大跨度斜拉桥抖振响应的气动导纳函数研究
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摘要
当代跨江跨海桥梁向着大跨度柔性方向发展,随着桥梁跨径的长大化,桥梁的抗风设计已经成为主要控制因素之一。目前普遍采用的由Scanlan和Davenport于20世纪60年代建立起来的桥梁风振理论框架是否需要补充和改进,以适应超大跨度桥梁的抗风设计是一个令人关注的课题。如何做到大跨度桥梁抗风精细化分析,气动导纳函数是桥梁抖振精细化研究的一个重要参数。本文开展了以下研究
(1)利用Scanlan二维流场中的升力和力矩的拟定常力模型,采用变尺度法对残差目标函数求无约束最优化,建立了MITD时域优化的颤振导数理论识别方法,通过对平板模型的数值仿真和解析解对比,验证了识别方法的有效性和适应程度。在风洞试验识别出了湍流风场中模型一(闭口扁平流线型钢箱梁模型)的颤振导数,再利用颤振导数和气动导纳的关系,进行气动导纳函数识别。
(2)通过讨论脉动风引起的非定常空气抖振力模型下的气动导纳函数识别理论和方法,建立了引入抖振力谱的气动导纳识别方法。通过对比风洞试验测得的类平板模型的气动导纳和Sears导纳函数,发现二者较接近,说明了该识别方法是可行的。
(3)针对三种典型桥梁截面模型一(闭口扁平流线型箱梁)、模型二(开口扁平流线型箱梁)和模型三(钝体主梁)的气动导纳风洞识别试验,试验内容包括:1)脉动风场模拟和测量技术,在风洞中建立了湍流强度均匀的格栅湍流场;2)介绍了高频动态天平测力的原理,建立了高频动态天平的动力学模型,并对5分量高频动态天平的精密度和准确度进行了校检。分析试验结果发现,1)箱梁底板开闭口、有无栏杆等模型气动外形变化和小幅度攻角变化对气动导纳函数的影响不明显;2)引入抖振力谱方法识别出来4种模型6个气动导纳函数均与Sears导纳函数具有很好的一致性,在测试段的低频段均比Sears函数略小一些,但在测试段的高频段几乎重合;3)栏杆、箱梁底板开槽和由类平板渐变到钝体等模型的气动外形变化对气动导纳值的影响在低频段模型外形越钝,气动导纳值越大,但不超过1 ,而在高频段对χLu2、χDu2和χMu2的影响不明显。
(4)应用引入气动导纳函数的多模态耦合斜拉桥抖振响应计算方法,对主跨720m的厦门-漳州跨海大桥北汊斜拉桥进行了抖振频域分析,计算出了多种气动导纳函数下的抖振响应。并通过与全桥气弹模模型抖振试验响应结果进行比较,验证气动导纳识别结果应用于实际桥梁工程的适用性及可靠性。
(5)通过计算厦门-漳州跨海大桥北汊桥720m主跨大跨度斜拉桥的抖振响应,得出气动导纳取1和Sears函数计算大跨度斜拉桥的抖振,都高估了它的抖振响应。采用试验拟合的气动导纳计算的抖振响应结果与全桥气弹模型试验抖振响应结果相近,得出本文试验拟合的气动导纳结果具有一定的可靠性。
The developmental trend of modern bridges is towards larger span and higher flexibility, which makes the wind-resistant design one of the key factors in bridge design. A topic of great concern is whether supplementation and improvement should be made to the currently widely adopted theoretical frame for bridge wind vibration established by Scanlan and Davenport in 1960s to suit the wind-resistant design of super-span bridges. To conduct refined analysis on the wind resistance of large-span bridges, aerodynamic admittance function is an important parameter in the refined study of bridge buffeting. This paper presents the following studies:
(1) Unconstrained optimization of the residual objective function was made with variable metric method using the quasi steady force model of the lift force and moment in Scanlan two-dimensional flow field; following that, a theoretical MITD-optimized identification method of flutter derivative was established.Then its effectiveness and adaptation degree were verified through numerical simulation of the plane model and analytic solution comparison. The flutter derivative of model one (closed streamlined flat steel box girder model) was identified in the wind tunnel test and then aerodynamic admittance function identification was conducted using the relation between flutter derivatives and aerodynamic admittance.
(2)Through discussion on the identification theory and method for aerodynamic admittance function with fluctuating wind-induced unsteady air buffeting force model, an identification method for aerodynamic admittance of buffeting force spectrum was established Comparison between the aerodynamic admittance of the quasi flat plate model measured in the wind tunnel test and the Sears admittance function indicated the closeness between them, which showed that the identification method in question was feasible.
