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。     

变化外形的水线对斜拉索风雨激振的激发作用

讨论变化外形的水线对斜拉桥拉索风雨激振的激发作用.首先,建立考虑水线外形变化的斜拉桥拉索风雨激振计算模型,并将由采用变化水线外形的模型得到的拉索最大振幅与固定水线外形模型的计算结果及试验实测结果对比,对模型进行验证;在模型得到验证的基础上,进一步讨论拉索和变化水线外形的水线振动稳定性及水线对拉索风雨激振贡献.计算结果表明,在四个典型工况下,考虑水线外形变化的模型得到的拉索计算振幅固定水线外形模型能更好地与试验实测振幅吻合;理论分析发现拉索速度和水线速度的耦合作用对水线运动的激发起到主导作用;水线的加速发散发生在拉索大幅激振之前.没有水线加速发散的时程中,拉索均不发生大幅激振.     

考虑塔梁影响的斜拉索随机激励参数振动分析

为了揭示随机激励下斜拉索参数振动特性，考虑塔、梁协同振动的影响，建立了高斯白噪声激励下斜拉索-桥塔-桥面梁耦合振动微分方程，推导了耦合体系的伊藤状态方程组，采用Milstein-Platen法构造了斜拉索振动时程求解迭代格式，研究了斜拉索振动的时程、统计和频域特性，分析了桥塔侧向扶正作用、激励强度和索塔梁初始位移对拉索振幅产生的影响．结果表明：随机激励下斜拉索振动呈现出双“拍”振现象，“拍”幅值和周期具有随机性；拉索随机位移均值、均方差在振动初期具有长时间的非平稳特性；拉索响应幅值对应的频率和拉索功率峰值对应的频率基本一致，但随机激励下的拉索幅值和功率峰值更大；拉索振动概率密度曲线满足高斯分布和马尔科夫性质；桥塔侧向扶正作用越强，拉索振幅越小；激励强度越小，拉索振幅越小；各结构初始位移越大，拉索振幅越大，且对桥面梁初始位移越敏感．     

斜拉桥塔-索-桥面连续耦合参数振动特性分析

针对端部激励作用下斜拉索与桥塔、桥面协同振动问题,考虑拉索几何非线性、倾角、阻尼以及拉索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,推导了拉索与桥塔和桥面共同在激励作用下的耦合振动方程组,研究了桥塔-索-桥面结构系统参数的振动特性,并用数值仿真方法分析桥面与拉索频率比、桥面激励幅值、索力及拉索阻尼对结构耦合振动特性的影响规律。结果表明:桥面与拉索的频率比分别为1∶2和2∶1时,拉索会发生不同模式的大幅振动;相比于超谐波共振模式,亚谐波共振模式的拉索振幅更大,但达到共振所需时间较长;拉索振幅随桥面激励幅值的增大呈非线性增大,桥面激励幅值越大,拉索积蓄共振能量所需的时间越短;拉索振幅随索力增大而减小;拉索自身阻尼对其振动的影响较小,增大拉索阻尼时,拉索振幅虽有减小趋势,但是减小幅度有限。     

拉索预应力巨型网格结构参激振动及动力稳定性研究

针对拉索预应力巨型网格结构的参激振动及动力稳定性问题进行了研究。首先建立索-拱简化模型，分析了桁架拱拉索参激振动的诱发机制与特征，并利用ANSYS软件进一步探究了参激振动的影响因素，然后对简谐荷载作用下拉索预应力桁架拱及整体结构的动力稳定性进行了分析。研究表明：当结构振动频率为索基频的2倍左右时，拉索会发生参激振动，振动响应特征与激励幅值、阻尼、拉索初张力、支承方式等相关；拉索预应力桁架拱在水平简谐荷载作用下一般会发生动力失稳破坏，在竖向简谐荷载作用下发生动力强度破坏，拉索预应力巨型网格整体结构在简谐荷载作用下通常发生动力失稳破坏。     

