斜拉桥地震响应分析中的索桥耦合振动和阻尼特性研究
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摘要
斜拉桥跨度越来越大,伴随着拉索长度的增大和加劲梁高度变小,拉索在各种外部荷载比如风、雨、冰、车辆、地震作用下容易发生各种形式的振动,轻则影响行车舒适度,重则容易引起锚固点疲劳破坏。结构的质量和刚度矩阵现在可以比较精确的模拟,但是结构阻尼特性由于来源复杂,机理目前还不是很清楚,阻尼矩阵的确定一直没有解决。而阻尼特性对斜拉桥动力响应的影响较大,必须正确的模拟结构的阻尼特性,才能提高斜拉桥动力计算的精度。
从上述问题出发,对斜拉桥使用过程中出现的拉索参数振动对动力特性和地震响应的影响,阻尼模式对斜拉桥地震响应的影响,比例阻尼参考振型的选取,斜拉桥非比例阻尼,斜拉桥阻尼识别等几个方面进行了深入的研究,并开发了相关的程序,可以计算考虑拉索局部振动的斜拉桥动力特性,振型能量与振型参与系数,采用多种阻尼模式计算斜拉桥地震响应,可以计算斜拉桥复数特征值及振型阻尼比。
利用子结构方法和广义自由度的概念,把拉索的振型作为自由度来考虑,提出了拉索局部振动的计算方法。对杭州湾跨海大桥北航道桥(设计方案)进行了动力特性分析,验证了拉索频率与主桥振型频率接近时出现的索桥耦合振动现象,索桥耦合振动一方面对振型频率有所影响,另一方面对各个子结构振型能量比例以及振型阻尼产生较大的影响。在斜拉桥动力特性分析中必须考虑拉索局部振动的影响。
考虑索桥耦合振动以后主要纵向振型的振型参与系数有不同程度的减小,根据杭州湾跨海大桥抗震设计提供的地震加速度反应谱,采用历史地震记录进行强度调整作为轴向输入计算了考虑拉索局部振动的斜拉桥地震响应。对于本文所选取的地震波,斜拉桥在考虑拉索局部振动以后地震响应增大,拉索位移时程出现了拉索局部振动现象,拉索脉动张力也有显著变化。
采用三种阻尼模式分别计算了斜拉桥地震响应,计算结果表明斜拉桥阻尼特性复杂,不能简单的用少数振型阻尼来表示,不同阻尼模式地震响应计算结果有较大的差别,常数阻尼不能考虑阻尼随频率的变化,Rayleigh阻尼参考振型选取不同地震响应结果有较大差异,相对而言,应变能比例阻尼能考虑斜拉桥阻尼分布特性,较为合理。根据Caughey阻尼理论推导了比例阻尼系数的确定方法,并根据单自由度系统地震响应的Duhamel积分,提出了一种以重要度为指标的比例阻尼参考振型选取方法,通过多种振型阻尼组合的计算分析表明,因为斜拉桥桥塔纵向和主梁竖向的耦合运动,以一个方向的重要度为指标选择的参考振型,往往对另一个方向的响应造成较大的误差,不能很好的预测地震响应。
With the span of cable-stayed bridge becomes longer, cable is also longer and deck height becomes short, which makes cable tends to vibration under various loads, such as wind, rain, ice, vehicle and earthquake. Light cable vibration can affect comfort of traffic, while serious cable vibration can lead to cable anchor point fatigue damage. Though structural mass and stiffness matrices can be calculated easily, it is difficult to find structural damping matrix, for damping sources and mechanism is complicated, and validate damping theory is not available yet. But structural dynamic response highly depends on damping of the structure, damping must be considered correctly in order to increase the precision of analysis.Research is carried out in five aspects to solve the problems mentioned above in this paper. Firstly and secondly the influence of cable local vibration on the dynamic characteristic and earthquake response of cable-stayed bridges is studied. Thirdly the effects of damping model on earthquake response of cable-stayed bridges and selection of reference modes in proportional damping are analyzed. Fourthly a method for definition of damping matrix based on calculation of non-proportional damping of cable-stayed bridges is presented. Fifthly damping parameter identification of cable-stayed bridges is expatiated. Relevant programs are developed, which can solve the problems of dynamic characteristic analysis, modal strain and modal damping, seismic response using various damping model, complex modal shape and modal damping ratio of cable-stayed bridges.An algorithm for cable local vibration is presented based on the method of substructure and generalized degree of freedom, in which cable local mode is looked as degree of freedom. The dynamic characteristic analysis of Hangzhou Bay Northern Bridge (scheme) is carried out. The phenomena of cable-deck or cable-tower coupled motion are validated when cable frequency is close to bridge frequency. Modal frequencies change slightly, but modal energy and modal damping are altered greatly when cable local vibration is considered. It is necessary to take into account cable local vibration in the dynamic characteristic analysis of cable-stayed bridges.The participation factor of major longitudinal modes decreases if the cable local vibration is considered. Seismic response analysis of Northern Channel Bridge of Hangzhou Bay Bridge is presented under longitudinal seismic wave input. The seismic wave is regulated using historical recording base on design acceleration spectrum. The seismic response of girder and tower is attenuated, the time history of displacement of cable is influenced by the cable local vibration, the dynamic tension of cable varies greatly
