Stability and Nonlinear Vibration Analysis of an Axially Loaded Nanobeam Based on Nonlocal Strain Gradient Theory
Stability and Nonlinear Vibration Analysis of an Axially Loaded Nanobeam Based on Nonlocal Strain Gradient Theory
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基于非局部应变梯度理论的轴向加载纳米梁的稳定性和非线性振动分析
DOI：
10.1142/s1758825119500698
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发表时间：
2019-10
影响因子：
3.5
通讯作者：
Dai Huliang
中科院分区：
文献类型：
--
作者：
Chen Wei;Wang Lin;Dai Huliang
基于非局部应变梯度理论，研究了轴向时变载荷作用下纳米尺度梁的尺寸相关稳定性机制和非线性动力学行为。首先，考虑纳米梁的几何非线性，利用汉密尔顿原理推导出纳米梁的运动方程。然后，通过使用Floquet技术和Bolotin的方法，一个线性分析研究的钉扎-钉扎边界条件的纳米梁的尺寸依赖的稳定性机制。结果表明，在大多数情况下，Floquet技术和Bolotin方法得到的结果彼此吻合。进一步推导了纳米梁系统稳定边界的解析表达式。结果发现，当尺寸依赖的纳米梁系统被减少到一个经典的，所获得的表达式的稳定性边界与以前的实验结果吻合得很好。最后，以时间轨迹、分岔图和相图的形式给出了纳米梁的非线性响应。结果表明，轴向激励的纳米梁总是经历极限环振荡。对于所有的稳定性边界和非线性响应的结果，尺寸依赖的影响被发现是显着的。
The size-dependent stability mechanism and nonlinear dynamics of a nano-scale beam under an axial time-dependent load are theoretically studied based on nonlocal strain gradient theory. First, with the consideration of geometric nonlinearity of the nanobeam, the equation of motion is derived with the aid of Hamilton’s principle. Then, by using both Floquet technology and Bolotin’s method, a linear analysis is employed to investigate the size-dependent stability mechanism of the nanobeam for pinned-pinned boundary conditions. It is demonstrated that the results obtained based on the Floquet technology and Bolotin’s method agree well with each other in most cases. Furthermore, the analytical expressions for stability boundaries of the nanobeam system are derived. It is found that when the size-dependent nanobeam system is reduced to a classical one, the obtained expressions for stability boundaries are in good agreement with previous experimental results. Finally, the nonlinear responses of the nanobeam are presented in the form of time traces, bifurcation diagrams and phase portraits. It is shown that the axially excited nanobeam always undergoes a limit cycle oscillation. For all results regarding stability boundaries and nonlinear responses, the size-dependent effects are found to be significant.
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影响因子：
3.4
作者：
Wang, C. M.;Zhang, Y. Y.;Kitipornchai, S.
通讯作者：
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影响因子：
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DOI：
10.1142/s021945542250047x
发表时间：
2022-02
影响因子：
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作者：
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影响因子：
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