变槽宽比双主梁断面悬索桥抖振响应特性

    沈正峰 李加武 王峰

    

    

    

    摘要: 为了研究变槽宽比双主梁断面悬索桥抖振响应,提出考虑自激力和抖振力沿展向变化的频域和时域抖振计算方法,对某景观大桥进行抖振分析。频域法研究了气动导纳函数、平均风速、脉动风交叉谱对抖振响应的影响,分析不同类型气动导纳函数对抖振响应的影响差异及原因。时域法通过在每个荷载步更新三分力系数进而更新气动力,并考虑结构的几何非线性效应。计算结果表明:考虑气动力展向变化的时域法能够捕捉到跨中单索面位置的局部峰值;时域抖振响应计算值在竖向大于频域计算值,在扭转方向要小于频域计算值;考虑气动力展向变化计算的抖振响应要大于采用跨中断面气动参数计算的抖振响应,其主要由抖振力的展向变化产生,自激力的展向变化对其影响较小,在实际工程中考虑气动力展向变化进行抖振分析更加安全。

    关键词: 抖振; 悬索桥; 变槽宽比; 多模态耦合频域; 气动导纳; 交叉谱

    中图分类号: U441+.3; U448.25 ?文献标志码: A ?文章编号: 1004-4523(2020)04-0824-10

    DOI:10.16385/j.cnki.issn.1004-4523.2020.04.021

    引 言

    近年来,基于多幅主梁断面气动特性的研究,多幅主梁断面成为长大桥梁的优选方案之一。比较著名的有西堠门大桥(主跨1650 m)[1],墨西拿海峡大桥(主跨3300 m)[2]。分幅式主梁能够应用到长大桥梁的主要原因是其出色的气动性能和良好的经济效益[3]。试验和理论分析认为分幅式主梁断面在增加槽宽比(SWR)的情况下能够显著提高颤振临界风速[4]。然而,Yang等[5]认为这并不是无条件的,其研究结果表明双幅箱型主梁的气动特性取决于箱梁的形状和槽宽比两个因素。大量风洞试验和CFD技术的研究结果表明槽宽比会影响主梁的三分力系数、颤振导数和气动措施对提高主梁颤振稳定性的有效性,甚至会使主梁在较低的风速下发生扭转发散[6-9]。虽然合适的槽宽比可能对主梁颤振稳定性有提高作用,但却造成主梁对涡振非常敏感[10]。已有研究结果表明槽宽比是引起主梁发生涡激振动的关键,其对主梁周围涡结构尺寸、涡分离位置、脉动压力和涡振幅值都有较大的影响[11-13]。由于槽宽比会影响断面的气动参数,进而影响到断面所受的自激力和抖振力,所以抖振响应必将受到槽宽比的影响。另外,周奇等[14-15]研究了双幅主梁断面的气动导纳函数和抖振力谱特性,结果表明气动导纳函数受槽宽比的影响显著,抖振力谱可以近似地线性分解为来流紊流抖振力谱和特征紊流抖振力谱。

    虽然槽宽比对主梁的稳定性和风致响应影响非常大,很多机理性问题正在寻求突破,但这不妨碍学者对混合型(单-双幅)主梁断面进行前瞻性研究,试图解决长大桥梁风致扭转位移过大和颤振稳定性问题[16]。基于这个想法,国内已经将变槽宽比主梁断面运用到实际工程。对于变槽宽比主梁断面,在具备等槽宽比主梁断面的一切特性以外,其截面特性和所受的气动力因槽宽比的变化都将沿展向发生变化。以往研究结果表明普通主梁断面的自激力沿展向相关性很高[17],因而经典抖振分析理论认为自激力沿展向是完全相关的。此外,影响抖振力的三分力系数与槽宽比有关[6, 8],考虑脉动风非定常特性的气動导纳函数与主梁断面宽度也密切相关,因而抖振力沿展向也会产生变化。以上分析表明,对于变槽宽比主梁断面,经典抖振分析方法明显不符合实际情况,那么在一定的试验条件下,如何通过有限的节段模型试验估算变槽宽比主梁断面的风致抖振响应,成为工程中亟待解决的问题。

