弹性地基输流管道的耦合模态颤振分析

推导出了弹性地基输流管道的固-液耦合振动微分方程,用幂级数法计算了Winkler模型地基和双参数模型地基输流管道的临界流速和复频率,分析了弹性地基对输流管道静力稳定性与动力稳定性的影响.结果表明,与不考虑弹性地基的情况相比较,弹性地基的作用可使管道发生静力失稳和动力失稳的临界流速增大,并且增大弹性地基参数可提高静力失稳和动力失稳的临界流速,从而推迟发散与颤振的发生.当质量比β较大时,管道会在某个地基参数组合下,在发生静力失稳后,会在较高流速下出现再稳定和再发散现象,然后发生耦合模态颤振.     

输流粘弹性曲管的稳定性分析

根据变质量弹性系统Hamilton原理,用变分法建立了输流粘弹性曲管的运动微分方程,并用归一化幂级数法导出了输流粘弹性曲管的复特征方程组．以两端固支Kelvin-Voigt模型粘弹性输流圆管为例,分析了无量纲延滞时间和质量比对输流管道无量纲复频率和无量纲流速之间的变化关系的影响．在无量纲延滞时间较大时,粘弹性输流圆管的特点是它的第1、2、3阶模态不再耦合,而是在第1、第2阶上先发散失稳,然后在1阶模态上再发生单一模态颤振．     

输液管道流固耦合非线性动力稳定分析

将弱约束输流管道非定常流液固耦合运动按波-流-振动系统建模成由4个非线性微分方程组成的分析模型,按模态进行分解研究系统在多种耦合状态下具有的运动稳定特性.以悬臂梁管道为例分析了耦合系统奇点的属性,得到了前四阶模态运动的相图.结果说明,多种耦合条件下输流管道的稳定性变得更为复杂,各阶模态运动具有不同的稳定特性.     

Influences of Attack Angles on Aerodynamic Derivatives and Flutter Characteristics of Flat Box Girders北大核心CSCD

以南京第四长江大桥扁平箱梁为研究对象,通过节段模型自由振动风洞试验详细测试了模型在不同风攻角下的颤振响应,探讨了系统非稳态及稳态临界振幅随风速的演化规律.首先,基于颤振响应振幅包络,结合Hilbert变换,识别了系统振幅依存的模态阻尼,并初步阐释了颤振形态随风攻角转变的机理.其次,提取了系统在不同风攻角下的模态参数,基于双模态耦合闭合解法,识别了断面在不同风攻角下的非线性颤振导数,研究了关键颤振导数振幅依存性随风攻角变化的规律及对断面颤振形态和特性的潜在影响.最后,通过逐项拆解模态阻尼,深入剖析了风攻角对非耦合及耦合气动阻尼的影响,并阐明了分项阻尼导致系统颤振性能差异性的动力学机理.     

柔性输流管泄流效应实验研究

基于模型试验研究了柔性输流管在恒定内流速度下由泄漏孔引入的泄流效应.研究发现:泄流效应可改变临界值,使得形变随流速增大近似线性增大;增加管道失稳时的形变幅值,可激发不同输流管的系统模态,引起管道多个频率的振动响应.研究结果为管道运输泄漏点定位提供了支撑,为数值模拟提供了实验参照.     

输送流体管道的固——液耦合动力学研究

根据Ｈａｍｉｌｔｏｎ原理推导输送流体管道固—液耦合振动方程，得到反对称的固—液耦合阻尼矩阵和对称的固—液耦合刚度矩阵；用ＱＲ法计算管道固有频率，给出了管道前４阶固有频率—流速曲线；讨论了流体的流速、压强变化以及固—液耦合阻尼和固—液耦合刚度对管道固有频率的影响；用Ｎｅｗｍａｒｋ法计算不同流速时管道对阶跃载荷的动力响应；发现了各阶固有频率都有随流速的提高而降低、再提高、再降低的周而复始现象·     

颤振分析中的特征值排序问题

颤振分析中判断颤振临界速度的重要依据是系统V-g和V-f图,即系统特征值随参数的变化曲线.在几乎所有商用软件及自编程序的输出结果中,有时会出现所谓的"窜支"现象,这给颤振临界速度和颤振穿越分支及耦合形式的判断带来很大不便.通过隐函数定理可以证明,除重特征值点以外,系统特征值连续依赖于系统参数变化.依据多元向量值函数连续性,建立对特征值的排列算法,给出系统特征根轨迹的正确曲线,再输出V-g和V-f图数据,从而避免"窜支"现象.编制应用程序,通过几个典型算例对算法进行了验证.该工作能够有效简化颤振分析的后处理工作,提高分析效率.     

