Study On Nonlinear Flutter Of Long Span Suspension Bridges And Its Analytical Method

Aerodynamic force in the widely adopted self-excited force model cannot consider its nonlinear changes on vibration amplitude since it is only expressed as a function of reduced wind speed,hence,corresponding long span flutter analysis frameworks are only capable of capturing flutter onset wind speed while cannot predict flutter amplitude and post-flutter state beyond the critical wind speed.Besides,the flutter stability of bridges under a non-small initial vibration amplitude condition cannot be properly evaluated either.Thus,it is difficult to satisfy the request of wind resistance design of super-long span bridges in the future.To this end,it is of necessity to developing nonlinear flutter analysis frameworks in order to obtain the vibration amplitude of nonlinear flutter under different initial conditions,to evaluate the nonlinear flutter stability,as well as to provide theoretical evidence for the wind resistance safety design of super long span bridges.A double-deck truss girder of the Yangsigang Yangtze River Bridge was used as an example in this study to comprehensively investigate the amplitude-dependent characteristics of nonlinear flutter of typical bridge girders by using a section-model free vibration wind tunnel test.A method concerning the identification of nonlinear aerodynamic parameters was proposed.The nonlinear flutter analysis frameworks in both the two-dimensional and threedimensional perspectives were built.The kinetic mechanism of the nonlinear flutter of typical bridge decks was revealed.The works of this study replenish the shortcoming of current nonlinear flutter analysis theories of long-span suspension bridges and provide important theoretical references for the wind-resistant design of super-long-span suspension bridges.The main research contents and results of this study are lists as follows:(1)The nonlinear flutter characteristics of an SDOF system in torsion and a 2DOF system in both the vertical and torsional directions of a double-deck truss girder were comprehensively investigated by a free vibration wind tunnel test with considering nonlinear dependence of structural damping ratios on vibration amplitude.The funnel shape characteristics of modal damping(Including aerodynamic damping)on vibration amplitude was revealed.Based on the nonlinear dependence of modal damping on vibration amplitude,the influence of vertical motion on coupled nonlinear flutter was quantified.The inner mechanism of the hysteresis response of steady-state amplitude was interpreted,and the important role of uncoupled aerodynamic damping on the generation of hysteresis response was highlighted.(2)The amplitude dependence characteristics of nonlinear modal properties(i.e.,modal damping ratio,amplitude ratio,phase difference,modal frequency)were identified based on displacement time histories measured from section-model free vibration wind tunnel test.A two-dimensional bending-torsion coupling nonlinear flutter analysis framework was proposed.A method aims at the identification of nonlinear flutter derivatives of bridge girder as functions of reduced wind speeds and vibration amplitudes was further proposed.The accuracy of the proposed method was cross-validated by a wind tunnel test.(3)A torsional nonlinear mathematical model and a coupled nonlinear mathematical model that capable of estimating nonlinear flutter response of bluff bridge decks were proposed from the nonlinear structural dynamics’ point of view.The nonlinear aerodynamic damping ratio as a function of time-varying displacement and the equivalent nonlinear damping ratio as a function of vibration amplitude were modeled and the algebraic nexus between these two models were built based on the harmonic balance technique,by which nondimensional aerodynamic parameters in these models can be well-identified.(4)Closed-form solutions concerning the 3-dimensional nonlinear flutter calculation and mechanism analysis of long-span suspension bridge associate with single-mode and bimodal coupled cases were proposed.Full bridge nonlinear flutter response of a long-span suspension bridge,which is referred to as the Yangsigang Yangtze bridge with a main span of 1700 m,was predicted.When mode shapes were accounted for,results showed that the onset wind speed of nonlinear flutter is dramatically changed as compared with that of a two-dimensional case,which is mainly attributed to the fact that nonlinear self-excited forces will be significantly affected by vibration amplitude at different span locations.Taking the bimodal coupling flutter case as an example,the mechanisms of structural damping ratio and aerodynamic shapes of bridge girders affecting nonlinear flutter response of long-span suspension bridges were described.(5)A multimode coupled analysis framework in terms of generalized modal coordinate,which was also referred to as the “double layer iterative eigenvalue analysis method”,was proposed for the calculation of nonlinear flutter response of long-span suspension bridges.A suspension bridge with a main span of 1700m(Double-deck truss girder)which is referred to as the Yangsigang Yangtze River Bridge,and another suspension bridge with a main span of1418m(Streamlined box girder)which is referred to as the Fourth Nanjing Yangtze River Bridge,respectively,are used in the analysis as numerical examples to illustrate the effectiveness and feasibility of the proposed analysis framework.The influence of the aerodynamic difference of bridge girder shapes on nonlinear flutter response of long-span suspension bridges was quantified,the inner mechanism of multi-mode coupling effects on nonlinear flutter responses was also revealed.