粘弹性介质中输流碳纳米管的动态稳定性分析

梁峰， 包日东， 金莹， 苏勇

(沈阳化工大学 能源与动力工程学院，沈阳110142)

摘要：应用非局部粘弹性夹层梁模型分析粘弹性介质中输送脉动流碳纳米管的动态稳定性。在经典的欧拉梁模型中考虑了由管道内、外壁上的薄表面层引起的表面弹性效应和表面残余应力，同时考虑纳米管道的非局部效应，得到了改进的欧拉梁模型。用平均法对其控制方程进行求解，得到了管道稳定性区域。数值算例揭示了纳米管的壁厚、粘弹性特性、表面效应及两个介质参数对管道动态稳定性的复杂影响，结论可为纳米流体机械的结构设计和振动分析提供理论基础。

关键词：输流碳纳米管；稳定性；参数共振；表面效应；粘弹性介质

中图分类号:O326文献标志码：A

Dynamicstabilityofafluid-conveyingcarbonnanotubeembeddinginlinearviscoelasticmedium

LIANG Feng, BAO Ri-dong, JIN Ying, SU Yong(SchoolofEnergyandPowerEngineering,ShenyangUniversityofChemicalTechnology,Shenyang110142,China)

Abstract:A nonlocal viscoelastic sandwich-beam model was developed to investigate the dynamic stability of a pulsating-fluid-conveying carbon nanotube (CNT) embedding in linear viscoelastic medium. The classical Euler-Bernoulli beam model was modified by considering the effects of surface elasticity and surface residual stress induced by thin surface layers presented on the inner and outer tube walls. The nonlocal effect of CNT was also taken into account. The governing equation was solved via the averaging method and the stability regions were obtained. Numerical examples were presented to reveal the complicated influences of tube thickness, viscoelasticity, surface effects and two medium parameters on the dynamic stability of the CNT. The conclusions drawn in the present paper are thought to be helpful to the structural design and vibration analysis of nanofluidic devices.

Keywords:fluid-conveyingcarbonnanotube;stability;parametricresonance;surfaceeffect;linearviscoelasticmedium

碳纳米管是1991年被发现的一种重要的纳米材料。研究表明，碳纳米管具有十分优异的力学、电磁学和化学性能，其强度是钢的100倍，是已知材料中最高的，但密度仅为钢的1/6，无论是强度还是韧性都远远优于任何已知纤维材料。碳纳米管作为复合材料的增强体，表现出了良好的强度、弹性、抗疲劳性，同时还具有耐强酸、强碱，在空气中973K以下基本不被氧化等优良性质。目前，碳纳米管已经在物理、化学、生物、电子和材料等领域得到了广泛的研究和应用。

由于碳纳米管具有小尺度、低密度、高强度和高硬度等特性，加之完美的空心圆柱形几何结构，使其成为纳米尺度下流体储藏与输运的重要载体。……