Parametric Oscillation Of Cables In Cable-stayed Bridges

Cables in cable-stayed bridges are prone to exhibit transverse oscillations of large amplitude due to their small rigidity, small mass and low damping. With the increase of the span length of cable-stayed bridges, stay cables become longer and longer, and the problems of cable oscillations have arose great concern in recent years. The dissertation deals with one kind of cable vibrations named parametric vibration which is caused by the parametric excitation due to the movement of towers and decks. By combination of analytic solutions and numerical computations, the mechanism of parametric vibration of stay-cables is studied. There are six chapters in the dissertation. The main contents in each chapter are shown below.Chapter 1 is the induction in which the state-of-the-art of the cable vibrations and in particular the parametrically excited vibrations in cable-stayed bridges are presented and the main contents of the dissertation are introduced.In Chapter 2, the static curve under self-weight of stay cables is studied. A second-degree parabola configuration is obtained without neglecting the chord component of cable self-weight. It is proved that the parabola has a simple form and higher precision than the traditional second-degree parabola which is universally used by now. And it can be used conveniently in the dynamic analysis in the following chapters.In Chapter 3, two simplified analytical models reflecting the coupling interaction between the stay cable and the deck in parametric vibration are established and studied. In the two models, the deck is simulated as a system composed of a mass and a spring, and only the first two modals of the stay cable are considered. Thus each model has 3 degree of freedoms. However, in the first model, the cable is simplified as a taut string without the sag curve, and in the second one, the sag curve of the cable is considered but the chord component of cable self-weight is neglected. By using multiple time scales method and numerical computation to solve the non-linear vibration equations, the approximate analytic solutions are obtained. And then the frequency ratios and the amplitude relations between the cable and the deck are deduced when the internal resonances occur. The amplitude relations illuminate the amplitudes are limited. By comparing the two models, it is found the responses characteristics between them are different, and the latter is more close to the real case. As for the second modal of the stay cable, its resonance condition is indicated. And in the actual cable-stayed bridges, the condition is difficult to be satisfied. So in the following chapters, it is reasonable to omit the second modal of cable to simplify the analysis.In Chapter 4, a more precise analytical model is presented based on Chapter 3. In the model, the cable sag, the cable inclination, the chord component of cable weight and the coupling interaction between the cable and the deck are all considered, the deck is simulated as a system composed of a mass and a spring, and only the first modal of the cable is taken into account. By using multiple time...