流体诱发水平悬臂输液管的内共振和模态转换(Ⅱ)

基于得到的水平悬臂输液管非线性动力学控制方程,详细研究了由流速最小临界值诱发的3∶1内共振．通过观察内共振调谐参数、主共振调谐参数和外激励幅值的变化,发现在内共振临界流速附近,流速导致系统出现模态转换、鞍结分岔、Hopf分岔、余维2分岔和倍周期分岔等非线性动力学行为,对应的管道系统的周期运动失稳出现跳跃、颤振和更加复杂的动力学行为．通过理论结果与数值模拟比较,表明了理论分析的有效性和正确性．     

扁壳压曲的蠕变效应

本文讨论了混凝土扁壳压曲的蠕变效应.基于弹性薄壳的非线性理论,发现椭圆抛物面扁壳,其荷载-挠度曲线的上临界荷载将随时间而降低,而下临界荷载则随时间而上升.至于扁壳的局部失稳问题,其临界荷载仅取决于压曲发生瞬间材料的弹性模量.     

剪切载荷作用下含损伤胶接材料界面动应力强度因子的研究

主要针对剪切载荷作用下,胶接材料接合区域界面裂纹尖端动态应力强度因子进行了分析,其中考虑了裂尖区域的损伤．通过积分变换,引入位错密度函数,奇异积分方程被简化为代数方程,并采用配点法求解;最后经过Laplace逆变换,得到动态应力强度因子的时间响应．Ⅱ型动应力强度因子随着黏弹性胶层的剪切松弛参量、弹性基底的剪切模量和Poisson比的增加而增大;随膨胀松弛参量的增加而减小．损伤屏蔽发生在裂纹扩展的起始阶段．裂纹尖端的奇异性指数(-0.5)是与材料参数、损伤程度和时间无关的,而振荡指数由黏弹性材料参数控制．     

Flow-induced and mechanical stability of cantilever carbon nanotubes subjected to an axial compressive load

In the present study, a modified nonlocal elasticity theory is used for flutter and divergence analyses of the cantilever carbon nanotubes (CNTs) conveying fluid. The CNT is embedded in viscoelastic foundation and is subjected to an axial compressive load acting at the free end. An extreme high-order governing equation as well as higher-order boundary conditions is developed using Hamilton's principle for vibration and stability analysis of the CNT. The numerical solution for flutter and divergence velocities is computed using the extended Galerkin method. The validity of the present analysis is confirmed by comparing with molecular dynamics simulation (MDS) and numerical solutions available in the literature. In the numerical results, the effects of nonlocal parameter, surface effects, viscoelastic foundation and compressive axial load on the stability boundaries of the system are investigated. The results show that the stability boundaries of the CNT are strongly dependent on the small scale coefficient and surface effects.     

Stability analysis of cantilever carbon nanotubes subjected to partially distributed tangential force and viscoelastic foundation

Dynamic instability of cantilever carbon nanotubes conveying fluid embedded in viscoelastic foundation under a partially distributed tangential force is investigated based on nonlocal elasticity theory and Euler–Bernouli beam theory. The present study has incorporated the effects of nonlocal parameter, Knudsen number, surface effects and magnetic field. And two main parameters have also considered, namely partially distributed tangential force and foundation. It is assumed that viscoelastic foundation has modeled as Kelvin–Voigt, Maxwell and Standard linear solid types. The size-dependent governing equation of transverse vibration is derived using Hamilton’s variational principle and discretized by the Galerkin truncation method. A detailed parameter study is carried out, indicating the stability behavior of the nanotubes. In the light of numerical results, it is shown that variables considered in nondimensional equations have significant effects on natural frequencies and flutter velocities, especially for the foundation distribution length and model as well as the partially distributed tangential force.     

Application of the differential transformation method to vibration analysis of pipes conveying fluid

In this paper, a relatively new semi-analytical method, called differential transformation method (DTM), is generalized to analyze the free vibration problem of pipes conveying fluid with several typical boundary conditions. The natural frequencies and critical flow velocities are obtained using DTM. The results are compared with those predicted by the differential quadrature method (DQM) and with other results reported in the literature. It is demonstrated that the DTM has high precision and computational efficiency in the vibration analysis of pipes conveying fluid.     

