具有刚性间隙约束输流管的碰撞振动

管道与间隙约束间的碰撞振动是工程输流管结构的一个重要动力学现象. 迄今,人们通常采用光滑的非线性弹簧来模拟管道与间隙约束之间的碰撞力,但这种光滑的碰撞力无法真实反映碰撞前后管道状态向量的非光滑传递特征. 本文基于非光滑理论建立了具有刚性间隙约束简支输流管的非线性碰撞振动模型,利用 Galerkin 法离散了无穷维的管道模型, 并引入恢复系数构造了碰撞前后管道各处状态向量的传递矩阵,运用四阶龙格库塔法分析了脉动内流激励下管道与刚性间隙约束的非光滑碰撞振动现象,着重讨论了刚性间隙约束参数对管道动态响应随流速脉动频率变化的影响规律,特别是碰撞振动的周期性运动规律. 研究结果表明,刚性约束间隙值对管道碰撞振动行为的影响较大,在某些脉动频率下管道会出现多周期和非周期性的运动形态,还可出现非光滑系统特有的黏滑现象. 此外,碰撞恢复系数对管道振动的影响也比较显著,较小的恢复系数值更容易使管道在大范围脉动频率区间出现复杂的非周期碰撞振动.      

分布式运动约束下悬臂输液管的参数共振研究

输液管道结构在航空、航天、机械、海洋、水利和核电等工程领域都有广泛应用,其稳定性、振动与安全评估备受关注.针对具有分布式运动约束悬臂输液管的非线性动力学模型,分别采用立方非线性弹簧和修正三线性弹簧来模拟运动约束的作用力,研究了管道在脉动内流激励下的参数共振行为.首先,从输液管系统的非线性控制方程出发,利用Galerkin方法进行离散化;然后,由Floquet理论得出线性系统在失稳前两个不同平均流速下脉动幅值和脉动频率变化时的共振参数区域;最后,考虑系统的几何非线性项和分布式非线性运动约束力的影响,求解了管道的非线性动力学响应,讨论了非线性项及运动约束力对管道参数共振行为的影响.研究结果表明,系统非线性共振响应的参数区域与线性系统的共振参数区域是一致的,分布式运动约束力对发生参数共振时管道的位移响应有显著影响;立方非线性弹簧和修正三线性弹簧模型所预测的分岔路径存有较大差异,但都可诱发管道在一定的参数激励下出现混沌运动.      

输液管模型及其非线性动力学近期研究进展

综述了输液管系统的各类物理模型及其相应的数学模型,在流体满足基本假设条件下,对于管道内径远远小于管道长度的直管和曲管,详细叙述了梁模型管动力学数学模型的建模过程以及建模方法,针对在水动压力作用下以及管道短而且薄的情形,综述了壳模型的输液管道的动力学方程.在此基础上,概述了近几年来输液管道的非线性振动、稳定性、分岔与混沌、特别是管道控制的研究现状,并对今后的发展趋势作了分析和预测.综观非线性动力学理论的发展历程可以发现选取研究对象和典型的数学模型是至关重要的.对于低维的非线性系统,常常选用van der Pol、Duffing、Mathieu、Lorenz等典型系统来进行研究工作的.通过本文可以看出,对于研究高维非线性系统动力学,流诱发输液管的动力学问题是非常典型的模型之一,它有着容易理解的工程背景、包含了梁和壳的振动问题,并且它的数学模型相对简单,然而却能包含非常复杂的非线性动力学现象,同时容易解释数学方法得到的结果易对应到工程中的实际现象.本文希望通过对输液管动力学模型及其非线性动力学和控制研究现状的综述,建立高维非线性动力学的分析模型,以便发展高维非线性动力学的分岔与混沌理论,同时建立相应的控制理论基础.      