when cable local vibration is considered for the seismic input in this paper.Seismic response is calculated using three different damping models. It is found that damping of cable-stayed bridges is scattered in frequency domain, and can't be represented by few modal damping. The response of the bridge of different damping models has great variety. The reason is that constant damping can't reveal the characteristic of damping which varies with frequency and the results of Rayleigh damping are highly dependent on the reference modes. Modal strain energy proportional damping is the best choice relatively. The method for determination of coefficients in Caughey damping is also represented A significant index in the choice of reference modes for proportional damping is proposed based on Duhamel integration of single freedom system. The seismic response results of several modal damping combination show that the significant index can't get better response results for the reason that longitudinal motion of tower is coupled with vertical motion of girder and significant index in one direction gives poor results in another direction.The damping ratio of structure is deduced based on modal strain energy proportional damping. The calculation of damping ratio in cable-stayed bridge is presented using complex eigenvalue method. In the hypothesis that damping coefficient of substructures (such as tower, girder, cable, support and so on) is a constant, a method for the calculation of damping coefficient of cable-stayed bridges is proposed. The damping coefficients and damping distribution of an example cable-stayed bridge are calculated which shows that this method has a very high precision.In order to raise the precision of damping coefficients of the substructures, parametric sensitivity analysis is carried out to find out the largest effect factors. Least square procedure is used for the prediction of parametric errors of four error examples. The results show this method has very high precision, more response parameters than parameters to be identified can be used for transfer matrix of errors. At last a more accurate prediction of damping coefficients is got and the distribution of damping matrix is also presented.Cable local vibration and damping determination are two troublesome problems in the dynamic research of cable-stayed bridges. The effects of cable local vibration on the dynamic characteristic and seismic response of cable-stayed bridges, effects of damping on the seismic response of cable-stayed bridges, selection of reference modes of proportional damping, damping matrix of cable-stayed bridge based on complex modes calculation, determination of damping matrix, damping parameter identification and so on are presented in this paper. All of these researches will be helpful in improving the precision of
从上述问题出发,对斜拉桥使用过程中出现的拉索参数振动对动力特性和地震响应的影响,阻尼模式对斜拉桥地震响应的影响,比例阻尼参考振型的选取,斜拉桥非比例阻尼,斜拉桥阻尼识别等几个方面进行了深入的研究,并开发了相关的程序,可以计算考虑拉索局部振动的斜拉桥动力特性,振型能量与振型参与系数,采用多种阻尼模式计算斜拉桥地震响应,可以计算斜拉桥复数特征值及振型阻尼比。
利用子结构方法和广义自由度的概念,把拉索的振型作为自由度来考虑,提出了拉索局部振动的计算方法。对杭州湾跨海大桥北航道桥(设计方案)进行了动力特性分析,验证了拉索频率与主桥振型频率接近时出现的索桥耦合振动现象,索桥耦合振动一方面对振型频率有所影响,另一方面对各个子结构振型能量比例以及振型阻尼产生较大的影响。在斜拉桥动力特性分析中必须考虑拉索局部振动的影响。
考虑索桥耦合振动以后主要纵向振型的振型参与系数有不同程度的减小,根据杭州湾跨海大桥抗震设计提供的地震加速度反应谱,采用历史地震记录进行强度调整作为轴向输入计算了考虑拉索局部振动的斜拉桥地震响应。对于本文所选取的地震波,斜拉桥在考虑拉索局部振动以后地震响应增大,拉索位移时程出现了拉索局部振动现象,拉索脉动张力也有显著变化。
采用三种阻尼模式分别计算了斜拉桥地震响应,计算结果表明斜拉桥阻尼特性复杂,不能简单的用少数振型阻尼来表示,不同阻尼模式地震响应计算结果有较大的差别,常数阻尼不能考虑阻尼随频率的变化,Rayleigh阻尼参考振型选取不同地震响应结果有较大差异,相对而言,应变能比例阻尼能考虑斜拉桥阻尼分布特性,较为合理。根据Caughey阻尼理论推导了比例阻尼系数的确定方法,并根据单自由度系统地震响应的Duhamel积分,提出了一种以重要度为指标的比例阻尼参考振型选取方法,通过多种振型阻尼组合的计算分析表明,因为斜拉桥桥塔纵向和主梁竖向的耦合运动,以一个方向的重要度为指标选择的参考振型,往往对另一个方向的响应造成较大的误差,不能很好的预测地震响应。
With the span of cable-stayed bridge becomes longer, cable is also longer and deck height becomes short, which makes cable tends to vibration under various loads, such as wind, rain, ice, vehicle and earthquake. Light cable vibration can affect comfort of traffic, while serious cable vibration can lead to cable anchor point fatigue damage. Though structural mass and stiffness matrices can be calculated easily, it is difficult to find structural damping matrix, for damping sources and mechanism is complicated, and validate damping theory is not available yet. But structural dynamic response highly depends on damping of the structure, damping must be considered correctly in order to increase the precision of analysis.Research is carried out in five aspects to solve the problems mentioned above in this paper. Firstly and secondly the influence of cable local vibration on the dynamic characteristic and earthquake response of cable-stayed bridges is studied. Thirdly the effects of damping model on earthquake response of cable-stayed bridges and selection of reference modes in proportional damping are analyzed. Fourthly a method for definition of damping matrix based on calculation of non-proportional damping of cable-stayed bridges is