Characteristic And Influence Of Local Cable Vibration On Long-span Cable-Stayed Bridges

Recently,as the main span of cable-stayed bridges increase continuously,the really local vibration features of inclined cables and coupled oscillation characteristics of the cable and the bridge are more and more becoming to be a new significant topic research in the design process of cable-stayed bridges.Based on the investigation both of domestic and international scholars,this paper researched systematically in the in-plane cable local vibration characteristics,the coupled analysis of out-of-plane oscillation and in-plane vibration of stayed-cables in spatial three-dimensional coordinates,the responses of Root Mean Square(RMS) property both in in-plane and out-of-plane under random excitations, and seismic time-history response of cable-stayed bridges with local cable vibration. Concretely,the researches in this paper include the following five aspects:(1) The inner nonlinear vibration behavior of cables subjected the the excitations at either beam or tower end was investigated.The inner oscillatory differential equation which considered the excitations at both beam and tower end was deduced,the modificatory coefficient of natural frequency and the parameters indicated initial equilibrium state in the cable vibration model was added defined,the forced vibration items and parametrical vibration items were modified,and the vibration characteristic relations with those ingredients such as physical parameters and excitation parameters are analyzed.Secondly,the inner single argument and double control coupling oscillatory differential equations in loosening and non-loosening state which considered the excitations at beam are deduced and uniformed,and the Runge-Kutta subsection integration method is applied to solve those equations,the whole alternate variation processes between loosening and non-loosening state are obtained.(2) Non-Linear vibration behavior of spatial inclined cables subjected to harmonic and arbitrary orientation displacement excitation at beam end or tower end is carried out,the three-dimensional non-linear coupling control oscillatory differential equations in loosening and non-loosening state which considered the arbitrary orientation excitations are deduced and uniformed.With different excitation orientation angles and frequences, the coupled oscillation analysis both in-plane and out-of-plane of an inclined cable is carried out,the relationship of vibration amplitude with matching ratio of natural frequencies of cable and excitation frequency is analyzed.Subsequently,the out-of-plane self-excited vibration is investigated and the minimum excitation amplitude arising self-excited vibration is obtained.Finally,with the figure of phase plane,Poincare section and the maximal Lyapunov exponent spectrum,the existence of chaotic motions in certain parameters are proved.(3) Non-Linear stochastic vibration behavior of inclined cables subjected to a Gaussian zero mean stationary white noise process displacement excitation at beam end or tower end and In-plane self-excited stochastic vibration behavior of inclined cables subjected to a Gaussian zero mean stationary white noise process excitation in transverse bridge orientation are carried out.The inner oscillatory differential equations which based on It(?) differential standard type are deduced.Gaussian closure method,stochastic linearization method and Falsone's innovated stochastic linearization method are applied to derive the second order mean square moment equations.The three-dimensional non-linear coupling control oscillatory differential equations of inclined cables are deduced,equivalent stochastic linearization method is applied to derive the 14 first-order nonlinear differential equations of state vectors of inclined cables,and the Runge-Kutta integration method is utilized to obtain the RMS response characteristics.The Lyaponov exponent is applied to investigate the stability property of the auto-parametric vibration under random excitations.(4) The dynamical behavior of global bridge model and local cable model of E DONG Bridge are analyzed in detail,combined with the analytical solution of the first order natural frequency of inclined cables considering the influences of sag effect and the initial equilibrium state in the above aspect,the models both considering local cable vibration(MECS) and ignore local oscillatory(OECS) are established.Subsequently,the relationship between the natural frequency of inclined cables and the global bridge is analyzed,and the serial number of cables which may present large amplitude vibration and the corresponding frequency relationship are estimated.In the end,the local vibration characteristics of selected representational cables of Z16 and Z30 is calculated applying the formulary in chapter 3,and the minimal modal damping ratios under distinct amplitude excitation are solved approximately.(5) Seismic time-history response of cable-stayed bridges with local cable vibration is investigated,taking E DONG Bridge for example,combined with the restart function and parameter transient variation commands in ANSYS,a general program to solve the geometrical nonlinear seismic time-history response was established based on the state of truly initial static equilibrium and time-varying effects with E_ep of cables,the solution was compared with the results under the time-invariant E_ep of cables calculated by the initial cable tension.By inputting two kinds of excitation earthquake with identical amplitudes but different spectral properties in the cable-stayed bridge model considering local cable vibrations,the additional damping effect and vibration amplificatory effect with different matching relationship of the frequencies were analyzed.