基于非局部效应和表面效应的输流碳纳米管稳定性分析简

应用非局部黏弹性夹层梁模型分析双参数弹性介质中输送脉动流碳纳米管的稳定性. 新模型中同时考虑了由管道内、外壁上的薄表面层引起的表面弹性效应和表面残余应力，经典的欧拉梁模型因此通过引入非局部参数和表面参数得到了改进. 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材料的非局部效应、表面效应及两个弹性介质参数对管道固有频率、临界流速和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.     

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。     

Fluid structure interaction of cantilever micro and nanotubes conveying magnetic fluid with small size effects under a transverse magnetic field

Micro and nanotubes have found major application in fluidic systems as channels for conveying fluid. In some micro and nanofluidic applications such as drug delivery, a transverse magnetic field can be used to guide the fluid flow by generating an axial force in the flow direction. An important issue in the design of micro and nanofluidic systems is the structural vibration caused by the fluid flow. In the current study, we investigate the effect of transverse magnetic field on the vibration of cantilever micro and nanotubes conveying fluid by considering the small size effects. We couple the nonlocal Euler–Bernoulli beam model with Navier–Stokes theory to determine a fluid structure interaction (FSI) model for the vibration analysis of the system. We modify the FSI governing equation by driving a velocity correction factor to consider the effect of transverse magnetic field on the fluid flow’s pattern through the tube. Then, we use the Galerkin’s method to obtain the frequency diagrams for the instability analysis of the system. We show that the transverse magnetic field can have a substantial effect on the dynamics of tube conveying fluid by increasing the system’s natural frequencies and critical flow velocity which contributes to the flutter instability. We also discover that although the transverse magnetic field plays a crucial role on dynamics of microstructures, its effect on the dynamics of nanotubes is not significant and can be ignored.     

Size-dependent vibration characteristics of fluid-conveying microtubes

In this paper, a new theoretical model is developed, based on the modified couple stress theory, for the vibration analysis of fluid-conveying microtubes by introducing one internal material length scale parameter. Using Hamilton's principle, the equations of motion of fluid-conveying microtubes are derived. After discretization via the Differential Quadrature Method (DQM), the analytical model exhibits some essential vibration characteristics. For a microtube in which both ends are supported, it is found that the natural frequencies decrease with increasing internal flow velocities. It is also shown that the microtube will become unstable by divergence at a critical flow velocity. More significantly, when the outside diameter of the microtube is comparable to the material length scale parameter, the natural frequencies obtained using the modified couple stress theory are much larger than those obtained using the classical beam theory. It is not surprising, therefore, that the critical flow velocities predicted by the modified couple stress theory are generally higher than those predicted by the classical beam theory.     

APPROXIMATE THEORY AND ANALYTICAL SOLUTION FOR DYNAMIC CALCULATION OF VISCOELASTIC LAYERED PERIODIC PLATE

由于周期性隔振结构动力计算中较少考虑轨道交通载荷及材料黏弹性,因此,本文以黏弹性层状周期板为研究对象,提出了垂向移动简谐载荷下,可以考虑材料黏弹性及板内横向剪切变形的黏弹性层状周期板动力计算近似理论并给出解析解答.设板中性面的横向剪切变形为横截面的整体剪切变形,利用Reissner-Mindlin假设及提出的剪切变形补充计算条件,得到了中性面法线转角与中性面剪应力的关系.基于平衡方程和应力连续条件,建立了黏弹性层状周期板振动控制方程,推导了对边简支对边自由条件下,板垂向位移的简化Fourier级数形式解.与经典层合板模型和有限元计算结果进行了比较,验证了本文解答的有效性.结果表明：（1）黏弹性层状周期板可以显著降低单一材料板在自振频率处的振动响应,但会引起局部低频频段的振动放大;（2）板的垂向位移随着载荷速度的增大而增大,当载荷速度超过300 km/h后,其对板振动响应的影响减弱;（3）黏弹性层剪切模量存在最佳设计值,可使结构的隔振性能最佳;（4）黏弹性层的阻尼特性在低频范围内对结构振动影响较小;（5）可在满足工程实际的情况下适当增加板长,以提高结构的隔振性能.     