输液管的非线性振动、分叉与混沌——现状与展望

围绕输液管的非线性振动、分叉与混沌问题，对近几年来的主要研究工作加以综述并提出预测，其中包括运动方程中非线性项的归纳与讨论、非线性动力分析的一些现代计算方法、定常流速下输液管的分叉与混沌行为、振荡流速下输液管的参数共振以及今后值得进一步研究的某些问题．     

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

The Newtonian method is employed to obtain nonlinear mathematical model of motion of a horizontally cantilevered and inflexible pipe conveying fluid. The order magnitudes of relevant physical parameters are analyzed qualitatively to establish a foundation on the further study of the model. The method of multiple scales is used to obtain eigenfunctions of the linear free-vibration modes of the pipe. The boundary conditions yield the characteristic equations from which eigenvalues can be derived. It is found that flow velocity in the pipe may induced the 3:1, 2:1 and 1:1 internal resonances between the first and second modes such that the mechanism of flow-induced internal resonances in the pipe under consideration is explained theoretically. The 3:1 internal resonance first occurs in the system and is, thus, the most important since it corresponds to the minimum critical velocity.     

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.     

Melnikov方法在输流管混沌运动研究中的应用

对基础简谐运动激励下两端固定输流管道的混沌运动进行了研究，推导出了系统的运动方程，确定了系统存在的平衡点及其稳定性，计算出了未扰系统的同宿轨道，并利用Melnikov方法得到了系统发生混沌运动时参数需满足的临界条件，同时还利用相平面图和：Poincare映射等方法对管道的混沌运动进行了数值模拟，通过比较发现，由Melnikov方法确定的临界参数值要稍小于数值模拟中首次观察到混沌运动时对应的临界值。     

FLUTTER INSTABILITY OF SUPPORTED PIPES CONVEYING FLUID SUBJECTED TO DISTRIBUTED FOLLOWER FORCES

In the past decades,it has been reported that divergence is the expected form of instability for fluid-conveying pipes with both ends supported.In this paper,the form of instability of supported pipes ...     

HOPF BIFURCATION OF A NONLINEAR RESTRAINED CURVED PIPE CONVEYING FLUID BY DIFFERENTIAL QUADRATURE METHOD

This paper proposes a new method for investigating the Hopf bifurcation of a curved pipe conveying fluid with nonlinear spring support. The nonlinear equation of motion is derived by forces equilibrium on microelement of the system under consideration. The spatial coordinate of the system is discretized by the differential quadrature method and then the dynamic equation is solved by the Newton-Raphson method. The numerical solutions show that the inner fluid velocity of the Hopf bifurcation point of the curved pipe varies with different values of the parameter,nonlinear spring stiffness. Based on this, the cycle and divergent motions are both found to exist at specific fluid flow velocities with a given value of the nonlinear spring stiffness. The results are useful for further study of the nonlinear dynamic mechanism of the curved fluid conveying pipe.     

谐激励作用下输流曲管的混沌振动研究

研究了谐激励作用下输流曲管在系统参数区域内的混沌振动.基于牛顿法导出了输流曲管模型的非线性控制方程,并利用微分求积法对此方程在空间域进行离散,导出了输流曲管的非线性动力学方程组.在此基础上,对输流管道的动力响应进行了数值模拟.采用分岔、相平面、时间历程和庞加莱映射图等手段分析发现,在流速和激励频率的参数区域内,系统将可能发生包括混沌振动在内的多种运动形式.系统可经由倍周期分岔或概周期运动通向混沌.分析结果为工程输流管道模型的合理设计提供了参考.     

输液曲管平面内振动的波动方法研究

采用Flügge曲粱模拟弯曲管道,推导了管内流体的加速度,在总体轴线不可伸长假定的基础上建立了曲管平面内振动的动力学方程;采用波动方法,获得了曲管内振动波的传播和反射矩阵,提出了计算曲管平面内振动固有频率的数值方法.算例分析中,通过计算两端固定半圆形曲管的临界流速并与已有文献结果对比,验证了论文方法的正确性.最后,计算了两端固定半圆形曲管在四种不同流速下的前四阶固有频率,结果表明,管内流速的增大会降低管道的固有频率,当流速增大到某一特定值时,管道的一阶固有频率消失.     

NONLINEAR DYNAMICS AND SYNCHRONIZATION OF TWO COUPLED PIPES CONVEYING PULSATING FLUID

In this paper, the nonlinear dynamical behavior of two coupled pipes conveying pulsating fluid is studied. The connection between the two pipes is considered as a distributed linear spring. Based on this consideration, the equations of motion of the coupled two-pipe system are obtained. The two coupled nonlinear partial differential equations, discretized using the fourth- order Galerkin method, are solved by a fourth-order Runge-Kutta integration algorithm. Results show that the connection stiffness has a significant effect on the dynamical behavior of the coupled system. It is found that for some parameter values the motion types of the two pipes might be synchronous.     

