Vibration Characteristics Of Inclined Cable Under Cable-end And Rain-Wind Excitation

Stay cables are used as the key elements of cable-stayed bridge and often prone to quite large transverse vibrations due to their relatively flexibility and low inherent damping under rain-wind or motion of the cable end.There are many types of cable vibration,parametric resonance and internal resonance or rain-wind induced vibration maybe occur simultaneously.Using numerical method,this paper firstly studied vibration characteristics of parameter resonance and internal resonance under cable-end excitation and rain-wind induced vibration under rain-wind excitation.Secondly,the coupled vibration under cable-end excitation and rain-wind excitation are investigated in detail.(1)The differential equation of three-dimensional motion of cable is established considering cable-end excitation,the finite difference method is used to solve the coupled differential equations of motion,vibration characteristics of parameter resonance and internal resonance under cable-end excitation are investigated.First,The correctness of the three-dimensional continuous cable stayed model is verified.Second,the influence of higher-order term on parametric resonance and internal resonance are discussed.Next,three dimensional continuous model and single degree model are compared.Then,the characteristics of internal resonance and parametric resonance are studied respectively.Finally,the influence of the excitation amplitude,the frequency ratio and the damping ratio of the cable are analyzed.(2)The diffcrential equation of three-dimensional motion of cable and water rivulet are established considering rain-wind excitation,the finite difference method and runge-kutta method are used to solve the coupled differential equations of motion,vibration characteristics of rain-wind induced vibration under rain-wind excitation is investigated.Firstly,the influence of higher-order term on rain-wind induced vibration is discussed.Secondly,the characteristics of rain-wind induced vibration and in/out of plane motion coupling are studied.Lastly,the influence of the damping ratio are analyzed.(3)The differential equation of three-dimensional motion of cable and water rivulet are established considering cable-end and rain-wind excitation,the finite difference method and runge-kutta method are used to solve the coupled differential equations of motion,characteristics of coupling vibration under cable-end and rain-wind excitation are investigated.First,coupling vibration of parametric resonance and rain-wind induced vibration is analyzed.Next,coupling vibration of internal resonance and rain-wind induced vibration is discussed.Then,coupling vibration of cable-end and rain-wind excitation is studied when the frequency ratio is 0.5.Finally,The effect of frequency ratio and wind speed on coupling vibration of cables are investigated.