轴向运动粘弹性板的横向振动特性

研究了轴向运动粘弹性矩形薄板的动力特性和稳定性问题．从二维粘弹性微分型本构关系出发,建立了轴向运动粘弹性板的运动微分方程．采用微分求积法,对四边简支、一对边简支一对边固支两种边界条件下粘弹性板的无量纲复频率进行了数值计算．分析了薄板的长宽比、无量纲运动速度及材料的无量纲延滞时间对其横向振动及稳定性的影响．     

Electro-thermo-mechanical vibration and stability analyses of double-bonded micro composite sandwich piezoelectric tubes conveying fluid flow

New sandwich panels and tubes have widely applications in nanotechnology such as transportation, naval, aerospace industries, micro and nanoelectromechanical systems and fluid storage. For example, carotid arteries play an important role to high blood rate control that they have a similar structure with flow conveying cylindrical shells. In the current study, stability and free vibration analyses of double-bonded micro composite sandwich piezoelectric tubes conveying fluid flow embedded in an orthotropic foundation under electro-thermo-mechanical loadings are presented. In fact, this work can be provided a valuable background for more research and further experimental investigation. It is assumed that the micro tubes are made of flexible material and smart piezoelectric composites reinforced by carbon nanotubes as core and face sheets, respectively. Energy method and Hamilton's principle are applied to derive the governing equations of motions based on Euler–Bernoulli beam model and using modified strain gradient theory. Moreover, generalized differential quadrature method is used to discretize and solve the governing equations of motions. Numerical results are investigated to predict the influences of length-to-radius, thickness of face sheets-to-thickness of core ratio, temperature changes, orthotropic elastic medium, Knudsen number, and carbon nanotubes volume fraction on the dimensionless natural frequencies and critical flow velocity of sandwich double-bonded piezoelectric micro composite tubes. The results of this article show that increasing the thickness ratio, volume fraction carbon nanotubes and orthotropic elastic constants lead to enhance the dimensionless natural frequency and stability of system, while decrease these parameters with increasing the temperature and length-to-radius ratio.     

Thermal-mechanical vibration and instability of a fluid-conveying single-walled carbon nanotube embedded in an elastic medium based on nonlocal elasticity theory

Based on the theories of thermal elasticity mechanics and nonlocal elasticity, an elastic Bernoulli-Euler beam model is developed for thermal-mechanical vibration and buckling instability of a single-walled carbon nanotube (SWCNT) conveying fluid and resting on an elastic medium. The finite element method is adopted to obtain the numerical solutions to the model. The effects of temperature change, nonlocal parameter and elastic medium constant on the vibration frequency and buckling instability of SWCNT conveying fluid are investigated. It can be concluded that at low or room temperature, the fundamental natural frequency and critical flow velocity for the SWCNT increase as the temperature change increases, on the other hand, while at high temperature the fundamental natural frequency and critical flow velocity decrease as the temperature change increases. The fundamental natural frequency for the SWCNT decreases as the nonlocal parameter increases, both the fundamental natural frequency and critical flow velocity increase as elastic medium constant increases.     

Convergence of the Equations for a Maxwell Fluid

The equations for the flow of a viscoelastic fluid of the Maxwell type are analyzed in a linear approximation. First, we establish that the solution depends continuously on changes in the relaxation time. Next, we investigate how the solution to the linearized Maxwell system converges to the solution to Stokes flow as the relaxation time tends to zero. Convergence in different measures is examined and specific a priori bounds are derived.     

Stability analysis of a single-walled carbon nanotube conveying pulsating and viscous fluid with nonlocal effect

For a single-walled carbon nanotube (CNT) conveying fluid, the internal flow is considered to be pulsating and viscous, and the resulting instability and parametric resonance of the CNT are investigated by the method of averaging. The partial differential equation of motion based on the nonlocal elasticity theory is discretized by the Galerkin method and the averaging equations for the first two modes are derived. The stability regions in frequency–amplitude plane are obtained and the influences of nonlocal effect, viscosity and some system parameters on the stability of CNT are discussed in detail. The results show that decrease of nonlocal parameter and increase of viscous parameter both increase the fundamental frequency and critical flow velocity; the dynamic stability of CNT can be enhanced due to nonlocal effect; the contributions of the fluid viscosity on the stability of CNT depend on flow velocity; the axial tensile force can only influence natural frequencies of the system however the viscoelastic characteristic of materials can enhance the dynamic stability of CNT. The conclusions drawn in this paper are thought to be helpful for the vibration analysis and structural design of nanofluidic devices.