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.     

三参量固体模型粘弹性输流管道的动力特性分析

推导了三参量固体模型粘弹性输流管道的振动微分方程,计算了在不同无量纲松弛系数和弹性常数比下管道的无量纲临界流速和无量纲自振复频率,并给出了前三阶复频率与流速的关系.计算结果表明,质量比、无量纲松弛系数及无量纲弹性常数比对输流管道的动力特性均有影响.     

FORCED VIBRATIONS WITH INTERNAL RESONANCE OF A PIPE CONVEYING FLUID UNDER EXTERNAL PERIODIC EXCITATION

Applying the multidimensional Lindstedt-Poincaré (MDLP) method, we study the forced vibrations with internal resonance of a clamped-clamped pipe conveying fluid under external periodic excitation. The frequency-amplitude response curves of the first-mode resonance with internal resonance are obtained and its characteristics are discussed; moreover, the motions of the first two modes are also analyzed in detail. The present results reveal rich and complex dynamic behaviors caused by internal resonance and that some of the internal resonances are decided by the excitation amplitude. The MDLP method is also proved to be a simple and efficient technique to deal with nonlinear dynamics.     

多跨管道流固耦合振动的波传播解法

采用Timoshenko梁模型提出了求解多跨管道流固耦合振动的波动方法.借助边界处的几何连续条件和力平衡条件,得到了波在固支、简支和自由三种端部条件下的反射模型;建立了波在中间弹性支撑处的散射模型;结合以上散射模型,得到了多跨管道流固耦合振动的频率特征方程;通过计算两端简支管道的临界流速,验证了所建立模型的正确性.最后,计算了一段40m长、七跨管道在三种工况下的前五阶固有频率.计算结果表明:波传播方法具有易于编程、执行效率高和计算精度高的优点.     

悬臂输流管道的运动分岔现象和混沌运动

研究受约束悬臂输流管道的稳定性和运动分岔问题.在静态与动态失稳区域边界上的一个交叉点附近,用理论分析的方法详细研究了该系统可能发生的复杂运动和运动分岔现象.在动态失稳区域内发现了输流管道的概周期运动和由于概周期运动环面破裂而导致混沌的现象.理论分析结果与数值模拟结果相吻合.     

DYNAMIC STABILITY OF A BEAM-MODEL VISCOELASTIC PIPE FOR CONVEYING PULSATIVE FLUID

The dynamic stability in transverse vibration of a viscoelastic pipe for conveying pulsative fluid is investigated for the simply-supported case.The material property of the beam- model pipe is described by the Kelvin-type viscoelastic constitutive relation.The axial fluid speed is characterized as simple harmonic variation about a constant mean speed.The method of mul- tiple scales is applied directly to the governing partial differential equation without discretization when the viscoelastic damping and the periodical excitation are considered small.The stability conditions are presented in the case of subharmonic and combination resonance.Numerical results show the effect of viscosity and mass ratio on instability regions.     

分析输流曲管临界流速的迁移矩阵法

提出了一种分析输液曲管临界流速的方法。与其它方法相比,该方法不但容易处理带任意多个中间支承和变刚度、变曲率的输液曲管问题,而且由于对各段位移、内力关系导出了一系列显式,故不管离散段数多少,最终都只需解一个三阶矩阵方程,因此计算量小、精度高。     

VIBRATION AND STABILITY OF VERTICAL UPWARD-FLUID-CONVEYING PIPE IMMERSED IN RIGID CYLINDRICAL CHANNEL

A theoretical model is developed for the vibration and stability of a vertical pipe subjected concurrently to two dependent axial flows. The external fluid, after exiting the outer annular region between the pipe and a rigid cylindrical channel, is conveyed upwards inside the pipe. This configuration thus resembles of a pipe that aspirating fluid. The equation of planar mo- tion is solved by means of the differential quadrature method （DQM）. Calculations are conducted for a slender drill-string-like and a bench-top-size system, for different confinement conditions of the outer annular channel. It is shown that the vibrations of these two systems are closely related to the degree of confinement of the outer annular channel. For a drill-string-like system with narrow annuli, buckling instability may occur in the second and third modes. For a bench-top-size system, however, both buckling and flutter may occur in the lowest three modes. The form of instability depends on the annuli size.