Nonlinear Dynamics Of Wind Induced Vibrations Of Cable Structure

Cable structure plays an important role in many civil and structure engineering,such as cables-stayed bridge, suspension bridge, guyed mast or tower and otherlong-spanspacestructures.Duetotheirgreaterflexibilityandlowerinherentdamping,however, cable structures are prone to vibration under different types of dynamicloadings, especially radial ones. Aerodynamic loading often becomes control loadingof cable structures when cable structures are in natural conditions. Large amplitudevibrationwasalwaysinducedbythecombinedeffectoflightrainandwind.However,the generation mechanisms of rain-wind-induce vibration of cable structure have notbeen entirely solved. The motion of cable structure is coupled with the motion of therivulet via fluid-structure interactions. The vibration can affect human comfort andeven the structural safety, which has become an urgent problem to be solved inengineering.Four aspects problem were studied in this project, One degree of freedom(DOF)galloping model of cable structure, the influence of parameters to two DOF ofrain-wind-induced vibrations (RWID) model of cable structure, the periodic motionsandchaosmotionsofrainwindinducedvibrationandthelocalbifurcationsofsystem.One DOF galloping model of cable structure was studied by CFD softwareFluent and averaging method. The model of cable structure with half cylinder formwas bulit by Gambit in incompressible flow at first, and then plot grid in detailaccording to the flow field characteristics around the cable structure. The parameterssuch as boundary pressure, fluid attribute etc. were set in CFD software Fluent. Theflow field characteristics around the cable structure and the drag coefficient and liftcoefficient according to different attack angel were achieved by Fluent also. Theexpression of drag coefficient and lift coefficient about attack angel were attained bypolynomial fitting method. The differential equation for one DOF galloping model ofcable structure was built. The original system was studied by numerical simulation.The phase portraits of cable vibration were achieved, which showed that theirmovement converged to limit circles. In aspect of analytical computation, the systemwas studied by averaging method. Approximate solution of one order of system wasachieved,thisresultfitswithexperimentresultwell.This paper proposes a two DOF model of rain-wind-induced vibrations of cablestructure with dynamic upper rivulet. The original system was studied by numerical methods with symbol algebra language software Mathematica. The influence ofdensity ratio of air to cable structure, damping ratio of cable, yaw angle of wind,natural frequency of upper rivulet etc was studied by Mathematica program. Theresults show that the density ratio of air to cable structure and damping ratio are thetwo most important factors to affect the amplitude of RWID of cable structure. Phaseplane trajectory and time history curves of cable structure and rivulet in differenttypesofresonancemodelswereachievedalso.TheyshowedthatthemotionofRWIDofcablestructuresisakindofcomplicatedperiodicmotions.Theordinarydifferential equations oftheoriginal system weremuchcomplicatedwhich have inertial coupling items. The original system was uncoupled in order tostudy by nonlinear dynamical method. The system of RWID of cable structure wasstudied bymulti-scale method.The phase portraits, time history curve and AmplitudeSpectrum of cable and rivulet were acquired by numerical method. The computationoflyapunovexponentwithdifferentparametersshowsthatthereweredoubleperiodic,almost multiple periodic and chaotic motion behavior in this system. Effect ofparameteronperiodicandchaoticmotionofsystemwasstudiedusingMathematica.The original system with inertial coupling items was studied by multi-scalemethoddirectly.Thebifurcationequationofsystem with higherordernonlinearitemswas obtained. Bifurcation behavior of RWID of cable structure was studied bysingularity theory. Many bifurcation models and transition sets are obtained. Therelationship between the parameters and the bifurcation behavior is constituted in thisstudy.