Investigation On The Dynamical Behavior Of Carbon Nanotubes Conveying Fluid

In1991, Japanese schoar S. Iijima first discovered carbon nanotubes(CNTs),which led to the upsurge research of CNTs in the world-wide. The unique molecularstructure of CNTs gives them many excellent mechanical, machinery, chemical,electrical and optical properties. Therefore they can be expected to be widely used inthe field of reinforced materials, electrochemical devices, sensors, hydrogen storage,drug delivery and nano-electronics. The hollow cylindrical geometry and highstrength of CNT makes it an important carrier of nano-scale fluid storage andtransport. CNTs can be used as nano-containers of gas storage, nano-pipes of fluidtransmission, the smallest capillary and nano-chemistry test tubes. We can also fillthe liquid metal inside CNT, making it the smallest thermometer. CNTs can also beused as drug delivery systems. As the transport properties of CNTs conveying fluidis very sensitive to the vibration mode and frequency, it is necessary to understandthe mechanical and physical properties of carbon nanotubes conveying fluid for theapplication of CNTs in nano-engineering. In-depth study of fluid-conveying CNTsdynamics which reveals the dynamical mechanism of transporting fluid can providea theoretical basis for the better applications of nano-materials in the field of energyand biomedical.In this paper, based on nonlocal elasticity theory and thermal elasticity theory,the dynamical behavior of single-walled CNTs, double-walled carbon nanotubes(DWCNTs) and CNT array conveying fluid are analyzed by utilizing the continuousEuler beam model. The main contents in this paper are as follows:Firstly, the thermal-mechanical vibration of SWCNTs embedded in elasticmedium conveying fluid is studied. Based on continuous Euler beam theory andnonlocal elasticity theory, the dynamics equation of fluid-conveying SWCNTsembedded in elastic medium under thermal load is formulated. The naturalfrequency and critical flow velocity is obtained by using the differential quadraturemethod. The influence of temperature changes, surrounding elastic medium andnonlocal parameter on the various order of natural frequencies and critical flowvelocity are discussed in detail. We find different results to the previous researchers.The centrifugal force and Coriolis force caused by the fluid play very importantroles in the dynamic characteristics of CNTs conveying fluid with consideringnonlocal effect, and cannot be ignored just for simplicity. Considering the largegeometric deformation of fluid-conveying CNTs and horizontal harmonic excitationforce, the nonlinear vibration equation of fluid-conveying SWCNTs under external excitation is established on the basis of the equation of SWCNTs conveying fluid.Using the multiple Lindstedt-Poincaré method, the cubic algebraic equation whichindicates the amplitude-frequency relatioship is obtained by the solvabilityconditions of the vibration equation. Based on the root discriminant of the cubicequation, the first order primary response, the relationship between internalresponses and the frequency and amplitude of the external excitation are analyzed.Secondly, the transverse vibration differential equations are established for themulti-walled CNTs conveying viscous fluid by using the multi-layer Euler beammodel for simulation of multi-walled CNTs, and the strict inter-tube van der Waalsinteraction is considered,. The natural frequency and critical flow velocity is gottenby using Galerkin method. The results show that the van der Waals force can greatlyimprove the stability of the system. Whether or not considering the van der Waalsforce, the critical flow velocity can decrease with the increase of nonlocalparameters, and increase with the increase of viscosity paramter of the internal fluid.The aspect ratio of CNTs and the surrounding elastic medium plays oppositeinfluence for with or without considering the van der Waals force.Thirdly, the thermal-mechanical vibration of fluid-conveying DWCNTsembedded in biological soft tissue is investigated. The effect of biological soft tissueis simulated by using the Kelvin-Voigt model. Then the transverse vibration modelof fluid-conveying DWCNTs coupled with thermal effect is established based onnonlocal elasticity theory. the differential quadrature method is used to solve thesystem considering three typical boundary conditions. The influence of the boundarysupport conditions and the physical parameters on the natural frequency and criticalflow velocity of system are discussed. It is found out that the increase of thedamping coefficient of the visco-elastic medium can decrease the system’s stabilityand the increase of the elastic parameter of visco-elastic medium can improve thesystem’s stability. Compared with SWCNTs, the effect of temperature change on thevibration of DWCNTs conveying fluid is small, and the thermal effect can reducethe effect of surrounding visco-elastic medium.Fourthly, the vibration of DWCNTs embedded in elastic medium withconsidering the nonlinear van der Waals force and geometrical large distortion isinvestigated. Based on Hamilton variation principle and the von Kármán typegeometric nonlinear theory, the nonlinear vibration equations of the double-wallCNTs under the nonlinear van der Waals force are established. The dynamicequations are converted into algebraic equations by using harmonic balancemethod, and Davidon-Fletcher-Powell (DFP) quasi-Newton method is utilized to getthe solutions of nonlinear equations of DWCNTs. The DWCNTs demonstrate two vibration states: coaxial vibration and non-coaxial vibration. The amplitudefrequency relationship of nonlinear vibration of DWCNTs is obtained, and theinfluence of geometric nonlinearity and nonlinear van der Waals force on the systemis discussed in detail.Finally, the dynamic characteristics of CNT arrays conveying fluid areresearchedd. Based on nonlocal elasticity theory, the simple CNT array composed oftwo CNTs connected through massless springs is established. The in-phase vibrationand out-of-phase vibration of the system composed of two CNTs are analyzed withthe simply supported boundary conditions at the ends, and the effect of nonlocalparameter and spring stiffness parameter on the critical flow velocity and naturalfrequencies are discussed.