斜拉索横向振动的积分应变反馈控制实验研究

提出采用积分应变反馈控制方法对斜拉索平面内多模态横向振动实施主动控制,采用粘贴在拉索表面的ＰＶＤＦ压电薄膜传感拉索横向振动时的动态应变信号． 文中介绍了实验系统的组成、特点、在斜拉索比例模型上的实验研究工作以及主动控制的实验结果． 理论与实验研究结果表明积分应变反馈控制方法能明显衰减斜拉索横向振动,避免模态截断引起的溢出问题,而且控制系统实现容易、易实用化．     

Nonlinear FE-based investigation of flexural damping of slacking wire cables

The flexural damping of wire cable due to the flexural hysteresis influences the dynamic behavior of slacking wire cables significantly. However, the details of the local model, accounting for the flexural hysteresis between the wire strands, are quite challenging to include in large-scale engineering applications. This paper addresses these difficulties by modeling the flexural damping of slacking wire cables using homogenized Rayleigh damping. By using the nonlinear finite element method and high-speed imaging technique, three aspects of the work were examined. First, the mechanical properties of the slacking cable were identified experimentally. Second, a sample cable was fixed at one end and allowed to vibrate freely at the other end. The shapes of the vibrating cable were captured by a high-speed digital camera and processed by photogrammetry. The cable demonstrated a high flexural damping at zero tension and its damping was measured to be as high as 37.7% of the critical damping. Third, the cable was modeled and analyzed using our newly developed nonlinear curved beam element with the Rayleigh damping. The finite element predictions of the cable motion agree well with the experimental measurement. These predictions demonstrate that the new element is capable of describing the dynamic response of the cable and that the Rayleigh damping is sufficient to model the flexural damping of slacking wire cables.     

Experimental and Analytical Investigation of Carbon Fiber Cable Vibration Damping

For structures deployed in space using cables where vibration damping is critical for structural stability, cable damping is significant to structural performance. To provide a better understanding of damping mechanism of carbon fiber cables, this paper describes the tests of cable damping under different experimental configurations (different cable length, tension and type), and presents an analytical method for modeling and therefore predicting cable damping. The method is developed using simplified but physically realistic assumptions on material constitutive properties and geometric compatibility conditions, and considered the contact forces and friction between helical wires. The results of the proposed method and several related issues are discussed and compared with those from experiments. These results show that the proposed method is useful and applicable for predicting cable damping value and its variation with cable tension, length and type of the cables.     

A unified approach to aerodynamic damping and drag/lift instabilities,and its application to dry inclined cable galloping

Inclined cables of cable-stayed bridges often experience large amplitude vibrations. One of the potential excitation mechanisms is dry inclined cable galloping, which has been observed in wind tunnel tests but which has not previously been fully explained theoretically. In this paper, a general expression is derived for the quasi-steady aerodynamic damping (positive or negative) of a cylinder of arbitrary cross-section yawed/inclined to the flow, for small amplitude vibrations in any plane. The expression covers the special cases of conventional quasi-steady aerodynamic damping, Den Hartog galloping and the drag crisis, as well as dry inclined cable galloping. A nondimensional aerodynamic damping parameter governing this behaviour is proposed, which is a function of only the Reynolds number, the angle between the wind velocity and the cable axis, and the orientation of the vibration plane. Measured static force coefficients from wind tunnel tests have been used with the theoretical expression to predict values of this parameter. Two main areas of instability (i.e. negative aerodynamic damping) have been identified, both in the critical Reynolds number region, one of which was previously observed in separate wind tunnel tests on a dynamic cable model. The minimum values of structural damping required to prevent dry inclined cable galloping are defined, and other factors in the behaviour in practice are discussed.     

