| Suspension bridge is an ancient type of bridge. Because of its many advantages such asstraightforward force line, slinky modeling and its large span ability, it has been used in theproject that across the sea and link the islands or across the valley more and more frequently。Because the span is increasing very quickly, the main load bearing member (including themain cable and the sling)will become more and more longer, as a result, the vibration problemof cable structures of great flexibility will be more and more prominent. In order to guaranteethe safety, durability, and using comfort level, the vibration problems caused the attention ofmany scholars. Based on a long-span suspension bridge suspension system’s maincomponents or its composition of the system has a possibility of engendering parametricvibration with great amplitude, this problem are studied systematically in the paper. Mainresearch work is as follows:(1) The Parabola to Catenary Iteration method(PTCI method for short)was carried outon the form-finding of suspension cable, and it is validated combined with the finite elementand the measured result. Analysis is starting from the cable unit static equilibrium relationship,in the process of gain the analytical solutions, according to the vertical distribution load lineon the cable element is a arc line or a chord line, it can be divided into two categories: onecorresponding cable form curve is parabola, another is catenary; then using the parabolaresults as the initial value for nonlinear iteration solution, eventually the cable element lineconverge for catenary. On the bases of the accurate element method, the calculation methodand process has been presented for unstressed cable length. Finally, comparing the results ofform-finding and unstressed cable length which are obtained from finite element software andthe measured values and the accurate method, we can get that this calculation theory needssmaller density for elements dividing, and get more quick iteration convergence rate, and canguarantee the necessary calculation accuracy.(2) This paper puts forward a calculation method of the natural characteristic values forthe suspension cable based on the PTCI method. After getting the accurate form of thesuspension cable, same with the micro-unit of suspension cable as the basic study object, starting from the static equilibrium relation, self-excited vibration of the cable element isdeduced. So we can get the right stiffness matrix and mass matrix of every suspension cablemicro-unit simulated with nonlinear catenary units, the following step is cable unit matrixintegrating into global stiffness and mass matrix of the whole cable, which will be substitutedinto the elastic dynamics equation of suspension cable system. So we can get the in-planenatural frequency and the corresponding vibration mode of every orders of the cable. Thenverifying the accuracy of the calculation method based on the comparison between the threeresults: one is the infinite software result, another is the measured value, the third result isfrom the right calculation method.(3) In the paper, a dynamic analysis finite element model of the AiZhai suspensionbridge was created by using a kind of finite element software. And the dynamiccharacteristics of the whole bridge on designed completed state had been analyzed, as well asthe local dynamic characteristics of the main cable and the sling in the same finite elementmodel. Finally, the effect of the suspension central buckle, end elastic cable and girder beamheight produced on the dynamic characteristics of the whole bridge.(4) In view of the empty loading state in the bridge construction stage of suspensionbridge, this paper analyzes the frequency ratio relations and response characteristics ofparametric vibration of the large span unhorizontal cable with large sag under the endexcitation. The parametric vibration dynamic equation of the main cable was deduced, inwhich the geometric nonlinear factors caused by the large sag and the large displacement hasbeen taken into account; then discrete the right equation by using Galerkin method; finallyanalytical analyzes and numerical analyzes the parametric vibration of the main cable byusing the Multi-scale perturbation method, then we can get the occurring conditions and theresponse characteristics of parametric vibration of the main cable.Two cases have been considering about the parametric vibration of the main cable,which respectively are it was excited by the low attitude tower and the high attitude tower.The main analysis include the relationship between the mid-span amplitude of the main cableand frequency, and the relationship between the vibration amplitude of the main cable and the excitation amplitude, and the time-history change of the main cable tension, and thetime-history change of the suspension cable midpoint displacement when parametric vibrationoccurred.Influence factors of the main cable parametric vibration have been analyzed, whichinclude the exciting amplitude, the initial tension of the cable, the cable length, the cable sag,and the quality of per unit cable length. Each influence factor are analyzed in two conditionsinclude its value increased by30%and reduced by30%. Analyze the influence degree of eachparameter on the relationship between the amplitude and the frequency ratio, the relationshipbetween the amplitude and the excite amplitude, the time-history change of cable tension, thetime-history change of the midpoint displacement when the parametric vibration occurred.(4)Aiming at the unstable characteristics of the long sling of the large span suspensionbridge, Simple sling mechanics model is established and deduced the parametric vibrationdifferential equation of the sling midpoint according to Newton’s law; then the variable wasdiscrete based on Galerkin method. Analyzed the single-mode and double-mode parametricvibration of the vertical sling under the ideal end excite using Multi-scale method andcombined with engineering instance parameters and get the right frequency ratio and responsecharacteristics. Finally the paper analyzed the difference to the parametric vibration responseof sling, which have made by some factors such as excite amplitude, cable length and theinitial disturbance.(5)In consideration of the flexible features of the whole suspended system of the largespan suspension bridge, on the premise of studying the parametric vibration under ideal exciteof the sling, this part analyzed the parametric vibration of vertical sling coupling with theflexible girder. Two degrees of freedom simplified mechanics model had been established.Then get the analytical resolution using the Multi-scale method, and combined with theAizhai suspension bridge engineering example, got the numerical occurring condition andresponse characteristics resolution of the two degree of freedom coupling system occurringparametric vibration by using Runge-Kutta method.On the basis of studying the two degrees of freedom system, this part further considering the influence of the flexible main cable, established three degrees of freedom(maincable-sling-girder)coupling parametric vibration mechanical model, and vibration differentialequation was derived according to Newton’s law, then carrying on the analytical resolution byusing Multi-scale method, following we can get the result about the combination resonancefrequency ratio of the parametric vibration of three degrees of freedom system. Finally thenumerical solution of three degrees of freedom coupling parametric vibration system wasavailable by using four orders Runge-Kutta method combined with the actual projectparameters, which are able to complement and verify the analytical solution. |
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