多场作用下输流单层碳纳米管的动力学特性

以非局部弹性理论为基础,采用欧拉-伯努利梁模型,考虑管型区域内滑移边界条件以及碳纳米管的小尺度效应,应用哈密顿原理获得了温度场与轴向磁场共同作用下的输流单层固支碳纳米管（SWCNT）的振动控制方程以及边界条件,依靠微分变换法（DTM法）对此高阶偏微分方程进行求解,通过数值计算研究了多场中单层固支输流碳纳米管的振动与失稳问题。结果表明：温度场、轴向磁场强度、Knudsen数及小尺度参数都会对系统振动频率以及失稳临界流速产生影响。     

Flow-induced flutter instability of cantilever carbon nanotubes

Carbon nanotubes are finding significant application to nanofluidic devices. This work studies the influence of internal moving fluid on free vibration and flow-induced flutter instability of cantilever carbon nanotubes based on a continuum elastic model. Since the flow-induced vibration of cantilever pipes is non-conservative in nature, cantilever carbon nanotubes conveying fluid are damped with decaying amplitude for flow velocity below a certain critical value. Beyond this critical flow velocity, flutter instability occurs and vibration becomes amplified with growing amplitude. Our results indicate that internal moving fluid substantially affects vibrational frequencies and the decaying rate of amplitude especially for longer cantilever carbon nanotubes of larger innermost radius at higher flow velocity, and the critical flow velocity for flutter instability in some cases may fall within the practical range. On the other hand, a moderately stiff surrounding elastic medium (such as polymers) can significantly suppress the effect of internal moving fluid on vibrational frequencies and suppress or eliminate flutter instability within the practical range of flow velocity.     

磁场对不同温度场中输流悬臂碳纳米管动态特性的影响

本文在采用经典欧拉-伯努利梁模型的基础上,引入考虑小尺度效应的非局部弹性理论,着重研究不同温度场中输流悬臂单层碳纳米管系统（SWCNT）在外加纵向磁场作用下的颤振失稳问题。基于哈密顿原理获得了该流固耦合系统的振动控制方程及相应的边界条件,应用微分变换法（DTM法）求解此高阶偏微分方程,通过数值计算研究了不同温度场中施加纵向磁场对系统动力学特性的影响。结果表明：施加纵向磁场在不同温度场中都将增强输流悬臂碳纳米管的动态稳定性。然而,这种增强程度却与温度场的变化量有关,在不同温度变化量下,磁场对系统稳定性的增强程度有一个峰值,这意味着,实际应用中,为了提高这类流固耦合系统的动态稳定性,一味提高纵向磁场强度并不可取。     

温度场作用下输流悬臂碳纳米管的颤振失稳分析

以非局部弹性理论为基础,采用欧拉-伯努利梁模型,考虑碳纳米管的小尺度效应,应用哈密顿原理获得了温度场作用下的输流悬臂单层碳纳米管（SWCNT）的振动控制方程以及边界条件,依靠微分变换法（DTM法）对此高阶偏微分方程进行求解,通过数值计算研究了温度场中悬臂单层输流碳纳米管的振动与颤振失稳问题。结果表明：管内流体流速、温度场中温度变化情况与小尺度参数都会对系统振动频率以及颤振失稳临界流速产生影响。其中,小尺度效应将会降低悬臂输流系统的稳定性,使系统更为柔软;而高温场与低温场对系统动态失稳的影响不同,低温场中随温度变化值的增加,系统的稳定性提高;高温场这一作用效果恰好与之相反。     

Natural Frequency and Stability Tuning of Cantilevered CNTs Conveying Fluid in Magnetic Field

This paper investigates the dynamics of cantilevered CNTs conveying fluid in longitudinal magnetic field and presents the possibility of controlling/tuning the stability of the CNT system with the aid of magnetic field. The slender CNT is treated as an Euler-Bernoulli beam. Based on nonlocal elasticity theory, the equation of motion with consideration of magnetic field effect is developed. This partial differential equation is then discretized using the differential quadrature method(DQM). Numerical results show that the nonlocal small-scale parameter makes the fluid-conveying CNT more flexible and can shift the unstable mode in which flutter instability occurs first at sufficiently high flow velocity from one to another. More importantly,the addition of a longitudinal magnetic field leads to much richer dynamical behaviors of the CNT system. Indeed, the presence of longitudinal magnetic field can significantly affect the evolution of natural frequency of the dynamical system when the flow velocity is successively increased.With increasing magnetic field parameter, it is shown that the CNT system behaves stiffer and hence the critical flow velocity becomes higher. It is of particular interest that when the magnetic field parameter is equal to or larger than the flow velocity, the cantilevered CNT conveying fluid becomes unconditionally stable, indicating that the dynamic stability of the system can be controlled due to the presence of a longitudinal magnetic field.     

