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。     

考虑非稳态风荷载斜拉索风雨激振响应分析

为研究自然风荷载对斜拉桥拉索风雨激振的影响,将数值模拟的非稳态风荷载作用到拉索振动微分方程中,对拉索振动响应进行了详细分析。首先,针对水线初始位置,使用最小二乘法拟合得到水线初始位置方程;接着,采用四阶Runge-Kutta法求解拉索振动响应。通过比较在非稳态风和稳态平均风作用下的拉索响应,发现在非稳态风荷载下拉索最大振幅的变化趋势并没有发生较大改变,皆是随着风速的增大先增大后减小;但拉索的整个振动过程发生了变化,伴随着节拍改变,其最大振幅也出现在不同振动周期内。此外,从风速-振幅曲线知,对频率为1 Hz,2 Hz和3 Hz的拉索,在一定风速范围内,考虑非稳态风荷载的拉索振幅反而更大,而且此时的风速范围也更大。     

考虑非稳态风荷载斜拉索风雨激振响应分析

为研究自然风荷载对斜拉桥拉索风雨激振的影响,将数值模拟的非稳态风荷载作用到拉索振动微分方程中,对拉索振动响应进行了详细分析。首先,针对水线初始位置,使用最小二乘法拟合得到水线初始位置方程;接着,采用四阶Runge-Kutta法求解拉索振动响应。通过比较在非稳态风和稳态平均风作用下的拉索响应,发现在非稳态风荷载下拉索最大振幅的变化趋势并没有发生较大改变,皆是随着风速的增大先增大后减小;但拉索的整个振动过程发生了变化,伴随着节拍改变,其最大振幅也出现在不同振动周期内。此外,从风速-振幅曲线知,对频率为1Hz,2Hz和3Hz的拉索,在一定风速范围内,考虑非稳态风荷载的拉索振幅反而更大,而且此时的风速范围也更大。     

斜拉索模态试验参数研究

试验模态分析是斜拉桥索力测试中广泛应用的方法。该方法的关键之一是采取合理的试验方案获取可靠的响应信号以识别出正确的索振动频率。本文通过试验,详细讨论了斜拉索模态测试中若干试验参数,如激振类型、激振位置、传感器位置以及频率分辨率对试验结果的影响;比较环境激励与锤击激励的效果,验证了环境激励的方法也可以准确识别索的频率;最后给出了较为合理的斜拉索模态试验方案,用该方案确定的索力与理论计算结果相差不超过 1. 5%。     

端点位移激励下斜拉索非线性振动计算方法研究

考虑拉索不同阶模态大幅振动之间的耦合效应,根据拉索的振动理论,详细地推导了单根拉索在端点位移激励下发生大幅振动时的非线性振动方程。根据某实际斜拉桥拉索参数,讨论了不同垂跨比对拉索振动特性的影响。使用四阶Runge-Kutta法求解拉索的非线性振动方程,通过对比有限元模型的非线性动力时程积分数值计算结果,验证了理论模型的可靠性与适用性。     

端点位移激励下斜拉索非线性振动计算方法研究Investigation on computing method of nonlinear vibration of the stayed cable with displacement excitation at the end point

考虑拉索不同阶模态大幅振动之间的耦合效应,根据拉索的振动理论,详细地推导了单根拉索在端点位移激励下发生大幅振动时的非线性振动方程。根据某实际斜拉桥拉索参数,讨论了不同垂跨比对拉索振动特性的影响。使用四阶Runge-Kutta法求解拉索的非线性振动方程,通过对比有限元模型的非线性动力时程积分数值计算结果,验证了理论模型的可靠性与适用性。     

斜拉桥塔-索-桥面耦合参数振动模型及响应分析

针对大跨度斜拉桥拉索与桥塔、桥面的协同振动问题,考虑拉索垂度、阻尼、倾角以及重力弦向分力的影响,引入拉索高精度抛物线形,建立了桥塔-索-桥面连续非线性精细化振动模型,推导了桥塔和桥面共同激励作用下斜拉索耦合振动方程,对比分析了2种激振模式下斜拉索的参数振动特性,并编制程序研究了桥面与拉索的频率比、桥面激励幅值、索力及阻尼对结构耦合振动特性的影响规律。结果表明：桥面与拉索频率比对系统振动的影响较大,频率比为1:2和2:1时拉索均产生强烈振动,但2:1激振模式下拉索振幅更大,达到共振时间较长;随着桥面激励幅值的增大,2:1亚谐波共振模式下的拉索振幅增长速率更快;拉索振幅随索力的增大呈非线性减小趋势;斜拉索阻尼超过2%时,继续提高自身阻尼不能有效减小其振动幅值,需要通过设置附加阻尼才能更好地抑制其振动。     

中心有刚体质量的环形薄板的非线性强迫振动

本文研究中心带有刚体质量外部固定铰支或活动铰支的环形薄板的非线性强迫振动。考虑板的弯曲变形、面内位移和几何非线性，用哈米尔顿原理建立板的运动方程，用Ｋａｎｔｏｒｏｖｉｃｈ平均法消去时间变量，然后用数值积分求得非线性振动的振幅随激振力的大小及激振力的频率而变化的关系。求解过程中用打靶法逐步改进未知参量，以保证边界条件的满足。最后讨论薄膜力、激振力的分布、板的内外半径比等因素对响应的影响     