两端弹性支承输流管道固有特性研究

输流管道广泛应用于航天航空、石油化工、海洋等重要的工程领域, 其振动特性尤其是系统固有特性一直是国内外学者研究的热点问题. 本文研究了两端弹性支承输流管道横向振动的固有特性, 尤其是在非对称弹性支承下的系统固有特性. 使用哈密顿原理得到了输流管道的控制方程及边界条件, 通过复模态法得到了静态管道的模态函数, 以其作为伽辽金法的势函数和权函数对线性派生系统控制方程进行截断处理. 分析了两端对称支承刚度、两端非对称支承刚度、管道长度以及流体质量比对系统固有频率的影响规律, 重点讨论了管道两端可能形成的非对称支承条件下固有频率的变化规律. 结果表明, 较大的对称支承刚度下管道的第一阶固有频率下降较快; 当管道两端支承刚度变化时, 管道的各阶固有频率在两端支承刚度相等时取得最值; 对于两端非对称支承的管道而言, 两端支承刚度越接近, 第一阶固有频率下降的越快, 而且相应的临界流速越小; 流体的流速越大, 其对两端非对称弹簧支承的管道固有频率的影响更为明显.      

THE CROSSING FREQUENCY AS A MEASURE OF HEAT EXCHANGER SUPPORT-PLATE EFFECTIVENESS

The crossing frequency is the number of times per second the vibration amplitude crosses the zero displacement line from negative displacement to positive displacement. In flow-induced vibration in which the motions are often random and/or a number of modes contribute to the vibration amplitudes, the crossing frequencies are modal-weighted average frequencies of the vibration. It is postulated in this paper that the crossing frequency can be used as a measure of heat exchanger support-plate effectiveness. Using a time-domain, nonlinear analysis technique, the crossing frequencies of a tube vibrating in support plates with oversized holes can be computed as a function of time and the tube-to-support-plate clearances. It was found that the fluid–elastic stability margin of a tube bundle, in the context of the original Connors' equation for tube bundle fluid–elastic instability, should be independent of the tube-to-support-plate clearances. A simple method of estimating the critical velocity based on the time-domain equation of fluid–elastic stability is suggested.     

FLUIDELASTIC ANALYSIS OF TUBE BUNDLE VIBRATION IN CROSS-FLOW

Tube bundles in cross-flow vibrate in response to motion-induced fluid-dynamic forces; hence, the resultant motions are considered to be a fluidelastic vibration. The characteristics of the vibration depend greatly on the features of the fluid-dynamic forces and the structure of the tube bundle. Therefore, in this study, the equations of motion of the tube bundle are derived. From the viewpoint of vibration, each tube is not independent of the surrounding tubes because its vibration is affected by fluid-dynamic coupling with the neighboring tubes. Thus, the equations are a set of coupled equations and the solution is obtained as an eigenvalue problem. The fluid-dynamic forces, which are indispensable in the calculation, have been obtained by experiments using a vibrating tube in the bundle; it was found that the forces depend strongly on the reduced velocity. Using these equations and the fluid forces, critical velocities of the tube bundle vibration are calculated, and it is found that the critical velocity is strongly dependent on the fluid-dynamic force characteristics, as they vary with the reduced velocity. Vibration tests of the tube bundle have also been conducted, and the critical velocities obtained in the tests are compared with the calculated values; agreement with the calculated values is good, demonstrating that the method of calculation is useful. The effects of mass ratio, frequency deviation and damping deviation of tubes in the bundle on the critical velocity are also examined theoretically. It is found that it is better to treat the mass ratio and the logarithmic decrement separately when the mass ratio is less than 10. Differences in natural frequencies make the critical velocity large. Similarly, differences in logarithmic decrement may distribute the vibration energy to other tubes and make the critical velocity large.     

