Size-Dependent Free Vibration of Axially Moving Nanobeams Using Eringen’s Two-Phase Integral Model
Size-Dependent Free Vibration of Axially Moving Nanobeams Using Eringen’s Two-Phase Integral Model
复制标题
DOI：
10.3390/app8122552
复制
发表时间：
2018-12
期刊：
影响因子：
--
通讯作者：
Yuanbin Wang;Zhi-mei Lou;Kai Huang;Xiaowu Zhu
中科院分区：
文献类型：
--
作者：
Yuanbin Wang;Zhi-mei Lou;Kai Huang;Xiaowu Zhu
本文利用Eringen两相非局部积分模型研究了轴向运动纳米梁的振动问题。积分模型首次考虑了几何非线性。利用汉密尔顿原理得到了简支梁和固支-固支梁的运动方程，并将其转化为非线性积分-微分方程。对于纳米梁的自由振动，数值计算得到了临界速度和固有频率。分析了各参数对临界流速和固有频率的影响。我们发现，对于两相非局部积分模型，无论考虑何种边界条件，临界速度和固有频率都随非局部参数和几何参数的增加而增加。
In this paper, vibration of axially moving nanobeams is studied using Eringen’s two-phase nonlocal integral model. Geometric nonlinearity is taken into account for the integral model for the first time. Equations of motion for the beam with simply supported and fixed–fixed boundary conditions are obtained by Hamilton’s Principle, which turns out to be nonlinear integro-differential equations. For the free vibration of the nanobeam, the critical velocity and the natural frequencies are obtained numerically. Furthermore, the effects of parameters on critical velocity and natural frequency are analyzed. We have found that, for the two-phase nonlocal integral model, regardless of the boundary conditions considered, both the critical velocity and the natural frequency increase with the nonlocal parameter and the geometric parameter.