大跨度中承式拱桥风致振动研究
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摘要
大跨度中承式拱桥属于柔性结构,在风振作用下很容易发生静风失稳、抖振和涡激振动等风致响应。与大跨度的悬索桥、斜拉桥等桥型不同,大跨度中承式拱桥属于三维受力结构体系,在风致振动时需要考虑主梁与主拱的协同作用。主拱风荷载比较复杂,需要考虑风速沿高度变化、荷载空间相关性以及主拱之间相互干扰等因素。并且,钝体截面的主拱在低风速下容易产生涡激振动。因此,根据大跨度中承式拱桥的上述特点,针对大跨度中承式拱桥静风稳定性、抖振以及涡激振动等方面进行了较为深入的研究。本文的工作主要有以下几个方面:
(1)系统地分析了单拱及双拱相互干扰下的静风荷载情况。以重庆菜园坝长江大桥为例,通过单拱与双拱节段模型风洞试验与流体力学数值模拟,讨论了不同攻角、不同间距下单拱与双拱相互干扰下静力三分力系数的变化规律。分析表明,单拱阻力系数变异性较小,升力系数与力矩系数变异系数较大。双拱的静力三分力系数、变异性以及受湍流度的影响等均与两拱间距宽度比及竖向相对位移有关。
(2)发展了大跨度中承式拱桥在静风荷载作用下的全过程位移响应分析方法,深入分析了静风作用下大跨度中承式拱桥的屈服失稳机理。分析表明,考虑静力三分力非线性使得极限风速减小,同一风速下计算的内力和位移偏大。静风初始攻角与材料的屈服强度对静风承载力影响较大。不同施工态的极限风速都由施工塔架的稳定性决定。
(3)提出了在湍流中两榀拱相互干扰下风荷载功率谱的求解方法。通过在湍流中的双拱测压节段模型试验,深入探索了由于两榀拱之间干扰而导致两拱抖振力的变化规律。以单拱脉动风速功率谱为参照,根据均方值等效的原则确定在湍流中两拱的脉动风速功率谱。实践表明,上述求解是比较准确的。
(4)推导了用于大跨度中承式拱桥抖振分析的运动方程。该方程考虑了风速随高度变化、主梁与主拱耦合振动以及多模态和模态耦合效应。分别采用SRSS法、CQC法以及虚拟激励法对重庆菜园坝长江大桥进行抖振分析。分析表明,SRSS法误差较大,高阶模态对结果有显著影响,水平风速谱对抖振起到主要作用,交叉风速谱在计算中可以不计,由于受干扰影响,后拱的荷载功率谱及响应结果都明显增大。
(5)模拟了大跨度中承式拱桥的三维风场,实现了大跨度中承式拱桥的时域分析。利用谐波合成法,考虑两拱抖振力功率谱相互干扰、空间相关性等因素实现了风场模拟。对随机数生成及时间间隔取值问题给出了建议。采用FFT变换、编程优化以及功率谱插值等技术,大大提高了模拟的效率。时域分析的结果与试验吻合较
Long span half-through arch bridges belong to flexible structure. The buckling under static wind, buffet and vortex shedding vibration will take place easily. Be differ from the long span cable-stayed bridges and suspension bridges, the long span half-through arch bridges belong to 3D structure. The coupled vibration between girder and arches should be taken into account when calculating wind induced response. The wind loads on arches are complex. Some factors, such as wind speeds changing with height and loads spatial correlation and interference between two arches should be taken into account. The vortex shedding vibration will take place at the relative low wind speed because of arches blunt section. So the static stability analysis, the buffeting analysis, the vortex-excited vibration analysis are discussed according to the long span arch bridges features. The research is mainly focused on the following aspects:
(1) The wind loads and interference of single arch and double arches are analyzed. Exampled on the Chongqing Caiyuanba Yangzi river bridge, the wind tunnel tests of single arch and double arches are carried out. The numerical simulations of tunnel tests are analyzed. The results show that drag force coefficients variability is small, and lift coefficients variability and moment variability are big. Arch forces coefficients and fluctuating buffeting forces are mainly decided by the space width ratio and the relatively vertical displacement.
(2) The methods of long span half-through arch bridges displacement response analysis under the static wind loads are developed. The yield and static stability mechanism of long span half-through arch bridges are analyzed. The results show that the responses are bigger when the static forces nonlinear are taken into account. The internal forces and displacements are bigger at the same wind speed. The static wind initial angle and material yield value have great effects on the limited wind speed. The construction stage limited wind speeds depend on the construction towers’stability.
(3) The method of calculating wind power spectrum density (PSD) before two arches is presented. By the fluctuated pressure tunnel tests, the fluctuating wind loads on arches are analyzed. According to the single arch buffeting forces PSD, the ratios between two arches buffeting forces PSD are calculated by equivalent root mean square (RMS), then the wind PSD before two arches are solved. The results show that the method is effective.