(3) Experiments on the identification of aerodynamic admittance in the wind tunnel were carried out relating to three typical bridge section models: model one (closed streamlined flat box girder), model two (open streamlined flat box girder) and model three (bluff main girder). Experiment contents included: 1) simulation and measurement technique of fluctuating wind field and the establishment of a grid turbulent flow field with uniform turbulence in the wind tunnel; 2) introduction of the force-measuring principle of high-frequency-force-balance, establishment of the mechanic model of high-frequency-force-balance and then verification on the precision and accuracy of 5-component high-frequency-force-balance. Analysis of the experimental results showed that: 1) no obvious effect on the aerodynamic admittance function was caused by the variation in model's aerodynamic configurations such as with open or closed bottom place, with or without railings and so on and slight variation in attack angles; 2) all 6 aerodynamic admittance functions of 4 models identified with buffeting force spectrum method were considerably identical to Sears admittance function; all being smaller than Sears function in the low-frequency section of the testing section, but almost coincident in the high-frequency section; 3) the effect of such variations in the model's aerodynamic configuration as with or without railings, with open or closed bottom plate and gradual changing from quasi flat plate to bluff body on the value of aerodynamic admittance had a characteristic that the bluffer the model configuration was the bigger the value of aerodynamic admittance would be, but not exceeding 1; and in high-frequency section there was no obvious effect onχLu2、2χDu andχMu2.
(4) Buffeting frequency domain analysis was conducted on the Beicha Cable-stayed Bridge with 720m main span of Xiamen-Zhangzhou Cross-sea bridge applying multi-mode coupling buffeting response calculation method for cable-stayed bridges with aerodynamic admittance functions and the buffeting responses under various aerodynamic admittance functions were obtained. Then, the adaptation and reliability of applying the identification results in actual bridge engineering were verified by comparing the results with those of the full-bridge aeroelastic model buffeting experiments.
(5) By calculating the buffeting response of the Beicha Cable-stayed bridge with the 720m main span of Xiamen-Zhangzhou Cross-sea bridge, the buffeting responses were obtained respectively when the value of the aerodynamic admittance was 1 and when Sears function was adopted. This showed that the buffeting response of this bridge was overestimated. The closeness between the buffeting responses calculated by the aerodynamic admittance fitted in the experiment and that of the full bridge aeroelastic model experiment indicates that the aerodynamic admittance results fitted in the experiment discussed in this paper is reliable to a certain degree.
(1)利用Scanlan二维流场中的升力和力矩的拟定常力模型,采用变尺度法对残差目标函数求无约束最优化,建立了MITD时域优化的颤振导数理论识别方法,通过对平板模型的数值仿真和解析解对比,验证了识别方法的有效性和适应程度。在风洞试验识别出了湍流风场中模型一(闭口扁平流线型钢箱梁模型)的颤振导数,再利用颤振导数和气动导纳的关系,进行气动导纳函数识别。
(2)通过讨论脉动风引起的非定常空气抖振力模型下的气动导纳函数识别理论和方法,建立了引入抖振力谱的气动导纳识别方法。通过对比风洞试验测得的类平板模型的气动导纳和Sears导纳函数,发现二者较接近,说明了该识别方法是可行的。
(3)针对三种典型桥梁截面模型一(闭口扁平流线型箱梁)、模型二(开口扁平流线型箱梁)和模型三(钝体主梁)的气动导纳风洞识别试验,试验内容包括:1)脉动风场模拟和测量技术,在风洞中建立了湍流强度均匀的格栅湍流场;2)介绍了高频动态天平测力的原理,建立了高频动态天平的动力学模型,并对5分量高频动态天平的精密度和准确度进行了校检。分析试验结果发现,1)箱梁底板开闭口、有无栏杆等模型气动外形变化和小幅度攻角变化对气动导纳函数的影响不明显;2)引入抖振力谱方法识别出来4种模型6个气动导纳函数均与Sears导纳函数具有很好的一致性,在测试段的低频段均比Sears函数略小一些,但在测试段的高频段几乎重合;3)栏杆、箱梁底板开槽和由类平板渐变到钝体等模型的气动外形变化对气动导纳值的影响在低频段模型外形越钝,气动导纳值越大,但不超过1 ,而在高频段对χLu2、χDu2和χMu2的影响不明显。
(4)应用引入气动导纳函数的多模态耦合斜拉桥抖振响应计算方法,对主跨720m的厦门-漳州跨海大桥北汊斜拉桥进行了抖振频域分析,计算出了多种气动导纳函数下的抖振响应。并通过与全桥气弹模模型抖振试验响应结果进行比较,验证气动导纳识别结果应用于实际桥梁工程的适用性及可靠性。
(5)通过计算厦门-漳州跨海大桥北汊桥720m主跨大跨度斜拉桥的抖振响应,得出气动导纳取1和Sears函数计算大跨度斜拉桥的抖振,都高估了它的抖振响应。采用试验拟合的气动导纳计算的抖振响应结果与全桥气弹模型试验抖振响应结果相近,得出本文试验拟合的气动导纳结果具有一定的可靠性。
The developmental trend of modern bridges is towards larger span and higher flexibility, which makes the wind-resistant design one of the key factors in bridge design. A topic of great concern is whether supplementation and improvement should be made to the currently widely adopted theoretical frame for bridge wind vibration established by Scanlan and Davenport in 1960s to suit the wind-resistant design of super-span bridges. To conduct refined analysis on the wind resistance of large-span bridges, aerodynamic admittance function is an important parameter in the refined study of bridge buffeting. This paper presents the following studies:
