STABILITY AND MODE EVOLUTION CHARACTERISTICS OF A CANTILEVERED FLUID-CONVEYING PIPE ATTACHED WITH THE LUMPED MASS 1)

本文主要研究通过调控集中质量对悬臂输流管稳定性和振动模态特性的影响规律,为输流管动力学性能的可控性提供理论指导和实验依据. 首先基于扩展的哈密顿原理,建立了含集中质量悬臂输流管的非线性动力学理论模型. 基于线性动力学特性分析,研究发现集中质量沿管道轴向位置变化对输流管发生颤振失稳的临界流速有重要影响.并通过伽辽金前四阶模态截断处理线性矩阵方程式,定性地分析了集中质量位置与质量比的变化对于输流管稳定性影响的变化.实验结果表明, 输流管的颤振失稳模态随集中质量位置的变化发生了转迁. 此外,基于动力学理论分析, 发现集中质量比值对失稳临界流速也有重要的影响,且主要取决于集中质量的安装位置. 基于非线性特性,进一步分析了集中质量对输流管振动幅值的影响. 实验和理论研究发现,集中质量位置从固定端向自由端变化时, 输流管振幅表现出先增大后减小趋势,且振动模态也从二阶转迁到三阶.本研究有望为输流管振动驱动应用提供理论支撑与指导意义.     

传递矩阵法分析约束悬臂裂纹管道失稳临界流速

研究了自由端受线性弹簧支承和扭转弹簧约束的悬臂输流管道在含有圆周非贯穿裂纹时的失稳临界流速;根据梁模型模态函数的一般表达式和裂纹处的关联式以及传递矩阵法推导出含裂纹梁的模态函数;根据特征方程具体分析了裂纹位置、裂纹深度、裂纹圆周角等参数对系统失稳临界流速的影响,并进行了数值仿真分析。结果表明:由于裂纹的存在,系统的失稳临界流速下降,动态失稳临界流速下降的速率和幅值均比静态失稳临界流速下的大;临界流速与裂纹位置、深度和裂纹圆周角等参数密切相关,特别是对颤振失稳临界流速的影响更明显,在裂纹位置、裂纹非贯穿圆周角、裂纹深度等参数影响下,管道的失稳形态将从屈曲失稳转变为颤振失稳。     

接地惯容式减振器对悬臂输流管稳定性和动态响应的影响研究

输流管道广泛应用于机械、航空、核电和石油等重要工程领域.为防止管道结构因流致振动破坏造成的损失, 很有必要对其稳定性、动力学响应及其调控进行深入研究.本文提出一种由惯容器、弹簧和阻尼器并联组成的减振器模型, 研究了这种接地惯容减振器对悬臂输流管稳定性和非线性振动的影响. 首先, 基于哈密顿原理给出了带有接地惯容减振器非保守系统的非线性动力学模型; 然后, 利用高阶伽辽金方法对非线性方程进行离散化; 最后, 分别从线性和非线性角度分析了不同减振器参数下输流管道的被动控制效果, 着重讨论了惯容系数和减振器安装位置对悬臂管稳定性和动态响应的影响机制.线性理论模型的研究结果显示, 接地惯容减振器可显著影响悬臂管的失稳临界流速, 故通过调节减振器参数能有效提高输流管道的稳定性;惯容系数和弹簧刚度对系统稳定性的控制效果还与减振器的安装位置密切相关.非线性理论模型的分析结果显示, 惯容系数和减振器位置对输流管的非线性动态响应也有显著影响, 且这种影响还依赖于管道的流速取值; 在某些参数条件下, 减振器还可使输流管道由周期运动演化为复杂的混沌行为. 本文研究结果表明, 通过设计合理的惯容式减振器参数, 可提升悬臂输流管道的稳定性并有效抑制其颤振幅值.      

分析弹性支承输流管道的失稳临界流速

研究了两端弹性支承输流管道静态失稳和动态失稳临界流速. 根据梁模型横向弯曲振动模态 函数，由两端弹性支承的边界条件得到了其模态函数的一般表达式. 根据特征方程具体分析 了弹性支承刚度、质量比、流体压力和管截面轴向力等主要参数对失稳临界流速的影响. 数 值计算结果表明，管道在弹性支承下的动力稳定性比较复杂，在较小的弹性支承刚度和较小 的参数范围内，管道主要表现为动态颤振失稳；在较大的弹性支承刚度和较大的参数作用下， 管道的失稳形式主要表现为静态失稳；并且失稳临界流速随流体压力和管截面轴向压力的增 加而下降，随管截面轴向拉力的增加而上升.     

温度场作用下悬臂输流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悬臂输流单层碳纳米管(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.     

