弹性基体对磁场中输流纳米管的振动影响  

Elastic Matrix Effect on Vibration Characteristics of Fluid-conveyed SWCNT Under A Longitudinal Magnetic Field

作　　者：李明[1] 邓乾 吕刘飞 Li Ming;Deng Qian;Lv Liufei(Department of Mechanics,Wuhan University of Science and Technology,Wuhan 430065,China)

机构地区：[1]武汉科技大学理学院,武汉430065

出　　处：《动力学与控制学报》2023年第3期63-68,共6页Journal of Dynamics and Control

基　　金：国家自然科学基金资助项目(51909196)。

摘　　要：基于非局部连续介质理论,对处于轴向磁场作用下嵌入弹性基体中的输流单层碳纳米管(SWCNT),应用哈密顿原理,采用Euler-Bernoulli梁模型,建立了固支边界条件下该系统的横向振动微分方程.方程中计及磁场力与小尺度效应,弹性基体等效为Pasternak弹性模型.应用微分变换法(DTM)求解方程,着重研究了弹性基体、轴向磁场及小尺度效应耦合作用时该纳米输流管道系统振动稳定性问题.数值计算结果表明:弹性基体与轴向磁场均能提升系统的稳定性;而小尺度效应则降低系统稳定性.进一步的研究表明:随着弹性基体的增强,磁场对系统稳定性的影响受到一定程度的抑制;而对于小尺度效应而言,弹性基体的剪切参数抑制小尺度效应对系统稳定性的影响,但弹性参数放大了这一影响作用.The nonlocal Euler-Bernoulli beam model is used to study the vibration instability characteristics of fluid transporting fixed-fixed supported single-layer carbon nanotubes(SWCNTs)embedded in elastic matrix under longitudinal magnetic field.Considering the magnetic field force and small-scale effect,the elastic matrix is equivalent to Pasternak's property model,and the higher-order vibration differential equation and boundary condition of the fluid-structure coupling system are established by using Hamilton principle.The differential transformation method(DTM)is used to solve the equation,and the stability of SWCNTs under the coupling of elastic matrix,longitudinal magnetic field and small-scale effect is studied.The numerical results indicate that the magnetic field and the elastic matrix improve the stability of the system.The increase of small-scale coefficient will reduce the stability of the system to a certain extent.Further research shows that the influence of longitudinal magnetic field on the stability of flow transporting SWCNTs embedded in elastic matrix will be restrained to varying degrees with the enhancement of the elastic matrix.For the small-scale coefficient,the two parameters of the elastic foundation have the opposite effect,that is,the shear parameter suppresses the influence of small-scale on the stability of the fluid-conveyed carbon nanotube system,while the elastic parameter amplifies the influence.

关 键 词：输流纳米管 轴向磁场 弹性基体 小尺度系数 微分变换法 

分 类 号：O353.1[理学—流体力学]