考虑阻尼的无限长小垂度缆索弹性波的传播

缆索结构被广泛应用于电气、土木、海洋和航空工程等领域,随着缆索在工程中的应用长度越来越长,高阶振动越来越明显,研究时应该考虑扰动沿着缆索的传播.现有对缆索弹性波传播的研究中,通常不考虑阻尼项,然而阻尼对于波的传播有着重要影响.文章考虑阻尼的影响,发展了包含阻尼项的三维弹性缆索运动方程.通过求解上述含阻尼项的运动方程,分别考察了面内面外弹性波的频率关系、相速度和群速度等自由传播特性,进而通过计算无限长弹性缆索在初始余弦型脉冲作用下的位移响应,分析扰动沿着该缆索的传播规律,考察波的色散现象以及阻尼对于缆索弹性波传播的影响.结果表明,考虑阻尼后,面内波和面外波均为色散波,面内波在曲率的作用下,为高度色散波.此外,在阻尼的影响下,波的峰值在传播过程不断减小,且波的后缘端点响应总是高于前缘端点响应.     

Numerical stability analysis and control of umbilical–ROV systems in one-degree-of-freedom taut–slack condition

In this paper, the stability of an umbilical–ROV system under nonlinear oscillations in heave motion is analyzed using numerical methods for the uncontrolled and controlled cases comparatively. Mainly the appearance of the so-called taut–slack phenomenon on the umbilical cable produced by interactions of monochromatic waves and an operated ROV is specially focused. Nonlinear elements were considered as nonlinear drag damping, bilinear restoring force and saturation of the actuators. Free-of-taut/slack stability regions are investigated in a space of physical bifurcation parameters involving a set of both operation and design parameters. They indicate a wide diversity in qualitative behaviors, both in the periodicity and possible routes to chaos from the stability regions to outside. For detection of periodicity of the nonlinear oscillations inside and outside the stability regions, a method based on Cauchy series is developed. The first part of the results is dedicated to the stability of the uncontrolled dynamics. These results suggest the design of a control system that is able to counteract hefty hauls of the cable during the sinking/lifting operation under perturbation. A combination of a force and cinematic controller based on nonlinear model–reference control is proposed. Through a comparative study of the stability regions for uncontrolled and controlled dynamics, it is shown that the control system can extend considerably these regions without appearance of the taut–slack phenomenon despite the presence of wave perturbations. The limits between the taut and taut–slack zones are defined by the wave steepness and the available energy of the actuators.     

Static and dynamic response of elastic suspended cables with damage

In cable-stayed structures cables are subjected to potential damage, mainly due to fatigue and galvanic corrosion. The paper presents an analysis of damage effects on the statics and dynamics of suspended cables. An elastic continuous monodimensional model for damaged cables, including geometric nonlinearities, is formulated for the purpose. The damage is described as a diffused reduction of the cable axial stiffness, and defined through its intensity, extent and position. Exact solutions of the equations governing the cable static equilibrium under self-weight are achieved, and the significance of the tension loss and sag augmentation resulting from damage are investigated under variation of practically significant parameters. The system spectral properties characterizing the free undamped dynamics are obtained in a closed-form fashion for shallow cables within the low frequency range. The sensitivity of the frequencies to the intensity and extent of damage is discussed, outlining two damage effects, which alternatively stiffen or soften the cable modes, whose respective static and geometric origin is recognized. Finally, the symmetry-breaking induced by damage on the static profile is verified to destroy the crossing phenomenon (crossover) characterizing the frequency loci of undamaged cables, which degenerates into a narrow frequency veering phenomenon.     

巨型钢框架--拉索支撑结构中拉索的抗侧机理

研究巨型钢框架-拉索支撑结构中预应力拉索的抗侧机理,为确定拉索参数提供理论依据. 基于预应力的作用形态及力学原理分析得到预应力拉索的抗侧机理,推导了预应力拉索抗侧刚度理论公式. 从模型试验的角度进一步研究,将模型试验的结果与理论推导及数值分析的结果进行对比分析,最终验证了预应力拉索的抗侧机理：预应力为柔性拉索建立轴向刚度和稳定性,使预紧过的拉索既可承受拉力,也可承受压力,从而为结构提供弹性约束支撑.     

