| Stay cable is a kind of flexible component with low damping,small mass,small bending stiffness and compressive stiffness.The stiffness and natural frequency of the super-long-span cable stayed bridge are reduced,and the modal frequency range where parametric vibration occurs is widened.Under the action of external excitation,largevalue parameter resonance is extremely easy to occur.The low damping of the cable itself cannot effectively suppress the large-value parameter resonance response,so special vibration control measures need to be taken.In recent years,many scholars have proved that the structural vibration control technology can effectively reduce the nonlinear vibration response of long-span cable under parametric excitation from the perspectives of theoretical and experimental research,numerical simulation and engineering application.Therefore,it has become a hot issue for researchers in the field of bridge engineering,nonlinear dynamics and vibration control to accurately analyze the vibration dynamic characteristics and mechanism of super long stay cables,study the vibration control methods and take reasonable vibration control measures.In this paper,the nonlinear parameter vibration control system for ultra-long cable stayed cables is taken as the research object,and the vibration characteristics and stability of the passive cable control system with cable-parameter vibration under the influence of the axial ideal displacement excitation and the influence of the cable-bridge coupling are analyzed.,As well as its parameter influence laws and design methods,the main research contents include the following points:(1)Establishing the differential equation of cable parametric vibration considering the first two modes under the influence of gravity chord component,and explore the influence of gravity chord component on the parametric vibration of long-span cable,as well as the parametric vibration characteristics of the first two modes.The multi-scale method is used to theoretically analyze the cable-stayed-parameter vibration system of the first two-order modes considering the influence of the gravitational chordal component force,and to explore the system stability and the critical conditions of vibration occurrence.(2)For the passive control system of the stayed cable parameter vibration under the end ideal displacement excitation,the stability conditions of the system are analyzed theoretically;the optimal additional damping coefficient of cable with sag is used to numerically analyze the influence of additional damping,external excitation frequency and amplitude,cable self damping and other parameters on the nonlinear parametric vibration dynamic characteristics of super long cable;the multi-scale method is used to analyze the stability and occurrence conditions of the main resonance and the main parameter resonance of the stay cable,and the influence of additional damping on the cable parameter vibration stability is explored.(3)Establishing a theoretical model of a passive cable control system that considers the stay cable-bridge coupling,and uses a viscous damper that considers the influence of bridge deck vibration to optimize the damping coefficient,analyze the characteristics of free vibration and forced vibration of the viscous damper control system of cable parameter vibration,and explore the influence of bridge-cable frequency ratio,mass ratio,additional damping ratio,external excitation frequency,amplitude and other parameters on the vibration characteristics of the system;The multi-scale method is used to analyze the parameter resonance condition and stability of cable-bridge-viscous damper system.For the cable-bridge-tuned mass damper(TMD)coupled vibration system,the design parameters of TMD are optimized to obtain the optimized additional damping ratio.the dynamic characteristics of the cable-bridge-TMD system are explored by using numerical analysis method,and the control effect of the damper is verified. |
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