MHD of a fractional viscoelastic fluid in a circular tube

We investigate the effect of a transverse magnetic field on the unsteady flow of a generalized second grade fluid through a porous medium in a circular tube. Using fractional partial differential equations, we are able to describe the velocity and stress fields of the flow. We also obtain exact analytic solutions of these differential equations in terms of the Fox’s H-function.     

THERMOELASTIC VIBRATION OF FLUID-CONVEYING MICROTUBES EMBEDDED IN ELASTIC MEDIUMS

研究热环境中被弹性介质包围的微米输流管道的横向振动问题. 根据Hamilton 原理及非线性热弹性理论建立管道横向振动控制方程,并利用复模态法对其进行求解,得到了系统的固有频率和屈曲失稳临界流速,讨论了环境温度和一些重要系统参数对管道振动特性的影响. 研究结果表明:环境温度变化、管道和流体的微尺度效应、管道外径及弹性介质刚度对输流微管道固有频率和临界流速都有很大影响.     

A reappraisal of the computational modelling of carbon nanotubes conveying viscous fluid

By using the Euler–Bernoulli classical beam theory to model the nanotube as a continuum structure, a reevaluation of the computational modelling of carbon nanotubes conveying viscous fluid is undertaken in this paper, with some fresh insights as to if the viscosity of flowing fluid does influence the free vibration of the nanotube. It is found that during the flow of a fluid through a nanotube, modelled as a continuum beam, the effect of viscosity of flowing fluid on the vibration and instability of CNTs can be ignored.     

The effect of magnetic fields on low frequency oscillating natural convection with pressure gradient

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FLEXURAL WAVE DISPERSION IN MULTI-WALLED CARBON NANOTUBES CONVEYING FLUIDS

Motivated by the great potential of carbon nanotubes for developing nanofluidic devices, this paper presents a nonlocal elastic, Timoshenko multi-beam model with the second order of strain gradient taken into consideration and derives the corresponding dispersion relation of flexural wave in multi-walled carbon nanotubes conveying fuids. The study shows that the moving flow reduces the phase velocity of flexural wave of the lowest branch in carbon nanotubes. The phase velocity of flexural wave of the lowest branch decreases with an increase of flow velocity. However, the effects of flow velocity on the other branches of the wave dispersion are not obvious. The effect of microstructure characterized by nonlocal elasticity on the dispersion of flexural wave becomes more and more remarkable with an increase in wave number.     

Fluctuating flow of an elastico-viscous fluid along an infinite porous plate with an applied magnetic field

The problem of oscillating free stream flow of an elastico-viscous, incompressible, and electrically conducting fluid along an infinite plate with suction varying periodically with time, is considered in the presence of a transverse magnetic field. The effect of the elasticity of the fluid, the magnetic fluid, and the fluctuation of suction velocity on the velocity and the skin friction is examined.     

VIBRATION AND STABILITY OF RING-STIFFENED THIN-WALLED CYLINDRICAL SHELLS CONVEYING FLUID

Based on the Flügge shell theory,equations of motion of ring-stiffened thin-walled cylindrical shells conveying fluid are developed with the aid of the Hamilton's principle.Analysis is carried out on t...     

Viscous lifting and drainage of a conducting fluid in the presence of a transverse magnetic field

A theoretical investigation of the effects of a transverse magnetic field on the combined problem of viscous lifting and drainage of a conducting fluid on a plate is presented. The effects of inertia and transverse magnetic field on the liquid film thickness is studied for two cases namely a plate withdrawn with a constant velocity and one withdrawn with a constant acceleration. The expressions for the flow rate and the free surface profiles are obtained for the above two cases. It is found that the free surface profiles are convex in nature as in the non-magnetic case thus showing that the inertia does not effect the general pattern of flow, and the effect of the magnetic field is to retard both the lifting and drainage of the fluid.     

