Parametric Vibration And Cable Force Indentification Of Staying Cable Of Large-span Bridges

Stay cables become longer and longer as the span of cable stayed bridge gets larger and larger (The longest cable of the Suzou-Nantong bridge is 580m). To guarantee safety, durability of bridges and extend useful time of bridge, vibration of cables is paid more attention to by researchers. According to parametric vibration which probably causes large amplitude vibration, parametric vibration and cable force identification of large span cable stayed bridge are studied systematically by theoretical analysis, experiment and project application. The research contents are as follows.Firstly cable - bridge coupled and uncoupled parametric vibration models of lateral cable are built without regard to cable angle. Using Galerkin method, the differential equations of two kinds of parametric vibration models are decoupled considering the first two orders of modal combinations. Then the vibration equation is solved approximately and internal resonant response of the model is discussed via multi-scale method, and The rule of internal resonant response and cable force history is studied by numerical simulation. The results have shown that substantial 'beat' vibration of cable first-order mode occurs at internal resonant point 2:1and 1:1 and substantial 'beat' vibration of cable second-order mode occurs at internal resonant point 2:1. Because of the external constant input of energy at ends, displacement response of cable - bridge non-coupled model under ideal excitation is larger than that of cable - bridge coupled model, and attenuates more slowly.Cable-bridge uncoupled parametric vibration models of stayed cable under ideal excitation, as well as cable-bridge and cable-bridge-tower coupled parametric vibration models of stayed cable under non-ideal excitation are built in view of cable angle. Vibration differential equations of the three models are derived by dimensionless method, and the vibration equation is solved approximately by multi-scale method. At last, coupled equations are solved numerically by numerical simulation method. Start-up time of parametric vibration is discussed. The ranges of parametric vibration frequency ratio of different length cable are compared and parametric analysis is processed. Under the state of cable-bridge-tower coupled vibration, when the ratio of bridge frequency and cable frequency is 2:1, namely 1:2:1 or 2:2:1 internal resonant occur, vibration diverges after period of time. But while 1:1:1 or 2:1:1 internal resonant occurs, coupled beat vibration of displacement of cable, tower and bridge, as well as vibration displacement of bridge and tower is much larger than initial displacement. Each part of system is excited completely.Besides parametric vibration is studied by simplifying bridge excitation as ideal excitation and spring-mass coupled system, nonlinear vibration model of stayed cable-beam composite structure is set up. Parametric vibration of stayed cable of cable-beam coupled model is studied. And coupled vibration differential equations in dimensionless style are solved approximately by multi-scale method. Afterwards property of internal resonant response of the model is discussed. Finally the rule of dynamic response of cable-beam coupled model at different internal resonant points is discussed by numerical simulation. The achievements have shown that under the state of large initial displacement of beam, whenωb equals 2 or 1, substantial 'beat' vibration of cable occurs. But under the state of small initial displacement of beam, whenωb is 2, substantial 'beat' vibration of cable occurs due to small excitation. It is concluded that substantial vibration of cable can be caused by small vibration of beam of bridge deck.Parametric vibration of stayed cable under bearing excitation is studied, based on the research of parametric vibration model considering cable-beam composite structure. There is an angle between the direction of bearing excitation and axial direction of stayed cable, which is different from the method which simplifies bridge deck as spring-mass under ideal axial excitation. Moreover nonlinear vibration model of stayed cable under bearing excitation is built, and vibration differential equations in dimensionless style are solved approximately by means of multi-scale method. It is discussed that while ratio of excitation frequency of bearing and stayed cable frequency satisfies internal resonant frequency ratio, substantial vibration of cable occurs. And when the combination of excitation frequency of bearing satisfy |ω|-_B±ω|-_A|= 0, |ω|-_B±ω|-_A|= 1 or |ω|-_B±ω|-_A|= 2, substantial vibration of cable occurs similarly. In particular, while meeting the parametric resonance, resonance response gets bigger.To make clear parametric vibration of stayed cable under bearing excitation, the indoor test is processed. According to actuator imitating bridge deck and exciting harmonic wave on the tip of stayed cable, multi-condition tests at the varying internal resonance frequency ratios 2:1, 1:1, 1:2 under different amplitude are carried out. It can be seen that vibration amplitude is larger as the frequency ratio is 2:1, and cable vibration is influenced greatly by rigid link component at the end and out-of-plan vibration. Thus the amplitude of experiment is identical with that of numerical simulation, and time interval of"beat'vibration of experimental cable is larger and attenuates faster. When the frequency ratios are 1:1 and 1:2, the results of experiment and numerical simulation are in good agreement. It can be shown that parametric vibration of stayed cable appearing under bearing excitation is verified by this experiment according to the comparison of the outcomes of experiment and numerical simulation.At last, in view of the precision of cable force identification on the spot, the method and the precision of cable force identification are investigated systematically. Afterwards the high-precision cable force tester is developed via the partial above-mentioned achievements.