斜拉桥中斜拉索的面内外耦合内共振分析

研究了桥面侧振引起的斜拉索非线性振动问题。基于Hamilton原理建立了拉索的非线性振动控制方程,并利用多尺度法得到了斜拉索振动方程的二阶近似解。通过具体算例分析了斜拉索面内一阶模态与面外一阶模态相互耦合发生内共振的可能性,讨论了拉索倾斜角对拉索振动的影响,比较了在零初始条件和非零初始条件下拉索振动响应的区别。研究发现:拉索内共振发生在一定的激励频率和激励幅值区域内;改变倾斜角度,会影响拉索发生内共振时激励频率区域的大小;初始条件的不同,拉索的振动形式会相差很大。     

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。     

雷暴冲击风下输电塔风振特性试验研究

基于自主开发的试验装置,在常规边界层风洞中实现了大比例稳态雷暴冲击风剖面的模拟,并以输电塔气弹模型为研究对象,采用非接触式位移测量仪测量模型的风振响应,分析了不同类型雷暴冲击风场下输电塔的平均位移特性,并与常规B类风场下的风振特性进行了对比。试验结果显示,输电塔的风振响应均以两个方向的一阶弯曲振型为主,扭转响应和高阶弯曲响应不显著。随风速增加,不同风场下输电塔位移响应均呈抛物线趋势增大,最大风速处于塔头部位的冲击风场引起的输电塔位移响应明显高于最大风速处于塔身中部冲击风下的响应值,B类风场下的响应介于两类冲击风场间,且不同风场下位移响应间的差距也随风速增加不断增大。     

随机风场下高层结构振动隔震与TMD混合控制研究

针对风荷载作用下高层建筑结构振动控制问题,基于建筑隔震和调谐质量阻尼器振动控制原理,利用ANSYS软件分别建立高层结构带隔震层和带调谐质量阻尼器(TMD)的单一控制策略以及两者相结合的混合振动控制策略。根据Davenport脉动风速谱,采用自回归模型(AutoRegressive,AR)法,考虑竖向相关性、平稳的多变量随机过程以及它的互谱密度矩阵模拟生成具有随机性的脉动风速时程曲线和风速谱的功率谱密度,并用于20层钢结构Benchmark结构模型。系统比较三种振动控制策略在顺风向脉动风载作用下的控制效果,结果表明隔震与TMD混合振动控制方法可以有效地抑制结构风振响应,控制效果很好地弥补了单一振动控制的缺陷。本文方法可应用于大尺度高层结构振动控制中,实现高层建筑结构风振响应的可靠控制。     

热荷载作用下薄板振动能流的可视化研究

基于振动声强法研究了热荷载作用下矩形薄板中振动能量的传递和分布特性.首先,得到热荷载作用下薄板的振动方程,并详细给出了热荷载作用下薄板振动声强的表达式,可利用模态叠加法求出薄板振动的横向位移.之后,利用流线可视化技术,通过流线图显示出薄板振动时能量流出的位置,能量被吸收的位置和能量的流动路径.最后,通过具体的数值算例分析了热荷载和机械荷载对薄板振动时能量流动的影响,数值模拟表明施加热荷载后会改变机械荷载对薄板中振动能量流动的影响,使振动能量的流动路径发生明显改变,且在不同的热荷载作用下,通过改变机械荷载可以抵消热荷载对振动能量流动的影响.     

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。     

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.     

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.     

Rainwater rivulets running on a stay cable subject to wind

Stay cables are likely to vibrate under the combined effect of rain and wind in the so-called phenomenon rain–wind-induced vibrations (RWIVs). Rain takes part in the phenomenon in the shape of water rivulets that run along the cables. In previous articles, the authors investigated the conditions under which such rivulets can be formed. Using a lubrication model, it was shown for a particular wind–cable configuration that rivulets can only be exhibited above a critical wind speed for which gravity is overcome. The rivulets’ position was also predicted with the model. The results were validated by experiments.In this paper, the wind speed at which rivulets appear and their position are expressed for an arbitrary wind–cable orientation. A maximum wind speed for the rivulets’ existence is then estimated as the result of a balance between the drag force and the surface tension. A wind speed interval is consequently obtained for the rivulets’ appearance and maintenance on a cylinder. The boundaries of this interval are expressed in term of Weber numbers, comparing the surface tension and wind effect. These predictions are successfully compared with all the measurements that have been published in the literature.     