在中支座可滑动的两跨连续索的静力分析

基于非线性弹性理论,从单索的平衡出发,在索元的无应力长度已知情况下,提出了两跨连续索在中间节点滑移的初始平衡位置确定及均布荷载作用下的静力响应分析方法,建立了其非缄性计算的基本理论、公式和求解方法,并进行了实例计算。     

大射电天文望远镜悬索馈源系统驱动力的研究

针对大射电天文望远镜馈源系统中悬索呈现出的柔性特征，在已知馈源舱的位置，姿态，速度和加速度的情况下，将悬索离散为柔性索杆单元，建立了系统的逆运动学及逆动力学模型。分析计算了悬索上各离散点的位置、速度、加速度和惯性力，推导了在重力和惯性力共同作用下悬索的空间挠曲线方程，研究了悬索的刚体位移和弹性变形。在此基础上，通过刚体-柔性的迭代计算，求出悬索馈源系统的驱动力，为高精度的大射电天文望远镜提供了必要的设计参数。     

Experimental investigation of wind-induced vibrations of main cables for suspension bridges in construction phases

The main cables of suspension bridges show a changing cross-sectional shape with the evolution of construction phases, and they may suffer from severe wind-induced vibrations at certain conditions. The primary objective of this research was to examine the aerodynamic performance of the main cable in construction phases and to develop appropriate countermeasures to eliminate the potential wind-induced vibrations. Two cross-sections with different shapes of a main cable were chosen, and a series of wind tunnel tests were performed in a reduced wind velocity range of 32–366 using elastically mounted sectional models. Galloping occurred for the two cross-sections under certain wind incidence angles when a critical velocity was reached. No obvious hysteresis phenomenon of galloping was observed in the tests. The steady amplitude of galloping increased linearly with wind velocity and the increasing rate almost kept constant for different structural damping ratios. The aerodynamic nonlinearity, rather than the structural damping nonlinearity, is the main source leading to the limited amplitude oscillation. An empirical expression of galloping amplitudes for the two cross-sections was derived based on the test data. Meanwhile, the critical wind velocity was studied in a Scruton (Sc) number range of 108–4196 (as varied by changing the initial structural damping ratio between 0.093% and 3.62%). Results showed that the Den Hartog criterion was applicable to forecast the possibility of galloping, but not able to estimate the critical wind velocity for the main cable. Linear fitting method can be used to predict the critical velocity based on the experimental data. Finally, three vibration mitigation measures were studied, and a combination of structural and aerodynamic measures was recommended for galloping mitigation of main cables.     

斜拉桥三维拉索风雨激振准两自由度模型

拉索风雨激振是当前桥梁工程和风工程界非常关注的研究课题。过去用于测量带人工水线的拉索模型都是二维的，所建立的理论模型也是建立在二维拉索气动力的基础上的。本文基于带人工水线三维拉索模型试验得到的气动力，建立了三维拉索风雨激振的准二自由度运动微分方程，讨论了运动方程中各种参数的取值，采用数值求解方法计算了拉索风雨激振振幅。计算结果和三维拉索人工降雨试验结果的对比表明，本文方法能较好地描述三维拉索风雨激振的特征。     

RESPONSE CHARACTERISTICS OF WIND EXCITED CABLES WITH ARTIFICIAL RIVULET

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工程索结构动力学:非线性建模与分析

索结构因其轻、柔及高强度等特性被作为受拉构件广泛应用于工程领域.一方面,环境载荷激励下索结构产生了复杂的大幅动力响应,给结构带来危害;另一方面,索结构是一个同时含有平方和立方非线性的典型力学系统,具有非常丰富的非线性动力学行为.因此,索动力学的研究受到了工程界和力学界的广泛关注,产生了大量的研究成果.本文尝试从索结构动力学建模、非线性内共振分析、支座运动激励下的索动力学以及复杂环境载荷作用4个方面对索动力学研究进行总结,并讨论目前研究的局限性.     

Theoretical and experimental studies on the aerodynamic instability of a two-dimensional circular cylinder with a moving attachment

Rain–wind induced vibration of cables in cable-stayed bridges is a worldwide problem of great concern. The effect of the motion of water rivulets on the instability of stay cables has been recognized as one of the mechanisms of this complex phenomenon. In order to investigate how the motion of rivulets affects the unstable vibration of cables without considering the effects of axial flow and axial vortex, a real three-dimensional cable was modeled as a two-dimensional circular cylinder, around which an attachment representing the rivulet can move. This could also be regarded as a new kind of two-dimensional 2-dof dynamic system. This paper studies the aerodynamic instability of the system theoretically and experimentally. Equations governing the motions of the cylinder and the attachment are first established. The Lyapunov stability criterion is applied to the equations of motion to derive the criterion for the unstable balance angle of the attachment. Moreover, a new two-dimensional 2-dof cable model system with a movable attachment is designed and tested in a wind tunnel. Parametric studies are carried out to investigate the effects of major factors such as wind speed, frequency and damping of the dynamic system on the unstable balance angle of the rivulet attachment. Theoretical and experimental results match well. These results may be valuable in elucidating the mechanism of rain–wind induced vibration of stay cables.     

