黏弹性地基中纳米输流管道振动与失稳分析  

Vibration and instability analysis of fluid-conveying nanotubes resting on viscoelastic foundation

作　　者：李明[1] 周俊汝 邓乾 LI Ming;ZHOU Junru;DENG Qian(College of Science,Wuhan University of Science and Technology,Wuhan 430065,China)

机构地区：[1]武汉科技大学理学院,湖北武汉430065

出　　处：《湘潭大学学报（自然科学版）》2024年第2期63-71,共9页Journal of Xiangtan University(Natural Science Edition)

基　　金：国家自然科学基金(51909196)。

摘　　要：该文基于哈密顿原理与非局部弹性理论,针对黏弹性地基中轴向磁场作用固支输流碳纳米管的振动失稳特性,建立了该系统的振动微分方程,其中黏弹性地基分别采用了Kelvin-Voigt模型与Maxwell模型.应用微分求积法(DQM)离散了该微分方程,得到了求解系统振动特性的广义特征值问题.数值计算结果表明:外加轴向磁场在任何参数情况下均能提高系统振动频率,从而提升系统稳定性;小尺度效应弱化系统刚度,从而使系统更易产生发散失稳.尤为关键的是,黏弹性地基若采用不同的地基模型,其与纳米管间的作用效果存在差异:Kelvin-Voigt模型阻尼参数的增加降低系统稳定性,弹性系数的增加提升系统稳定性;Maxwell模型随两参数的增加,系统稳定性均表现出“先升后抑”的效果.Based on Hamilton's principle and nonlocal elastic theory,the vibration differential equation of the system was established for investigating the vibration instability of clamped-clamped carbon nanotubes(CNTs)conveying fluid under longitudinal magnetic field resting on viscoelastic foundation.The Kelvin-Voigt and Maxwell linear solid types of viscoelastic foundations were utilized to model the interaction between CNTs and surrounding viscoelastic medium.The resulting equations of motion were transformed to a general eigenvalue problem by applying the differential quadrature method(DQM).Results show the longitudinal magnetic field effects increase the natural frequency,thus makes the system more stable.However nonlocal parameter reduce system stiffness,making the system more prone to divergent instability.Specifically,this study showed different foundation models are used for viscoelastic foundations,and there are differences interaction between nanotubes and surrounding viscoelastic medium.For Kelvin-Voigt model increasing in damping coefficients reduces system stability,while the increase in elastic coefficient enhances system stability.For Maxwell model exhibits a"first up then down"effect on system stability with the increase of damping and elastic parameters.

关 键 词：碳纳米管 发散失稳 Kelvin-Voigt模型 Maxwell模型 轴向磁场 

分 类 号：O353.1[理学—流体力学]