    目前,对变槽宽比主梁断面的抖振响应研究不多,如何经济有效地评估计算结果的正确性成为一个问题。现阶段,抖振响应计算方法主要有频域法和时域法。频域法程序化强,但无法考虑非线性影响;时域法虽然能考虑非线性因素,但是程序编制通用性差。李永乐等[18]指出频域结果和时域结果的一致性是计算结果可靠性的一种验证。因而,本文为了研究变槽宽比双主梁断面悬索桥抖振响应的特性,通过风洞试验实测四个典型断面的气动参数,提出考虑抖振力和自激力沿展向变化的频域和时域抖振响应计算方法,并进行对比性研究;同时研究了沿展向变化的气动导纳函数、脉动风交叉谱和平均风速对抖振响应的影响,研究结果为类似工程抗风设计提供参考。

    1.2 非线性时域分析

    目前,抖振时域计算一般通过数值方法生成满足特定功率谱密度和空间相干函数的脉动风时程,在有限元程序中施加等效荷载。根据文献[24]自激力可以在ANSYS中使用Matrix27单元分别表示成刚度矩阵和阻尼矩阵。通过提取每个荷载步断面位置来考虑瞬时风攻角变化效应,在下一荷载步更新抖振力和自激力大小,这种分析方法可以考虑结构的几何非线性和气动力非线性效应,在国内被广泛使用。由于每个断面特性不同,本文采用输入每个主梁节点的三分力系数及其导数,建立每个节点的气动刚度矩阵和气动阻尼矩阵,施加沿展向变化的气动力,计算抖振响应。

    2 工程概况

    某景观大桥是一座单跨400 m单双索面交替的悬索桥,跨中为单索面,两边各1/4跨径为双索面,其跨度在单跨单索面悬索桥中居中国第一、世界第二,其效果图如图1所示。由图可见此桥主梁断面为分离式变槽宽比双钢箱结构,双箱之间通过横梁连接,两幅钢箱梁从跨中到桥塔距离变化为2-14.45 m,单边箱梁宽度为11.45 m。主跨跨中桥面距水面高度为29.5 m,10 m高度处的基本风速为32.285 m/s,地表粗糙度系数α=0.12,假设风剖面满足指数律,则桥面设计基准风速为36.76 m/s。

    为了进行抖振响应计算,考虑拉索垂度效应,建立单主梁有限元模型,前10阶模态分析结果如表1所示。

    编制APDL命令提取主梁各阶振型归一化模态坐标,第2阶振型在各自由度模态位移结果如图2所示。

    3 风洞试验

    槽宽比是一个尺寸比的无量纲量,一般指主梁开槽宽度和箱梁宽度的比值。本文的槽宽比定义采用文献[5]中开槽宽度和两个主梁宽度之和的比值。根据变槽宽比抖振计算理论,考虑气动力沿展向变化需要用到主梁断面在各个槽宽比下的三分力系数和颤振导数,其试验工作量较大,也不现实。为了简便,本文通过试验测量典型断面的三分力系数来表示气动力。节段测力模型采用的几何缩尺比为1∶50,模型长300 mm,制作槽宽比为0.087,0.226,0.395和0.631四个节段模型,断面位置如图3所示。图4是槽宽比为0.087状态下的测力试验模型。槽宽比为0.087和0.631工况下的三分力系数如图5所示,使用多项式拟合不同角度下的三分力系数曲线,求出三分力系数一阶导数,主梁其他节点三分力系数及一阶导数按照线性插值进行计算。

    不考虑模态耦合,如图14(a)所示,经过移项,得出考虑变槽宽比效应的气动参数更能增加结构的阻尼效应。由于抖振力系数的平方将影响抖振力谱,如图14(b)所示,采用跨中断面的气动参数将减小抖振力谱值。综合以上,采用跨中断面气动参数将会降低增加结构阻尼的幅值,同时降低抖振力,后者影响更大,总体使结構响应降低。同理,扭转和竖向可以采用类似方法分析。分析三个方向抖振响应减弱的原因表明:抖振力的展向变化导致模态抖振力的变化是造成抖振响应差异的主要原因,自激力的展向变化对其影响较小。

    5 结 论

    本文提出考虑断面抖振力和自激力展向变化的抖振频域和时域分析方法,系统研究了变槽宽比双主梁断面悬索桥抖振响应特性,得出以下结论:

    (1)三种展向变化的气动导纳函数对抖振响应有明显的减弱作用,对扭转自由度减弱程度最小,Holmes函数对抖振响应减弱最明显。

    (2)交叉谱密度函数对抖振响应的影响很小,抖振响应与平均风速成正相关,抖振响应增加速率大于风速增加速率。

    (3)时域计算的抖振响应在竖向要大于频域计算值,在扭转方向要小于频域计算值。考虑气动参数展向变化的时域法能够捕捉到跨中抖振响应的局部峰值。

    (4)时域法和频域法都表明考虑气动力展向变化计算的抖振响应要大于采用跨中断面气动参数计算的抖振响应,其主要原因是由于抖振力的展向变化,自激力的展向变化对此贡献较小。

    参考文献:

    [1] Zhang Z T, Ge Y J, Yang Y X. Torsional stiffness degradation and aerostatic divergence of suspension bridge decks[J]. Journal of Fluids and Structures, 2013, 40:269-283.