海洋热塑性增强管(RTP)涡激振动数值计算

基于Van der Pol尾流振子模型和多体系统传递矩阵法(transfer matrix method for multibody systems, MSTMM), 建立了可以快速预测海洋热塑性增强管(reinforced thermoplastic pipe, RTP)振动特性和涡激振动响应的动力学模型. 仿真结果与ANSYS软件仿真结果以及文献实验数据对比, 验证了本文模型的准确性. 研究了考虑RTP立管刚性接头, 不同顶张力, 不同来流分布等情况对RTP立管涡激振动响应的影响. 计算结果表明: 流速越大, 立管涡激振动激发出的模态越高; 立管涡激振动主要受低阶模态控制; 立管的刚性接头对立管的湿模态影响较小, 但是对较高阶模态为主所激发出的涡激振动振幅分布影响较大; 剪切流对沿立管轴向的涡激振动振幅分布影响较大, 低流速能量小所引起的涡激振动幅值较小, 但是当剪切流流速达到能激发出较高阶模态时, 相比同等流速的均匀流所引起的涡激振动振幅要大.      

安装固定气动翼板的大跨桥梁抖振分析

建立了安装固定气动翼板的大跨桥梁多模态耦合抖振分析框架，推演了作用在整个桥梁-气动翼板系统上的抖振力和自激力的显式表达式，考虑了多模态耦合效应．基于有限元法，作用在主梁-气动翼板系统上的抖振力转化为节点力，进一步得到作用在整个桥梁上的抖振力并导出了其功率谱密度矩阵；作用在主梁．气动翼板系统上的气弹自激力转化为节点力，并将其表达为气弹刚度矩阵和气弹阻尼矩阵．通过组集得到系统的运动方程，然后运用虚拟激励法在频域计算系统的抖振响应．以某大跨斜拉桥为例进行研究，结果表明：在主梁下方安装-对固定气动翼板后，主梁的扭转角位移、角加速度以及侧向加速度响应能够得到有效控制。     

Study on the role of rivulet in rain–wind-induced cable vibration through wind tunnel testing

Rain–wind-induced vibration (RWIV) of stay cables has become a concern in bridge engineering over the past decades. The excitation mechanism of RWIV remains unclear. Many researchers believe that the upper rivulet is crucial to RWIV. However, experimental study on rivulet is challenging and limited. The current study designs and tests a cable model of 160 mm in diameter in an open jet wind tunnel. The upper rivulet movement and cable vibration are simultaneously measured. The importance of the upper rivulet in RWIV is directly demonstrated by alternately controlling the upper and lower rivulets. The characteristics of the upper rivulet movement and the effects of this movement on RWIV are investigated in detail. The experiment shows that the rivulet–cable system is coupled, which causes the cable and upper rivulet to vibrate at different amplitudes under the same wind speed. The upper rivulet harmonic movement changes the wind loading on the cable, causing the harmonic vibration of the cable, which in turn exerts a harmonic inertia force on the rivulet. A large vibration of the coupled system then develops.     

Numerical simulation and analysis of the effects of water-film morphological changes on the aerodynamic lift of stay cables

The cables in cable-stayed bridges can vibrate at large amplitudes during rain and windy conditions, a phenomenon known as rain-wind induced vibration (RWIV). Previous studies have demonstrated that the formation and oscillation of rivulets on stay cable surfaces play an important role in RWIV.This paper presents a new numerical method for simulating the evolution of rivulets on stay cable surfaces based on a combination of the gas–liquid two-phase theory and the volume of fluid method (VOF method), which allows for the straightforward determination of the cables’ aerodynamic lift when RWIV occurs. To verify the accuracy of this method and analyze the effects of wind velocity on the water film and the aerodynamic lift around the cable, three cases with different loadings were investigated using the computational fluid dynamics (CFD) software CFX. To verify the method’s accuracy, the aerodynamic lifts calculated from these cases were applied to the cable to obtain its vibrational response. In accordance with the experimental results, the numerical results demonstrated that an upper rivulet with a periodic oscillation was formed at a specific wind speed, causing the aerodynamic lift to change with a similar periodicity. The aerodynamic lift’s frequency was approximately the cable’s natural frequency, and induced large vibrations in the cable. No obvious upper rivulets were formed at sufficiently low wind speeds. The frequency of an aerodynamic lift that was significantly larger than the cable’s natural frequency induced small vibrations in the cable. When the wind speed was sufficiently high, despite the eventual formation of a continuous upper rivulet, the frequencies of the upper rivulet’s oscillation and the aerodynamic lift remained distinct from the natural frequency, and the cable continued to exhibit small-amplitude vibrations. These observations confirmed the conclusion that periodic variations in the water film morphology could lead to periodic changes in the aerodynamic lift that would induce RWIV.     