Effect of hoisting cable elasticity on anti-sway controllers of quay-side container cranes

Oscillation frequency of crane payloads is the main and most important factor in crane anti-sway control systems design. In the summer of 2005, a Smart Sway Control system (SSC) was installed on a 65-ton quay-side container crane at Jeddah Port. During the calibration phase of the installation, it was observed that heavy payloads combined with the dynamic stretch of the hoist cables had a significant impact on the configuration of the hoisting mechanism and the pattern of oscillation. This introduced considerable change in the oscillation frequency of the payload, which resulted in a significant impact on the performance of the anti-sway control system. Empirical formulas had to be used to compensate for the change in the frequency approximation used in the controller algorithm. In this work, an analytic approximation of the oscillation frequency of the hoisting mechanism of a quay-side container crane is developed, which takes into consideration the elasticity of the hoisting cables. A parametric study is performed to investigate the extent of the effect of the hoisting cables stretch on the system behavior for a typical range of payload masses and cable lengths. The performance of the delayed feedback control system used in the SSC controller is simulated on an elastic cables model using both the elastic and rigid cable frequency approximations.     

张拉结构非线性分析两节点曲线单元有限元法

提出适合张拉结构几何非线性分析的两节点曲线单元有限元方法．假定索元的初始形状呈二次抛物线,根据单索的平衡条件、几何和物理关系建立了索元的位移函数;由拉格朗日应变的定义建立了可以考虑任意次高阶位移影响的索元轴向应变的精确表达式,并基于拉格明日描述方法和虚功原理得到了索元的非线性平衡方程与切线刚度矩阵．采用荷载增量法与Newton－Raphson法相结合的混合法进行了实例计算,结果表明：本文方法的精度明显优于两节点直线索单元,适合于大跨度索阿、索穹顶等张拉结构的几何非线性分析．     

Random vibrations of an isochronous SDOF bilinear system

A single-degree-of-freedom (SDOF) system with bilinear restoring force and damping characteristics is excited by a white-noise force. For the case of small damping the asymptotic method of quasi-conservative stochastic averaging is applied, which reduces the problem to that of a single Ito stochastic differential equation (SDE) for total energy of the response. A special case of the isochronous system is considered, where the static equilibrium position coincides with the slope discontinuity point of the system's characteristics, such as that of a moored body without slack and pretension in the mooring cable. For this case an analytical solution is obtained for autocorrelation function of the response energy. For the limiting case of a vibroimpact system the results are shown to agree with the exact solution.     

行进绳索在横向流体激励下的运动

给出横向流体对行进绳索的作用力描述,建立了绳索的动力学方程。由于该方程具有零刚度特征,引入Pilipchuk变换,以自平衡状态起度量的径向振动和回转运动来描述绳的运动,获得非零刚度系统。然后,用两变量参数摄动法求得绳索关于扩张振动和回转运动的约化型,使得绳索运动可近似由一个二维动力系统来描述。最后,用数值方法讨论了行进速度和重力对绳索运动形态的影响。     

巨型钢框架——拉索吊挂结构拉索参数确定方法

如何确定拉索参数是巨型钢框架——拉索吊挂结构的关键问题. 基于简化模型推导了竖向载荷下结构内力及变形的求解方程;依据牛顿定律分析了水平载荷作用下, 不同的滑移状态拉索对框架受力变形的影响, 得到了拉索索力增量最大值的关系式;最终, 根据"正常使用状态下, 巨型梁的挠度满足规范要求"的拉索参数确定准则, 建立了首先确定拉索截面积、再确定拉索预拉力的确定方法. 为巨型钢框架-拉索吊挂结构的性能评判和初步设计奠定理论基础.