(4) The finite element method of long span half-through arch bridges couple frequency domain buffeting vibration analysis is derived. The change of wind speed with the height is taken into account. The square root of the sum of squares (SRSS) and complete quadratic combination (CQC) and pseudo excited methods are adopted on the
(1)系统地分析了单拱及双拱相互干扰下的静风荷载情况。以重庆菜园坝长江大桥为例,通过单拱与双拱节段模型风洞试验与流体力学数值模拟,讨论了不同攻角、不同间距下单拱与双拱相互干扰下静力三分力系数的变化规律。分析表明,单拱阻力系数变异性较小,升力系数与力矩系数变异系数较大。双拱的静力三分力系数、变异性以及受湍流度的影响等均与两拱间距宽度比及竖向相对位移有关。
(2)发展了大跨度中承式拱桥在静风荷载作用下的全过程位移响应分析方法,深入分析了静风作用下大跨度中承式拱桥的屈服失稳机理。分析表明,考虑静力三分力非线性使得极限风速减小,同一风速下计算的内力和位移偏大。静风初始攻角与材料的屈服强度对静风承载力影响较大。不同施工态的极限风速都由施工塔架的稳定性决定。
(3)提出了在湍流中两榀拱相互干扰下风荷载功率谱的求解方法。通过在湍流中的双拱测压节段模型试验,深入探索了由于两榀拱之间干扰而导致两拱抖振力的变化规律。以单拱脉动风速功率谱为参照,根据均方值等效的原则确定在湍流中两拱的脉动风速功率谱。实践表明,上述求解是比较准确的。
(4)推导了用于大跨度中承式拱桥抖振分析的运动方程。该方程考虑了风速随高度变化、主梁与主拱耦合振动以及多模态和模态耦合效应。分别采用SRSS法、CQC法以及虚拟激励法对重庆菜园坝长江大桥进行抖振分析。分析表明,SRSS法误差较大,高阶模态对结果有显著影响,水平风速谱对抖振起到主要作用,交叉风速谱在计算中可以不计,由于受干扰影响,后拱的荷载功率谱及响应结果都明显增大。
(5)模拟了大跨度中承式拱桥的三维风场,实现了大跨度中承式拱桥的时域分析。利用谐波合成法,考虑两拱抖振力功率谱相互干扰、空间相关性等因素实现了风场模拟。对随机数生成及时间间隔取值问题给出了建议。采用FFT变换、编程优化以及功率谱插值等技术,大大提高了模拟的效率。时域分析的结果与试验吻合较
Long span half-through arch bridges belong to flexible structure. The buckling under static wind, buffet and vortex shedding vibration will take place easily. Be differ from the long span cable-stayed bridges and suspension bridges, the long span half-through arch bridges belong to 3D structure. The coupled vibration between girder and arches should be taken into account when calculating wind induced response. The wind loads on arches are complex. Some factors, such as wind speeds changing with height and loads spatial correlation and interference between two arches should be taken into account. The vortex shedding vibration will take place at the relative low wind speed because of arches blunt section. So the static stability analysis, the buffeting analysis, the vortex-excited vibration analysis are discussed according to the long span arch bridges features. The research is mainly focused on the following aspects:
(1) The wind loads and interference of single arch and double arches are analyzed. Exampled on the Chongqing Caiyuanba Yangzi river bridge, the wind tunnel tests of single arch and double arches are carried out. The numerical simulations of tunnel tests are analyzed. The results show that drag force coefficients variability is small, and lift coefficients variability and moment variability are big. Arch forces coefficients and fluctuating buffeting forces are mainly decided by the space width ratio and the relatively vertical displacement.
(2) The methods of long span half-through arch bridges displacement response analysis under the static wind loads are developed. The yield and static stability mechanism of long span half-through arch bridges are analyzed. The results show that the responses are bigger when the static forces nonlinear are taken into account. The internal forces and displacements are bigger at the same wind speed. The static wind initial angle and material yield value have great effects on the limited wind speed. The construction stage limited wind speeds depend on the construction towers’stability.
(3) The method of calculating wind power spectrum density (PSD) before two arches is presented. By the fluctuated pressure tunnel tests, the fluctuating wind loads on arches are analyzed. According to the single arch buffeting forces PSD, the ratios between two arches buffeting forces PSD are calculated by equivalent root mean square (RMS), then the wind PSD before two arches are solved. The results show that the method is effective.
(4) The finite element method of long span half-through arch bridges couple frequency domain buffeting vibration analysis is derived. The change of wind speed with the height is taken into account. The square root of the sum of squares (SRSS) and complete quadratic combination (CQC) and pseudo excited methods are adopted on the
引文
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