    [2] Baldomir A, Kusano I, Hernandez S, et al. A reliability study for the Messina Bridge with respect to flutter phenomena considering uncertainties in experimental and numerical data[J]. Computers & Structures, 2013, 128:91-100.

    [3] Trein Cristiano Augusto, Shirato Hiromichi, Matsumoto Masaru. On the effects of the gap on the unsteady pressure characteristics of two-box bridge girders[J]. Engineering Structures, 2015, 82:121-133.

    [4] Sato Hiroshi, Kusuhara Shigeki, Ogi Kenichi, et al. Aerodynamic characteristics of super long-span bridges with slotted box girder[J]. Journal of Wind Engineering and Industrial Aerodynamics, 2000, 88(2-3): 297-306.

    [5] Yang Yongxin, Wu Teng, Ge Yaojun, et al. Aerodynamic stabilization mechanism of a twin box girder with various slot widths[J]. Journal of Bridge Engineering, 2014, 20(3): 04014067.

    [6] Yang Yongxin, Zhou Rui, Ge Yaojun, et al. Aerodynamic instability performance of twin box girders for long-span bridges[J]. Journal of Wind Engineering and Industrial Aerodynamics, 2015, 145:196-208.

    [7] Yang Yongxin, Zhou Rui, Ge Yaojun, et al. Flutter characteristics of twin-box girder bridges with vertical central stabilizers[J]. Engineering Structures, 2017, 133:33-48.

    [8] Zhou Rui, Yang Yongxin, Ge Yaojun, et al. Comprehensive evaluation of aerodynamic performance of twin-box girder bridges with vertical stabilizers[J]. Journal of Wind Engineering and Industrial Aerodynamics, 2018, 175:317-327.

    [9] Tang Haojun, Shum K M, Li Yongle. Investigation of flutter performance of a twin-box bridge girder at large angles of attack[J]. Journal of Wind Engineering and Industrial Aerodynamics, 2019, 186:192-203.

    [10] Alvarez A J, Nieto F, Kwok K C S, et al. Aerodynamic performance of twin-box decks: A parametric study on gap width effects based on validated 2D URANS simulations[J]. Journal of Wind Engineering and Industrial Aerodynamics, 2018, 182:202-221.

    [11] Laima Shujin, Li Hui. Effects of gap width on flow motions around twin-box girders and vortex-induced vibrations[J]. Journal of Wind Engineering and Industrial Aerodynamics, 2015, 139:37-49.

    [12] Chen Wen-Li, Li Hui, Hu Hui. An experimental study on the unsteady vortices and turbulent flow structures around twin-box-girder bridge deck models with different gap ratios[J]. Journal of Wind Engineering and Industrial Aerodynamics, 2014, 132:27-36.

    [13] Kwok Kenny C S, Qin Xian-rong, Fok C H, et al. Wind-induced pressures around a sectional twin-deck bridge model: Effects of gap-width on the aerodynamic forces and vortex shedding mechanisms[J]. Journal of Wind Engineering and Industrial Aerodynamics, 2012, 110:50-61.

    [14] 周 奇, 朱樂东, 任鹏杰, 等. 气动干扰对平行双幅断面气动导纳影响研究[J]. 振动与冲击, 2014, 33(14): 125-131.

    Zhou Qi, Zhu Ledong, Ren Pengjie, et al. Aerodynamic interference effect on the aerodynamic admittance of paralleled double girders[J]. Journal of Vibration & Shock,2014,33(14):125-131.

    [15] 周 奇, 朱乐东, 赵传亮. 开槽断面斜拉桥的随机抖振数值分析[J]. 土木工程学报, 2014, 47(08): 98-106.

    Zhou Qi, Zhu Ledong, Zhao Chuanliang. Numerical analysis on stochastic buffeting of cable-stayed bridge with slotted deck[J] China Civil Engineering Journal,2014,47(08):98-106.

