Dynamical Instability Analysis of nanotubes Using nonlocal shear Beam Theory
Dynamical Instability Analysis of nanotubes Using nonlocal shear Beam Theory
复制标题
使用非局部剪切梁理论进行纳米管动态不稳定性分析
DOI：
10.1142/s0218127411030350
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发表时间：
2011
期刊：
影响因子：
--
通讯作者：
A. Tylikowski
中科院分区：
文献类型：
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作者：
A. Tylikowski
在过去的半个世纪中，分布式系统（连续体）的动态稳定性一直受到广泛关注。有许多论文可以研究周期性和随机力作用下的各向同性和层压梁、轴、板和壳。大多数论文在振动和稳定性分析中应用了有限维或模态近似。本文基于 Eringens 非局部弹性理论和剪切梁理论，重点研究微纳米棒的随机参数振动。涉及阻尼系数、结构和载荷参数的几乎确定的渐近不稳定性准则是使用李雅普诺夫直接法导出的。使用适当的类能量李亚普诺夫泛函，推导出未偏转形式梁几乎肯定渐近不稳定性的充分条件。非局部剪切梁解释了尺度效应，在处理短微米和纳米棒时，尺度效应变得很重要。从获得的解析公式可以清楚地看出，小尺度效应增加了动态不稳定区域。不稳定区域是轴向力方差、轴向力恒定分量和阻尼系数的函数。
The dynamics stability of distributed systems (continua) has been an object of considerable attention over the past half century. Numerous papers are available on isotropic and laminated beams, shafts, plates and shells under periodic and random forces. Most papers have applied finite dimensional or modal approximations in the analysis of vibration and stability. This paper focuses on the stochastic parametric vibrations of micro- and nanorods based on Eringens nonlocal elasticity theory and shear beam theory. The almost sure asymptotic instability criteria involving a damping coefficient, structure and loading parameters are derived using Liapunov's direct method. Using the appropriate energy-like Liapunov functional, sufficient conditions for the almost sure asymptotic instability of undeflected form of beam are derived. The nonlocal shear beam accounts for the scale effect, which becomes significant when dealing with short micro- and nanorods. From the obtained analytical formulas it is clearly seen that the small scale effect increases the dynamic instability region. Instability regions are functions of the axial force variance, the constant component of axial force and the damping coefficient.