Cable-deck Coupled Vibration And Damping Characteristic Research In The Seismic Response Analysis Of Cable-stayed Bridges

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 greatlywhen 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...