简支Mexwell模型粘弹性输流管道的稳定性分析

在弹性输流管道研究的基础上,采用递推格式的有限差分法,对简支Maxwell模型粘弹性输流管道（回转守恒系统）,探讨了其动力特性和稳定性问题,具体分析了材料的松弛时间对无量纲流速与前三阶模态的无量纲频率的实部及虚部之间的变化曲线的影响。发现发散临界流速随松弛时间的减小而降低,随后发生的耦合模态颤振临界流速随松弛时间的减小而增大;甚至在质量比较大时,随着松弛时间的减小,可推迟乃至不发生耦合模态颤振。当无量纲松弛时间达到10^3量级以上时,即可将其按弹性管道处理。甚至在H为10^2量级时,按弹性管道处理也不会带来太大的误差。     

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．     

正三角形排列管束结构流弹失稳流体力模型数值研究

研究了流弹失稳流体力模型.选取阻尼机理控制下的流弹稳定性问题为研究对象,在多种入口流速下对正三角形排列管束结构中单管可动情况的流致振动过程进行了模拟.用管子速度和位移的多项式函数作为流体力模型,结合流体力和管子位移数值模拟结果,计算了流体力系数.对不同流速工况下的流体力系数与流速之间的关系进行拟合,将流速的影响引入到流体力模型中.最终得到了与管子速度、位移以及入口流速相关的流体力模型.用建立起的流体力模型对管束结构流弹失稳临界流速进行了预测,结果较好.这种以管束结构流致振动数值仿真为基础,结合给定的函数形式建立起的流体力模型,能反映管束结构和流体相互作用过程中的主要特征,该模型对流弹失稳临界流速有一定的预测能力.     

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.     

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.     

超声速蒙皮颤振微分积分方程的特征值问题

根据二维线化理论讨论超声速薄钣的动力稳定性,导致一类新颖的数学物理问题:非自共轭Volterra型四阶微分积分方程的复特征值问题.求得这一气动弹性系统的严格解.与其它近似分析对比,本法的临界曲线与实验数据符合良好,在低超声速范围不存在发散问题.此外,在数学物理实质方面,发现:(1)颤振频谱与固有频谱有互为间隔现象;(2)临界Mach数有简并现象.指出本法可以推广应用于三维机翼模型和燃气轮中叶栅的超声速颤振问题.     

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．     

弹性拱振动失稳的突变模型

本文是将突变理论应用于工程结构的动力稳定性的一个尝试.作者不仅得到弹性拱振动失稳的突变模型,而且给出发生失稳的条件.     

关于弹性半无限体表面的稳定性

本文综合报道有关弹性半无限体表面稳定性的若干工作.对于不可压缩弹性半无限体,概述在双向受载下自由表面的失稳分析,给出失稳的临界条件.对于可压缩弹性材料情况,分析了由标准材料组成的半无限体的表面轴对称失稳,得到失稳临界参数对于材料参数的依赖关系.     

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.     

Vibration analysis of conveying fluid pipe via He’s variational iteration method

In this paper, a recently new semi-analytical method, i.e., He’s variational iteration method is developed to apply to free vibration analysis of conveying fluid pipe. The critical flow velocity and frequency of pipe conveying fluid are obtained with considering the various boundary conditions. The results are compared with the ones of different transform method, and prove VIM that has the same precision and efficient with DTM. The mode shapes of cantilevered pipe and both ends with elastic support pipe are shown under different flow velocity.     

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.     

旋转输液管动力稳定性理论分析北大核心CSCD

基于Lagrange原理和假设模态法建立了旋转输液管的动力学模型.通过降阶升维的方法求解系统的特征值问题,并分析了旋转输液管自由振动特性.得到了不同端部集中质量和转速下,系统特征值随流速升高的演变轨迹.揭示了临界流速随系统参数的变化规律.研究发现,内部流体的流动对旋转输液管动力学特性存在显著影响.在某些参数组合下,系统低阶模态能够形成不同形式的内共振关系.预示了旋转输液管模型蕴含丰富的动力学现象.     

Nonlinear Frequency Analysis of FGM Pipes Based on the Homotopy Method北大核心CSCD

Based on the homotopy analysis method, the nonlinear vibration of porous functionally graded material (FGM) conveying pipes under generalized boundary conditions was studied. Based on the power-law distribution of the FGM and the Voigt model, the physical properties of the porous pipe material were described. Under the Euler-Bernoulli beam theory and the von Kármán nonlinear theory, and by means of Hamilton’s variational principle, the dynamic control equations and generalized boundary conditions for porous FGM conveying pipes were established. The homotopy analysis method was used to solve the nonlinear vibration characteristics of the porous FGM conveying pipe under generalized boundary conditions. The numerical results show that, the translation spring has little effect on the critical velocity of instability, while the rotation spring increases the critical velocity of instability, making the system more stable; in the nonlinear system, the viscoelastic coefficient does not change the critical velocity; the pipe length, the power-law exponent and the porosity all influence the nonlinear free vibration of the porous FGM conveying pipe. © 2023 Editorial Office of Applied Mathematics and Mechanics. All rights reserved.     

Nonlinear Dynamics of Pipes with Pulsatile Flow

The dynamic behaviour of pipes conveying flowing fluid can be significantly influenced by the periodically changing flow. The fluid is considered to be incompressible, frictionless and its velocity relative to the pipe is harmonic function of time of which magnitude does not depend on spatial coordinates. The pipe is modelled as an inextensible continuum. The investigations were performed using three bifurcation parameters: the frequency, the perturbation amplitude and the mean flow velocity. In super‐critical case the nonlinear dynamics was shown in bifurcation diagrams.     

Wave propagation analysis in buried pipe conveying fluid

A study of wave propagation in buried pipe conveying fluid is presented in the paper. The Flüggle shell model is adopted for pipe and surrounding solid is modeled as elastic matrix by using Winkle model. Wave dispersion curves of a buried vacant pipe and a pipe conveying fluid are obtained numerically by considering coupling conditions. Results show that wave velocity exhibits sharp drop points in dispersion curves, and remains to an identical values before and after the points for both of vacant pipe and pipe conveying fluid. Effects of wall thickness, elastic matrix properties and fluid velocity are also discussed.     

流体诱发水平悬臂输液管的内共振和模态转换(Ⅰ)

运用牛顿法导出水平悬臂刚性输液管的非线性动力学数学模型．为了对该模型进行理论分析,通过对各个相关实际物理量的量级定性分析,给出了模型中各个物理参数的量级．在此基础上,应用多尺度法首先得到输液管自由振动模态的特征函数,利用悬臂管的边界条件给出了特征值满足的特征方程, 发现管内流体速度可以诱发第一阶模态和第二阶模态3种形式的内共振分别是3∶1、2∶1和1∶1内共振, 从理论上解释了流速诱发水平悬臂输液管系统内共振的机理．由于3∶1内共振所对应的流速最小,因此这种形式的内共振是最先出现的,也是最重要的．