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。     

双通道旋转输流管临界流速和振动模态分析

旋转叶片是航空发动机重要零件之一,服役条件十分恶劣,常常因振动过量导致其失效.为了合理设计含冷却通道的叶片,保证其可靠性与安全性,需对含冷却通道的叶片的振动特性进行研究.基于EulerBernoulli梁理论,将叶片简化为含两通道的悬臂旋转输流管,考虑了通道轴线偏移量对流体动能的影响,采用Lagrange原理结合假设模态法建立包含双陀螺效应的运动控制方程,采用降阶扩维的方法求解系统特征值.研究两通道模型的流速比、转速和长细比等对前3阶特征根曲线影响.将文章模型退化为简支单通道输流管,与文献报道结果进行对比,部分验证建模方法的正确性.研究发现:在相同的管道截面积下,两通道模型的临界流速值大于单通道模型的;旋转运动引入的陀螺效应会使得第2, 3阶特征根轨迹发生绕圈现象,并多次穿越虚轴;随着长细比的增大,系统会表现出类似非旋转的悬臂输流管的动力学行为;系统的横向位移模态响应呈现出行波特性,且在不同参数组合下,阻尼因子对前3阶模态产生不同的增强或减弱作用.     

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.     

输流管道动力有限元建模及实验研究

在输流管道系统中由结构-流体相互耦合作用导致的管道振动对工业生产的安全性、经济性具有重要影响。工程中常用有限元中的管单元建立管道动力学模型,用附加质量法或顺序耦合方法进行输流管道系统的动力学分析,这种建模和分析方法可能会造成管道中结构-流体相互耦合效应的缺失。本文搭建了输流管道系统的实验平台,分别在管道无水和充水两种状态下进行管道系统模态实验,并将实验结果分别与所建立的无水管道有限元模型和充水管道流固耦合模型分析结果进行了对比,验证了壳单元及实体单元管道动力学模型的合理性。通过实验和数值分析研究其动力特性发现：壳单元动力学模型更合理准确,管道系统由于流固耦合作用的影响产生了新的振动形态;附加质量法分析结果缺失了系统的某些低阶模态,表明了输流管道系统流固直接耦合动力学建模的必要性。     

轴向流中悬臂柔性板流固耦合动力特性研究

论文从理论分析和实验研究两方面对轴向流中悬臂柔性板流固耦合动力特性作了研究.基于板的轴向不可延伸假设,采用Hamilton变分原理,推导了轴向流中悬臂板非线性运动偏微分方程,通过面元法计算悬臂板上下面压力差.采用伽辽金法离散该非线性运动偏微分方程,通过无量纲化物理参数,研究了系统无量纲颤振临界速度,给定流速下悬臂板末端...     

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.     

Extremely large-amplitude oscillation of soft pipes conveying fluid under gravity

In this work, the nonlinear behaviors of soft cantilevered pipes containing internal fluid flow are studied based on a geometrically exact model, with particular focus on the mechanism of large-amplitude oscillations of the pipe under gravity. Four key parameters, including the flow velocity, the mass ratio, the gravity parameter, and the inclination angle between the pipe length and the gravity direction, are considered to affect the static and dynamic behaviors of the soft pipe. The stability analyses show that, provided that the inclination angle is not equal to π, the soft pipe is stable at a low flow velocity and becomes unstable via flutter once the flow velocity is beyond a critical value. As the inclination angle is equal to π, the pipe experiences, in turn,buckling instability, regaining stability, and flutter instability with the increase in the flow velocity. Interestingly, the stability of the pipe can be either enhanced or weakened by varying the gravity parameter, mainly dependent on the value of the inclination angle.In the nonlinear dynamic analysis, it is demonstrated that the post-flutter amplitude of the soft pipe can be extremely large in the form of limit-cycle oscillations. Besides,the oscillating shapes for various inclination angles are provided to display interesting dynamical behaviors of the inclined soft pipe conveying fluid.     

FLOW-INDUCED INTERNAL RESONANCES AND MODE EXCHANGE IN HORIZONTAL CANTILEVERED PIPE CONVEYING FLUID (Ⅱ)

Based on the nonlinear mathematical model of motion of a horizontally cantilevered rigid pipe conveying fluid, the 3:1 internal resonance induced by the minimum critical velocity is studied in details. With the detuning parameters of internal and primary resonances and the amplitude of the external disturbing excitation varying, the flow in the neighborhood of the critical flow velocity yields that some nonlinearly dynamical behaviors occur in the system such as mode exchange, saddle-node, Hopf and co-dimension 2 bifurcations. Correspondingly, the periodic motion losses its stability by jumping or flutter, and more complicated motions occur in the pipe under consideration.The good agreement between the analytical analysis and the numerical simulation for several parameters ensures the validity and accuracy of the present analysis.     