相近参数拉索的同/异步振动特性研究

辅助索被认为是一种具有潜力的减振手段,但仅在拉索间发生异步振动时才能取得良好的效果．然而,目前对拉索同/异步振动机理尚缺乏系统研究,为此对双水平索进行了模型试验研究．试验主要关注两根不同垂跨比水平拉索跨中面内响应的相位关系．首先对模型进行不同激励频率和保持激励幅值不变下的振动测试,发现垂跨比相同时,两根索相位差基本保持一致;垂跨比不同时,两根索由同步振动转为异步振动．同时采用有限元软件模拟测试实验,其结果与实验吻合良好．为更进一步探究其机理,对试验模型进行了相同激励幅值下的扫频试验．通过对双索幅频特性和相频特性的分析,发现拉索相近参数导致共振区错位是双索存在异步振动现象的根本原因．     

RESPONSE CHARACTERISTICS OF WIND EXCITED CABLES WITH ARTIFICIAL RIVULET

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Rainwater rivulets on a cable subject to windFilets d'eau de pluie sur un câble soumis au vent

Rainwater rivulets appear on inclined cables of cable-stayed bridges when wind and rain occur simultaneously. In a restricted range of parameters this is known to cause vibrations of high amplitudes on the cable. The mechanism underlying this effect is still under debate but the role of rainwater rivulets is certain. We use a standard lubrication model to analyse the dynamics of a water film on a cylinder under the effect of gravity and wind load. A simple criterion is then proposed for the appearance and position of rivulets, where the Froude number is the control parameter. Experiments with several geometries of cylinder covered with water in a wind tunnel show the evolution of the rivulets with the Froude number. Comparison of the prediction by the model with these experimental data shows that the main mechanism of rivulet formation and positioning is captured. To cite this article: C. Lemaitre et al., C. R. Mecanique 334 (2006).     

Nonlinear Assessment of Cable Vibration in a Stayed Bridge

An experimental study for cables in a stayed bridge is presented. In this analysis, the tensions on the cables were calculated considering linear and nonlinear approaches; for the nonlinear analysis a 2D model was used to evaluate vibration modes and responses under wind and traffic loads. The 8 semi-harp cable stayed bridge used for this study has 112 cables and vibration measurements were done under normal operational conditions. Tensions computed from the nonlinear model were compared with those from the traditional linear model, where average differences were within 3.3%. The estimated tensions from vibration tests have good correlation with the experimental values measured from load tests, while the vibration procedure was carried out in less than 2 days without limiting the bridge operation; converse to the load tests where approximately 30 days are necessary and the bridge traffic has to be closed for short periods during measurements.     

Nonlinear dynamic responses of high-speed railway vehicles under combined self-excitation and forced excitation considering the influence of unsteady aerodynamic loads

The dynamic characteristics of a railway vehicle system under unsteady aerodynamic loads are examined in this study. A dynamic analysis model of the railway vehicle considering the influences of aerodynamic loads was established. The model not only considers the forced excitation effect of unsteady aerodynamic loads but also accounts for the effect of unsteady aerodynamic loads on the change of the wheel–rail contact normal forces as well as changes of the wheelset creep coefficients and creep forces/moments. Therefore, this model also considers the influences of unsteady aerodynamic loads on the self-excited vibration characteristics of the vehicle system. The time-history curves, phase trajectory diagrams, Poincaré sections, and Lyapunov exponents of the vehicle system running on a smooth straight track under unsteady aerodynamic loads were determined. The results show that when the critical speed is exceeded, the vehicle system usually performs quasi-periodic motion under unsteady aerodynamic loads, which is significantly different from the periodic motion under steady aerodynamic loads. In different cases, the amplitude and phase of motion are significantly different. The amplitude of the motions can be increased by more than 159%, and the difference of phase can be up to 173°. (The phase is almost reversed.) The dynamic responses of the vehicle system under unsteady aerodynamic loads contain abundant frequency components, including the frequency of the self-excited vibration, the frequency of the forced excitation, and combinations of their integer multiples. The vibration forms corresponding to the main harmonic components under unsteady and steady aerodynamic loads were compared, and the self-excited vibration component of the vehicle system under unsteady aerodynamic loads was identified. The variations in the critical speed with various parameter combinations were computed. The variation range of the critical velocity can reach 73%.