| Due to relatively small mass, very small structural damping and large deflections,cables are prone to be subjected to oscillations in cable-stayed bridges. Among thosevibrations of cables, parametric vibration is one kind of nonlinear vibrations, presentinglarger amplitude, and it may affect the bridge safety. Therefore, simulating the parametricvibration accurately is very essential to investigate and study cable vibration incable-stayed bridges. As for this, this paper has conducted some following researchingwork about the finite element method for analyzing global cable-stayed bridge.(1) The cable element and calculating approach of removing cable self-weight areproposed in the analysis of cable nonlinear vibration, which are verified through thenonlinear static analysis, natural vibration and parametric vibration analysis of a singlecable, that is to say, nonlinear vibration including parametric vibration of sagging cables,from flat-sag cables to large-sag ones, can be taken into account by using the proposedelement and approach.(2) The calculating approach of global cable-stayed bridge considering cable’s nonlinearvibration is proposed, which can be used to obtain the parametric vibration of stay cables,as well as the interaction between these cables and main structure (main girder and maintower). As for the problems had to be solved in the dynamic analysis of the cable-stayedbridge, the eigenvalue analysis process using dynamic condensation is proposed for sortingout the key natural modes of the main structure from several modes of the whole bridge.Besides, the extended Rayleigh damping is obtained to create the damping matrix of thecable-stayed bridge, considering the different damping constants of the stay cables, whichhave small structural damping, and the girder/tower, which has relatively greater damping.(3) The finite element method mentioned above is taken to analyze a cable-stayed-beammodel of the experiment conducted by Professor Fujino in Japan. Compared to thenumerical analysis of this experiment, the finite element method can be used to calculatecable parametric vibration and the interaction between the cable and beam. Moreover, thismethod has an advantage over the numerical analysis, because it involves more free-degrees and vibrating modes of the structure in calculating process, making the resultscloser to the real value accordingly.(4) Taking a concrete cable-stayed bridge with one tower as the studying case, theapplication of the finite element analysis for global cable-stayed bridge in real project isdiscussed. When the bridge is subjected to torsional excitation, the main girder vibrateswith very small amplitude, however, the vertical parametric vibration in the secondunstable region (1:1) or horizontal parametric vibration in the principal unstable region(2:1) are generated in some stay cables.(5) From the comparison between the results of the approximate approach, whichignores the influence of stay cable’s vibration on main structure, and the whole bridgeapproach proposed in this paper, it is found that, due to the interaction between the staycables and main structure, the amplitude of cable’s parametric vibration in second unstableregion increases by18%, and the horizontal parametric vibration in principal unstableregion is generated in some stay cables. At the same time, the main girder has large axialforce and in-plane bending moment resulting from the large amplitude vibration of staycables, which can not be concluded through the approximate approach. Therefore, it issuggested that the finite element analysis of global cable-stayed bridge, named WholeBridge Approach, should be taken in the dynamic analysis of cable-stayed bridge, in orderto consider the interaction between the stay cables and main structure. |
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