Vibration analysis of fluid-conveying nanotubes embedded in an elastic medium considering surface effects

An analytical model is developed to study the surface effects on the vibration behavior including the natural frequency and the critical flow velocity of fluid-conveying nanotubes embedded in an elastic medium. The effects of surface elasticity and residual surface stress are accounted through the surface elasticity model and the Young-Laplace equation. A Winkler-type foundation is employed to model the interaction of nanotubes and the surrounding medium. The results show that the surface effects have more prominent influences on the nature frequency with smaller nanotube thickness, larger aspect ratio and larger elastic medium constants. Both surface layers and the elastic medium enhance the stability of nanotubes. This study might be helpful for designing the fluid-conveying nanotube devices in NEMS and MEMS systems.     

FREE VIBRATION ANALYSIS OF FLUID-CONVEYING CARBON NANOTUBE VIA WAVE METHOD

The wave method is introduced to vibration analysis of the fluid-conveying carbon nanotube. The constitutive relation of carbon nanotube on micro-scale is founded using the non- local elastic theory. The governing equation on micro-scale is obtained. And the first five orders of the natural frequency of the carbon nanotube conveying fluid with various speeds are calculated through the wave method. Besides, the critical flow velocity when the carbon nanotube loses stability is obtained. Meanwhile, a contrast is made between the result obtained through tile wave method and that in previous researches.     

单跨架空索道货物脱钩跳跃弦振动响应分析

以单跨全悬增力式架空林业集材索道为例,研究在货物脱钩等突发情况下,承载索因积蓄的弹性能瞬间释放而产生自由振动. 基于弦振动理论,建立了在指定位置脱钩的悬索振动方程,分析了脱钩工况下悬索振动固有频率、周期、波长等特征参数及主振动、自由振动、总能量等响应变化规律,并以三维图形进行直观表征与分析. 说明了脱钩振动分析对林业架空索道的安装设计、技术改进与使用安全规程的指导意义.     

THE TRANSVERSE NONLINEAR FREE VIBRATION AND THE BUCKLING OF A COMPRESSIVE BAR ON AN ELASTIC FOUNDATION

基于Hamilton 原理,运用假设时间模态法,得到了弹性基础上压杆的横向非线性自由振动与屈曲的位移型常微分控制方程. 考虑一端固定另一端可移简支边界条件,采用打靶法得到了结构第一至第三阶结构频率与一阶屈曲载荷的数值结果. 结果表明：随轴心压力增加,结构频率减小;随弹性基础刚度增加,结构频率与屈曲载荷均增加;弹性基础刚度对结构频率的影响随振型阶数增加在减小;在小振幅的情形下,不同振型对一阶屈曲载荷的影响很小.     

弹性支撑圆柱绕流稳定性分析

基于CFD 技术,采用系统辨识方法,建立了亚临界雷诺数(Re < 47) 下绕圆柱流动的非定常气动力模型(reduced order model, ROM). 耦合结构运动方程和降阶气动力模型,建立了弹性支撑圆柱绕流的稳定性分析模型. 算例分析了亚临界雷诺数下,结构固有频率、质量比等参数以及支撑方式对弹性系统稳定性的影响. 对于单自由度横向支撑圆柱,当结构固有频率趋近流动最不稳定模态频率时,弹性系统会在一定频率范围内失稳,这种现象最低可在Re~20 时出现. 旋转自由度的释放能够进一步降低系统的稳定性,可将临界雷诺数进一步降低至18 左右. ROM 方法不仅具有很高的效率,而且清晰地指出了弹性系统失稳的根本原因:流动模态和结构模态耦合作用导致结构模态失稳所致. 因此,失稳状态下系统振荡频率锁定于结构固有频率. 基于ROM 技术预测的失稳边界与直接CFD/CSD 仿真结果吻合,证明了该方法的正确性和精度.      