    [16] Ogawa K, Shimodoi H, Oryu T. Aerodynamic characteristics of a 2-box girder section adaptable for a super-long span suspension bridge[J]. Journal of Wind Engineering and Industrial Aerodynamics, 2002, 90(12-15): 2033-2043.

    [17] Haan Fred L Jr, Wu Teng, Kareem Ahsan. Correlation structures of pressure field and integrated forces on oscillating prism in turbulent flows[J]. Journal of Engineering Mechanics, 2016, 142(5): 04016017.

    [18] 李永乐 廖海黎, 强士中. 桥梁抖振时域和频域分析的一致性研究[J]. 工程力学, 2005, 22(2): 179-183.

    Li Yongle, Liao Haili, Qiang Shizhong.Bridge buffeting analysis in time and frequency domains[J]. Engineering Mechanics, 2005, 22(2): 179-183.

    [19] Katsuchi Hiroshi, Jones Nicholas P, Scanlan Robert H. Multimode coupled flutter and buffeting analysis of the Akashi-Kaikyo Bridge[J]. Journal of Structural Engineering, 1999, 125(1): 60-70.

    [20] iseth Ole, Rnnquist Anders, Sigbjrnsson Ragnar. Simplified prediction of wind-induced response and stability limit of slender long-span suspension bridges, based on modified quasi-steady theory: A case study[J]. Journal of Wind Engineering and Industrial Aerodynamics, 2010, 98(12): 730-741.

    [21] Kaimal J C, Wyngaard J C, Izumi Y, et al. Spectral characteristics of surface-layer turbulence[J]. Quarterly Journal of the Royal Meteorological Society, 1972, 98(417): 563-589.

    [22] Simiu Emil, Scanlan Robert H. Wind Effects on Structures: Fundamentals and Application to Design[M]. New York:John Willey & Sons Inc., 1996.

    [23] Matsuda Kazutoshi, Hikami Yuichi, Fujiwara Tohru, et al. Aerodynamic admittance and the ‘strip theory for horizontal buffeting forces on a bridge deck[J]. Journal of Wind Engineering and Industrial Aerodynamics, 1999, 83(1-3): 337-346.

    [24] 曾憲武, 韩大建. 大跨桥梁风致抖振时域分析及在ANSYS中的实现[J]. 桥梁建设, 2004, (1): 9-12.

    Zeng Xianwu,Han Dajian. Time-domain analysis of wind-induced buffet on long-span bridges and implementation of analysis in ANSYS[J]. Bridge Construction,2004,(1):9-12.

    [25] 李加武, 张 斐, 吴 拓. 桥梁断面颤振导数识别的加权最小二乘法[J]. 振动工程学报, 2017, 30(6): 993-1000.

    Li Jiawu, Zhang Fei, Wu Tuo, Weighted least square method for identification of flutter derivatives of bridge section[J]. Journal of Vibration Engineering, 2017, 30(6): 993-1000.

    [26] Holmes John D. Wind Loading of Structures[M]. Boca Raton, FL:CRC Press, 2015.

    Abstract: To study the buffeting response of the double main girder section suspension bridge with variable slot width ratios, the frequency domain and time domain buffeting calculation methods are proposed considering both the self-excited force and buffeting force changing along the span direction. Based on a landscape bridge, the influence of the aerodynamic admittance function, mean wind speed and turbulence wind cross spectrum on buffeting response is investigated in frequency domain analysis. The causes of the difference in buffeting response under different kinds of aerodynamic admittance functions are discussed. In the time domain analysis, the nonlinear effects of aerodynamic force are considered by updating the static wind load coefficient at each load step, where the structural geometric nonlinear effect is also taken into account. The results indicate that the time domain calculation method considering the change of aerodynamic parameters along the span direction can capture the local peak buffeting response of the single cable plane in the mid-span. Comparing the results of the two calculation methods shows that the calculated value of the buffeting response in time domain is greater than that in frequency domain in the vertical direction and smaller than that in frequency domain in the torsional direction. In addition, the buffeting response considering the change of aerodynamic parameters along the span direction is greater than that calculated by using the aerodynamic parameters of the mid-span section, which is mainly caused by the change of buffeting force. The change of self-excited force along the span direction has little effect on the buffeting response. Therefore, it is safer to consider changes of aerodynamic parameters along the span direction in buffeting analysis in the actual project.

    Key words: buffeting; suspension bridge; variable slot width ratios; multimode coupled frequency domain; aerodynamic admittance; cross spectrum