presented. Fifthly damping parameter identification of cable-stayed bridges is expatiated. Relevant programs are developed, which can solve the problems of dynamic characteristic analysis, modal strain and modal damping, seismic response using various damping model, complex modal shape and modal damping ratio of cable-stayed bridges.An algorithm for cable local vibration is presented based on the method of substructure and generalized degree of freedom, in which cable local mode is looked as degree of freedom. The dynamic characteristic analysis of Hangzhou Bay Northern Bridge (scheme) is carried out. The phenomena of cable-deck or cable-tower coupled motion are validated when cable frequency is close to bridge frequency. Modal frequencies change slightly, but modal energy and modal damping are altered greatly when cable local vibration is considered. It is necessary to take into account cable local vibration in the dynamic characteristic analysis of cable-stayed bridges.The participation factor of major longitudinal modes decreases if the cable local vibration is considered. Seismic response analysis of Northern Channel Bridge of Hangzhou Bay Bridge is presented under longitudinal seismic wave input. The seismic wave is regulated using historical recording base on design acceleration spectrum. The seismic response of girder and tower is attenuated, the time history of displacement of cable is influenced by the cable local vibration, the dynamic tension of cable varies greatly
when cable local vibration is considered for the seismic input in this paper.Seismic response is calculated using three different damping models. It is found that damping of cable-stayed bridges is scattered in frequency domain, and can't be represented by few modal damping. The response of the bridge of different damping models has great variety. The reason is that constant damping can't reveal the characteristic of damping which varies with frequency and the results of Rayleigh damping are highly dependent on the reference modes. Modal strain energy proportional damping is the best choice relatively. The method for determination of coefficients in Caughey damping is also represented A significant index in the choice of reference modes for proportional damping is proposed based on Duhamel integration of single freedom system. The seismic response results of several modal damping combination show that the significant index can't get better response results for the reason that longitudinal motion of tower is coupled with vertical motion of girder and significant index in one direction gives poor results in another direction.The damping ratio of structure is deduced based on modal strain energy proportional damping. The calculation of damping ratio in cable-stayed bridge is presented using complex eigenvalue method. In the hypothesis that damping coefficient of substructures (such as tower, girder, cable, support and so on) is a constant, a method for the calculation of damping coefficient of cable-stayed bridges is proposed. The damping coefficients and damping distribution of an example cable-stayed bridge are calculated which shows that this method has a very high precision.In order to raise the precision of damping coefficients of the substructures, parametric sensitivity analysis is carried out to find out the largest effect factors. Least square procedure is used for the prediction of parametric errors of four error examples. The results show this method has very high precision, more response parameters than parameters to be identified can be used for transfer matrix of errors. At last a more accurate prediction of damping coefficients is got and the distribution of damping matrix is also presented.Cable local vibration and damping determination are two troublesome problems in the dynamic research of cable-stayed bridges. The effects of cable local vibration on the dynamic characteristic and seismic response of cable-stayed bridges, effects of damping on the seismic response of cable-stayed bridges, selection of reference modes of proportional damping, damping matrix of cable-stayed bridge based on complex modes calculation, determination of damping matrix, damping parameter identification and so on are presented in this paper. All of these researches will be helpful in improving the precision of
引文
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