A parametric study on nonlinear flow-induced dynamics of a fluid-conveying cantilevered pipe in post-flutter region from macro to micro scale

A mathematical formulation is proposed to investigate the nonlinear flow-induced dynamic characteristics of a cantilevered pipe conveying fluid from macro to micro scale. The model is developed by using the extended Hamilton's principle in conjunction with the inextensibility condition and laminar and turbulent flow profiles as well as modified couple stress theory. The current model is capable of recovering the classical model of cantilevered pipe conveying fluid by neglecting the couple stress effect. The governing equation of motion is presented in dimensionless form in a convenient and usable manner. To solve the problem at hand, the integro-partial-differential equation of motion is discretized into a set of ordinary differential equations via Galerkin method. Afterward, a Runge–Kutta's finite difference scheme is employed to evaluate the nonlinear dynamic response of the cantilevered pipe conveying fluid. A parametric study is carried out to examine the influences of mass parameter and dimensionless mean flow velocity on the nonlinear dynamic characteristics of the cantilevered pipe conveying fluid in post-flutter region. The role of size-dependency in the nonlinear behavior of pipe is explored by converting the new set of dimensionless parameters into the conventional one. Eventually, some convergence studies are performed to indicate the reliability of present results.     

Nonlinear Forced Vibration of Cantilevered Pipes Conveying Fluid

The nonlinear forced vibrations of a cantilevered pipe conveying fluid under base excitations are explored by means of the full nonlinear equation of motion, and the fourthorder Runge-Kutta integration algorithm is used as a numerical tool to solve the discretized equations. The self-excited vibration is briefly discussed first, focusing on the effect of flow velocity on the stability and post-flutter dynamical behavior of the pipe system with parameters close to those in previous experiments. Then, the nonlinear forced vibrations are examined using several concrete examples by means of frequency response diagrams and phase-plane plots. It shows that, at low flow velocity, the resonant amplitude near the first-mode natural frequency is larger than its counterpart near the second-mode natural frequency. The second-mode frequency response curve clearly displays a softening-type behavior with hysteresis phenomenon, while the first-mode frequency response curve almost maintains its neutrality. At moderate flow velocity,interestingly, the first-mode resonance response diminishes and the hysteresis phenomenon of the second-mode response disappears. At high flow velocity beyond the flutter threshold, the frequency response curve would exhibit a quenching-like behavior. When the excitation frequency is increased through the quenching point, the response of the pipe may shift from quasiperiodic to periodic. The results obtained in the present, work highlight the dramatic influence of internal fluid flow on the nonlinear forced vibrations of slender pipes.     

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

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FLOW-INDUCED INTERNAL RESONANCES AND MODE EXCHANGE IN HORIZONTAL CANTILEVERED PIPE CONVEYING FLUID （Ⅱ）

Based on the nonlinear mathematical model of motion of a horizontally can-tilevered rigid pipe conveying fluid, the 3:1 internal resonance induced by the minimum critical velocity is studied in details. With the detuning parameters of internal and primary resonances and the amplitude of the external disturbing excitation varying, the flow in the neighborhood of the critical flow velocity yields that some nonlinearly dynamical behaviors occur in the system such as mode exchange, saddle-node, Hopf and co-dimension 2 bifurcations. Correspondingly, the periodic motion losses its stability by jumping or flutter, and more complicated motions occur in the pipe under consideration. The good agreement between the analytical analysis and the numerical simulation for several parameters ensures the validity and accuracy of the present analysis.     

Nonlinear dynamics of cantilevered pipes conveying fluid: Towards a further understanding of the effect of loose constraints

The nonlinear dynamics of a fluid-conveying cantilevered pipe with loose constraints placed somewhere along its length is investigated. The main objective of this study is to determine the effects of several geometrical and physical parameters of the loose constraints on the characteristics and behavior of pipes conveying fluid. Based on the full nonlinear equation of motion, the dynamical behavior of the pipe system is investigated. Phase portraits and bifurcation diagrams are constructed for a selected set of system parameters. Typical results are firstly compared to numerical ones reported previously and excellent agreement is obtained. Then, the threshold flow velocities for several key bifurcations including pitchfork, period doubling, chaos, and sticking behaviors are predicted, showing that in many cases, the gap size, stiffness, and asymmetry of the loose constraints have remarkable effects on the nonlinear responses of the cantilevered pipe conveying fluid. For a pipe system with small/large constraint gap sizes, small constraint stiffness, or large constraint offset, some of the complex dynamical behaviors including chaos and period-doubling bifurcations would disappear, at least in the flow velocity range of interest.