Analysis of coupled-mode flutter of pipes conveying fluid on the elastic foundation

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THE DYNAMIC BEHAVIORS OF VISCOELASTIC PIPE CONVEYING FLUID WITH THE KELVIN MODEL

Based on the differential constitutive relationship of linear viscoelastic, material, a solid-liquid coupling vibration equation for viscoelastic pipe conveying fluid is derived by the D'Alembert's principle. The critical flow velocities and natural frequencies of the cantilever pipe conveying fluid with the Kelvin model (flutter instability) are calculated with the modified finite difference method in the form of the recurrence formula. The curves between the complex frequencies of the first, second and third mode and flow velocity of the pipe are plotted. On the basis of the numerical, calculation results, the dynamic behaviors and stability of the pipe are discussed. It should be pointed out that the delay time of viscoelastic material with the Kelvin model has a remarkable effect on the dynamic characteristics and stability behaviors of the cantilevered pipe conveying fluid, which is a gyroscopic non-conservative system.     

The effects of Knudsen-dependent flow velocity on vibrations of a nano-pipe conveying fluid

In this paper, we investigate the effect of nano-flow on vibration of nano-pipe conveying fluid using Knudsen (Kn). We use Euler–Bernoulli plug-flow beam theory. We modify no-slip condition of nano-pipe conveying fluid based on Kn. We define a Kn-dependent flow velocity. We consider effect of slip condition, for a liquid and a gas flow. We reformulate Navier–Stokes equations, with modified versions of Kn-dependent flow velocity. We observe that for passage of gas through nano-pipe with nonzero Kn, the critical flow velocities decreased considerably as opposed to those for zero Kn. This can show that ignoring Kn effect on a gas nano-flow may cause non-conservative design of nano-devices. Furthermore, a more impressive phenomenon happens in the case of clamped-pinned pipe conveying gas fluid. While we do not observe any coupled-mode flutter for a zero Kn, we can see the coupled-mode flutter, accompanying the second-mode divergence, for a nonzero Kn.     

A Dynamic Inflation Test for Soft Materials

We developed a dynamic inflation experiment to measure the elastodynamic behavior of soft materials. In the experiments, a shock tube was used to apply dynamic pressurization to thin polydimethylsiloxane specimens. Two high-speed cameras were used to image the deforming specimen and three-dimensional digital image correlation was used to determine the three-dimensional displacement field of the specimen surface. We applied dynamic Kirchhoff plate bending theory and concepts from structural dynamics to derive a mathematical expression for the dynamic Young’s modulus. The phase velocity of the initial transverse wave propagation response and the vibration frequency of the long-time response were captured during our experiments and were applied in the calculation of the dynamic Young’s modulus.     

Effect of the magnetic field on the pulsatile flow through a rigid tube

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Nonlinear steady states of hyperelastic membrane tubes conveying a viscous non-Newtonian fluid

We study possible steady states of an infinitely long tube made of a hyperelastic membrane and conveying either an inviscid, or a viscous fluid with power-law rheology. The tube model is geometrically and physically nonlinear; the fluid model is limited to smooth changes in the tube’s radius. For the inviscid case, we analyse the tube’s stretch and flow velocity range at which standing solitary waves of both the swelling and the necking type exist. For the viscous case, we first analyse the tube’s upstream and downstream limit states that are balanced by infinitely growing upstream (and decreasing downstream) fluid pressure and axial stress caused by fluid viscosity. Then we investigate conditions that can connect these limit states by a single solution. We show that such a solution exists only for sufficiently small flow speeds and that it has a form of a kink wave; solitary waves do not exist. For the case of a semi-infinite tube (infinite either upstream or downstream), there exist both kink and solitary wave solutions. For finite-length tubes, there exist solutions of any kind, i.e. in the form of pieces of kink waves, solitary waves, and periodic waves.     

固—液耦合Timoshenko管道的稳定性分析

根据Ｈａｍｉｌｔｏｎ原理的固－液耦合振同分方程用幂级数法计算了Ｔｉｍｏｓｈｅｎｋｏ管道的固有频率和临界流速。给出了管道前三阶固有频率－流速的关系曲线,分析了转动惯量对该输流管道的稳定特性的影响。计算结果表明,转动一对两端简支的固－液合Ｔｉｍｏｓｈｅｎｋｏ管道的静力失稳没有影响,但对其频率特性和动力失稳有影响。