Nonlinear and chaotic vibrations of cantilevered micropipes conveying fluid based on modified couple stress theory
Nonlinear and chaotic vibrations of cantilevered micropipes conveying fluid based on modified couple stress theory
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基于修正应力偶理论的悬臂微管道输送流体非线性混沌振动
DOI：
10.1016/j.ijengsci.2016.04.014
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发表时间：
2016-08-01
影响因子：
6.6
通讯作者：
Qian, Q.
中科院分区：
文献类型：
--
作者：
Hu, K.;Wang, Y. K.;Qian, Q.
本文的目的是建立一个非线性理论模型的悬臂微管道/微梁输送流体，并探讨可能的尺寸依赖的非线性响应的基础上修改的偶应力理论。与以往的工作相比，这种新开发的非线性模型可以用来预测流体输送微悬臂梁的不稳定后的非线性动力学比其线性动力学。在考虑几何非线性、重力和下游端松动支承影响的情况下，利用汉密尔顿原理推导了非线性运动方程。控制偏微分方程进一步离散的Galerkin的方法的援助。数值结果表明，流体输送微悬臂梁能够表现出丰富的动力学行为。对于一个“水平”或“悬挂”微管输送流体，它被发现，颤振不稳定性发生在临界流速，超过该微管将经历一个极限环运动;对于一个“站立的微管相对较长的长度，但是，屈曲和颤振不稳定性可能会发生。对于一个在其顶端具有松散支撑的改进的微管系统，得到了更有趣的动力学行为。在非线性约束力作用下，以流速为变参数的分岔图和相应的相平面图表明，在发生一系列倍周期分岔后，确实会出现混沌振动。研究还表明，小尺度的存在可以提高微管的稳定性。然而，系统的颤振后响应的尺寸依赖性并不明显。(C)2016爱思唯尔有限公司版权所有。
The aim of this paper is to develop a nonlinear theoretical model for cantilevered micropipes/microbeams conveying fluid and to explore the possible size-dependent nonlinear responses based on the modified couple stress theory. Compared to previous work, this newly developed nonlinear model can be utilized for predicting the post-instability nonlinear dynamics of fluid-conveying micro-cantilever more than its linear dynamics. By considering the geometric nonlinearities, the gravity, and the effect of loose supports at the downstream end, the nonlinear equation of motion is derived using the Hamilton's principle. The governing partial differential equation is further discretized with the aid of Galerkin's approach. Numerical results show that the fluid-conveying micro-cantilever is capable of displaying rich dynamical behaviors. For a 'horizontal' or 'hanging' micropipe conveying fluid, it is found that flutter instability occurs at a critical flow velocity, beyond which the micropipe would undergo a limit cycle motion; for a 'standing micropipe with relatively long length, however, both buckling and flutter instabilities could occur. More interesting dynamical behavior has been obtained for a modified micropipe system with loose supports at its tip end. In the presence of nonlinear constraining force resulted from loose supports, construction of bifurcation diagrams with the flow velocity as variable parameter and some corresponding phase-plane portraits have shown that chaotic vibrations do indeed arise, following a sequence oof period-doubling bifurcations. It is also demonstrated that the presence of small length scale can enhance the stability of the micropipe. However, size dependence of the post-flutter responses for the system is not pronounced. (C) 2016 Elsevier Ltd. All rights reserved.