(1) Unconstrained optimization of the residual objective function was made with variable metric method using the quasi steady force model of the lift force and moment in Scanlan two-dimensional flow field; following that, a theoretical MITD-optimized identification method of flutter derivative was established.Then its effectiveness and adaptation degree were verified through numerical simulation of the plane model and analytic solution comparison. The flutter derivative of model one (closed streamlined flat steel box girder model) was identified in the wind tunnel test and then aerodynamic admittance function identification was conducted using the relation between flutter derivatives and aerodynamic admittance.
(2)Through discussion on the identification theory and method for aerodynamic admittance function with fluctuating wind-induced unsteady air buffeting force model, an identification method for aerodynamic admittance of buffeting force spectrum was established Comparison between the aerodynamic admittance of the quasi flat plate model measured in the wind tunnel test and the Sears admittance function indicated the closeness between them, which showed that the identification method in question was feasible.
(3) Experiments on the identification of aerodynamic admittance in the wind tunnel were carried out relating to three typical bridge section models: model one (closed streamlined flat box girder), model two (open streamlined flat box girder) and model three (bluff main girder). Experiment contents included: 1) simulation and measurement technique of fluctuating wind field and the establishment of a grid turbulent flow field with uniform turbulence in the wind tunnel; 2) introduction of the force-measuring principle of high-frequency-force-balance, establishment of the mechanic model of high-frequency-force-balance and then verification on the precision and accuracy of 5-component high-frequency-force-balance. Analysis of the experimental results showed that: 1) no obvious effect on the aerodynamic admittance function was caused by the variation in model's aerodynamic configurations such as with open or closed bottom place, with or without railings and so on and slight variation in attack angles; 2) all 6 aerodynamic admittance functions of 4 models identified with buffeting force spectrum method were considerably identical to Sears admittance function; all being smaller than Sears function in the low-frequency section of the testing section, but almost coincident in the high-frequency section; 3) the effect of such variations in the model's aerodynamic configuration as with or without railings, with open or closed bottom plate and gradual changing from quasi flat plate to bluff body on the value of aerodynamic admittance had a characteristic that the bluffer the model configuration was the bigger the value of aerodynamic admittance would be, but not exceeding 1; and in high-frequency section there was no obvious effect onχLu2、2χDu andχMu2.
(4) Buffeting frequency domain analysis was conducted on the Beicha Cable-stayed Bridge with 720m main span of Xiamen-Zhangzhou Cross-sea bridge applying multi-mode coupling buffeting response calculation method for cable-stayed bridges with aerodynamic admittance functions and the buffeting responses under various aerodynamic admittance functions were obtained. Then, the adaptation and reliability of applying the identification results in actual bridge engineering were verified by comparing the results with those of the full-bridge aeroelastic model buffeting experiments.
(5) By calculating the buffeting response of the Beicha Cable-stayed bridge with the 720m main span of Xiamen-Zhangzhou Cross-sea bridge, the buffeting responses were obtained respectively when the value of the aerodynamic admittance was 1 and when Sears function was adopted. This showed that the buffeting response of this bridge was overestimated. The closeness between the buffeting responses calculated by the aerodynamic admittance fitted in the experiment and that of the full bridge aeroelastic model experiment indicates that the aerodynamic admittance results fitted in the experiment discussed in this paper is reliable to a certain degree.
引文
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