Three-phase coupled modelling research on rain–wind induced vibration of stay cable based on lubrication theory

Cables of cable-stayed bridges may vibrate with large amplitude under wind and rain, which is known as rain–wind induced vibration (RWIV). According to the pervious researches, the formations and oscillations of rivulets on stay cable surface play important roles in RWIV. In this paper, four different 2D models are presented based on lubrication theory, and the best way of simulating RWIV through lubrication theory is confirmed by the comparisons of rivulet motions and cable vibration responses between these four models and pervious researches. On this basis, the relations among rivulet motions, cable aerodynamic forces and vibration responses are investigated to reveal the mechanism of RWIV. Numerical simulation results show that when RWIV occurs, the periodic oscillations of rivulets around cable lead to the periodic fluctuations of cable lift and drag, whose frequencies are almost equal and close to cable natural frequency. Under the periodically fluctuant lift and drag, cable vibrates with large amplitude in across-wind and along-wind directions, which may further enhance the circumferential oscillations of rivulets conversely. These confirm the conclusion that the resonance between rivulets and cable oscillation may be one of the main reasons for RWIV.     

Aerodynamic characteristics of an inclined and yawed circular cylinder with artificial rivulet

Stay cables of cable-stayed bridges often experience vibrations with large amplitudes induced by wind or jointly by both wind and rain. To understand the aerodynamic characteristics of the stay cables and excitation mechanics of rain–wind-induced vibration (RWIV), an inclined and yawed circular cylinder with and without an artificial upper rivulet is studied through a series of wind tunnel tests. The impacts of upper rivulet and axial flow on the aerodynamics of the cylinder are investigated. It is found that for an inclined and yawed cylinder without rivulet there exists a non-zero lift force at large wind angle. Furthermore, the wind pressures and aerodynamic forces acting on both the cylinder and the upper rivulet are obtained, which can be used to develop more rational theoretical models for RWIV of stay cables. Results show that the upper rivulet can both enhance and depress Karman vortex shedding depending on the position of the rivulet. As a result, dramatic variations of the aerodynamic forces acting on the cylinder and the rivulet will occur, which may eventually result in RWIV. Also axial flow may have a noticeable influence on the aerodynamic characteristics of the inclined and yawed cylinder. And the presence of the rivulet can enhance such influence from the axial flow.     

RESPONSE CHARACTERISTICS OF WIND EXCITED CABLES WITH ARTIFICIAL RIVULET

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A numerical and experimental hybrid approach for the investigation of aerodynamic forces on stay cables suffering from rain-wind induced vibration

The aerodynamic forces on a stay cable under a rain-wind induced vibration (RWIV) are difficult to measure directly in a wind tunnel test. This paper presents a hybrid approach that combines an experiment with computational fluid dynamics (CFD) for the investigation on aerodynamic forces of a stay cable under a RWIV. The stay cable and flow field were considered as two substructures of the system. The oscillation of the stay cable was first measured by using a wind tunnel test of a RWIV under an artificial rainfall condition. The oscillation of the cable was treated as a previously known moving boundary condition and applied to the flow field. Only the flow field with the known moving cable boundary was then numerically simulated by using a CFD method (such as Fluent 6.3). The transient aerodynamic forces of the stay cable with a predetermined cable oscillation were obtained from numerical calculations. The characteristics of the aerodynamic forces in the time domain and frequency domain were then analysed for various cases. To verify the feasibility and accuracy of the proposed hybrid approach, the transient aerodynamic forces were applied to a single-degree-of-freedom model (SDOF) of the stay cable to calculate the RWIV of the cable. A comparison was performed between the oscillation responses of the stay cable obtained from the calculated (SDOF model) and experimental results, and the results indicate that the hybrid approach accurately simulates the transient aerodynamic forces of the stay cable. The equivalent damping ratios induced by the aerodynamic forces were obtained for various wind speeds. Furthermore, a nonlinear model of the aerodynamic force is proposed based on the calculation results, and the coefficients in the model were identified by a nonlinear least-squares technique.     

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.     

Numerical investigation of the coupled interaction between an unsteady aerodynamic flow field and a water film coating on a circular cylinder

Rain–wind induced vibration is an aeroelastic phenomenon that occurs on the inclined cables of cable-stayed bridges and arises due to the interaction between the unsteady wind loading and the formation of water rivulets on the cable surface. A new numerical method has been developed at the University of Strathclyde to simulate the influence of the external flow field on the rivulet dynamics and vice versa. The approach is to couple a Discrete Vortex Method solver to determine the external flow field and unsteady aerodynamic loading, and a pseudo-spectral solver based on lubrication theory to model the evolution and growth of the water rivulets on the cable surface under external loading. Results of this coupled model are presented, to provide detailed information on the development of water rivulets and their interaction with the aerodynamic field. In particular, the effect of the initial water film thickness and the angle of attack in plane on the resulting rivulets are investigated. The results are consistent with previous full scale and experimental observations with rivulets forming on the upper surface of the cable only in configurations where rain–wind induced vibration has been observed. Additionally, the thickness of the lower rivulet is found to be self-limiting in all configurations. The results demonstrate that the model can be used to enhance the understanding of the underlying physical mechanisms of rain–wind-induced vibration.