基于三阶剪切变形理论的悬臂输流管道自由振动

采用三阶剪切变形理论,结合有限元法研究了悬臂输流管道的自由振动问题．利用虚功原理建立了输流管系统的有限元方程,同时将悬臂端弹性支承以势能的形式引入到系统方程中,求解了系统前三阶的复频率．分别探讨了流体速度和弹簧刚度对系统复频率实部和虚部的影响,重点分析了弹簧刚度与前三阶固有频率间的关系．在弹性支承刚度为零的特例下,对比了本文结果与Timoshenko梁理论的结果,证明了本文方法的可靠性．研究发现系统固有频率的实部恒为负值,表明一端带有弹性支承的约束形式有利于提高悬臂输流管道自由振动的稳定性;流体的流动对管道振动起到了阻尼作用,在流动速度足够大的情况下,各阶振动固有频率均趋于零;当弹簧刚度为无穷大,且流体速度足够大时,输流管道将发生失稳．     

紫藤萝复叶气动特性的风洞实验研究

树叶的形状重构和减阻能力在太阳能帆板、机翼结构、仿生天线设计和新型发电技术等方面具有应用价值.紫藤萝羽状复叶垂直悬挂于风洞中,在风速0~25m/s范围内进行正面和反面迎风测试.发现存在前期稳定、中间过渡和后期稳定3个阶段以及5个临界风速.在前期阶段叶轴随风速弯曲变化剧烈,出现小叶分层飞翼和分层多形状稳定.过渡阶段出现叶轴大幅低频振动和部分小叶小幅高频振动两种不稳定形式.后期出现两层或单一整体稳定,横截面形状分为锥形、楔形和U形.随着风速增大,复叶宽度减小,小叶层数逐步减少,直至出现流线形单一整体.随着雷诺数增大,复叶阻力系数先是快速下降,后又缓慢地趋于常数.复叶Vogel负指数绝对值$\vert \alpha \vert$随小叶数目的增大而增大.反面迎风时$|\alpha|$比正面迎风时大,但随着小叶数目增加两者趋于一致.当复叶旋涡脱落频率与叶轴固有频率接近时,叶轴出现大幅振动.理论分析得到叶轴振动的第二临界风速$V_2/\sqrt{E/\rho}$是$b/l$和$d/l$的函数,其中$E$,$\rho$,$d$和$l$分别为叶轴弹性模量、密度、直径和长度,$b$为变形后的复叶宽度,并由实验数据得到了其变化图.      

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.     

旋转圆板振动的热力控制

本文研究发现,热力对旋转圆盘动力特性有明显影响.可将此特征应用于旋转圆盘振动的热力自适应控制.仿真和试验均表明,这种控制方法对一些结构振动控制将是一种有效的方法.     

Velocity profile characterization in sub-millimeter diameter tubes using molecular tagging velocimetry

Fluid flow through microtubes is of interest to many industries and there exists a need for detailed measurements of the velocity field. Velocity profile data are critical for momentum, mass, and heat transport analysis, and thus the design of devices utilizing microgeometries. This paper outlines a measurement technique that has led to time-resolved measurements of velocity profiles in microtubes (less than 1,000 μm). The research program was experimental in nature and consisted of an extension of molecular tagging velocimetry to the microscale. Average velocity and rms profile data in the fully developed region, in addition to mass flow rate and pressure drop data, are presented for numerous Reynolds numbers ranging from 600 to 5,000 in a tube of diameter 705 μm. Received: 20 December 1999 / Accepted: 20 March 2001     

磁场中轴向运动导电梁弯曲自由振动分析

研究磁场环境下轴向运动导电梁的弯曲自由振动．首先给出系统的动能、势能以及电磁力表达式,进而应用哈密顿变分原理,推得磁场中轴向运动导电梁的磁弹性弯曲振动方程．在位移函数设定基础上,应用伽辽金积分法分别推出三种不同边界约束条件下,轴向运动梁的磁弹性自由振动微分方程和频率方程,得到固有频率表达式．通过算例,得到了弹性梁固有振动频率的变化规律曲线图,分析了轴向运动速度、磁感应强度和边界条件对固有振动频率和临界值的影响．     

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。