the generalized Hamilton principle. The governing equations take into account the characteristic of the material, the shear strain, the rotation strain and the effect of longitudinally varying tension due to the axial acceleration. The equations are decoupled into a nonlinear partial-integro-differential equations when the transverse nonlinear vibration is small. For the principal parametric resonances, the steady-state frequency responses are obtained by the multiple scales method. The stable and unstable interval are analyzed for the trivial and nontrivial steady-state response. Effects of the system parameters on the amplitude have been investigated. The results show that the material parameter (i.e, in-plane Poisson ratio) has a significant effect on the amplitude and the nonlinear vibration behavior type. The amplitude decrease with the growth of the in-plane Poisson ratio. The total potential energy has play a very important role in determining the amplitude of frequency response according to model analysis. Lastly, comparisons among the analytical solutions and numerical solutions are made and good agreements for the amplitude are found.