Nonlinear Flutter Characteristics Of Long-Span Bridges And Its Analytical Method

With the continuous growth of span length,modern long-span bridges have become softer and their structural damping has become lower and lower.As a result,they become more susceptible to wind actions.Flutter is the most dangerous wind-induced vibration,which is caused by negative aerodynamic damping and would initiate large amplitude or even divergent type of instability.The current wind resistance design is based on Classical linear flutter theory,under which,the design and construction cost of super long-span bridges has increased significantly and thus has a major impediment to the further development of super long-span bridges.Therefore,it is urgent to understand the nonlinear flutter characteristics of long-span bridges and build relevant nonlinear analysis theory,so as to provide a theoretical basis for the construction of post-flutter design standards.Although a lot of research has focused on the nonlinear flutter of some typical bridge sections,the relevant theories are still developing and the three-dimensional nonlinear flutter analysis method is still very scarce.Therefore,in this paper,the nonlinear aeroelastic characteristics of typical single/double-deck truss girder sections were systematically studied based on large amplitude free-vibration sectional model tests,a two degree of freedom coupled nonlinear self-excited force model suitable for blunt-body girder sections was proposed,an identification method of amplitudedependent flutter derivative was established,methods about three-dimensional nonlinear flutter in the frequency domain and time domain were proposed,and the relevant mechanism of nonlinear flutter was revealed.The main contents are summarized as follows:(1)The wind tunnel test of nonlinear aeroelastic behavior of a typical single-deck truss girder section model was carried out by using a novel spring-suspended device that allows the large vertical-torsional coupling motion.An experimental procedure that can extract the nonwind-induced added aerodynamic effect was designed.the mechanical nonlinear characteristics of the spring-suspended device were analyzed and the nonwind-induced added aerodynamic effect of the section model was quantified;The nonlinear flutter response characteristics of the section model at attack angles of-3°,0°,+3°,+5°,+7° are studied in detail;a significant coupling vertical deformation was observed and it was found that it is a function of aerodynamic shape and torsional amplitude;The evolution of aerodynamic torsional center and nonlinear flutter mode was discussed;The effects of mechanical damping,nonwindinduced added aerodynamic damping,and wind-induced added aerodynamic damping on nonlinear flutter were quantitatively compared;The main reasons for the existence of stable limit cycle oscillation(LCO)and unstable LCO under a given wind speed were revealed;Finally,the influence of mechanical damping on post flutter performance was analyzed.(2)A nonlinear analysis framework suitable for vertical-torsional coupled nonlinear flutter analysis was established.Based on the nonlinear flutter characteristics of the singledeck truss section model,a vertical-torsional coupled nonlinear self-excited force model was proposed,and the corresponding identification method of aerodynamic parameters was established;Then the aerodynamic parameters of the self-excited force model were identified based on the data from the wind tunnel tests,and the evolution of aerodynamic parameters with reduced wind speed was analyzed;The nonlinear flutter response of the single-deck truss section model was calculated,and the calculated results were compared with the experiment results to verify the correctness and feasibility of the nonlinear self-excited force model;Finally,the proposed nonlinear analysis framework that can predict the bifurcation behavior was verified.(3)The free vibration tests with large amplitudes of a single degree of freedom(SDOF)system and a two-degree-of-freedom(2DOF)system were carried out for a typical doubledeck truss girder section model.The nonlinear flutter characteristics of the SDOF system and 2DOF system were compared and analyzed,then the influence of the vertical degree of freedom on vertical-torsional coupled nonlinear flutter was quantified;The evolution of coupled aerodynamic damping and uncoupled aerodynamic damping in nonlinear flutter were revealed,and their main roles in nonlinear flutter were clarified.(4)A method for identifying amplitude-dependent flutter derivatives based on the closedform solutions of coupled flutter was proposed.the closed-form solutions of amplitudedependent flutter derivatives were derived according to closed-form solutions;Based on the experimental data from wind tunnel tests,the amplitude-dependent flutter derivatives of the double-deck truss girder section model were identified;Then closed-form solutions for twodimensional vertical-torsional coupled nonlinear flutter was proposed.The nonlinear flutter response was calculated,and the calculated results were compared with the experiment results to verify the correctness and feasibility of the flutter derivatives identification method and the closed-form solutions of coupled flutter.(5)Methods for frequency-domain analysis of three-dimensional nonlinear coupled flutter of long-span bridges were proposed,which mainly include closed-form solutions of bimodal coupled nonlinear flutter,a multimode coupled nonlinear flutter analysis framework,and a full-mode coupled nonlinear flutter analysis framework.The three-dimensional nonlinear flutter analysis of a long-span suspension bridge with a main span of 1650m and four main cables was carried out;The influence of the three-dimensional modal effect on nonlinear flutter was studied,and its negative mechanism on nonlinear flutter was revealed;Then the influence of lateral flutter derivatives on nonlinear flutter was analyzed;The nonlinear flutter response considering different natural modes were compared,and the influence of multimode coupled effect on nonlinear flutter was clarified;The differences between the results of full-mode analysis and multimode analysis were compared,and the necessity of full-mode coupled nonlinear flutter analysis was clarified.(6)A time-domain nonlinear unsteady self-excited force model expressed by multilevel rational functions was proposed.The three-dimensional nonlinear flutter analysis in the timedomain of Yanji Yangtze River Bridge with a main span of 1650m and Miaozui Bridge with a main span of 838m was carried out,and the influence of geometric nonlinearity on the nonlinear flutter response was studied;The superharmonic resonance behavior induced by geometric nonlinearity in nonlinear flutter was observed,and the superharmonic resonance behavior is the main physical mechanism that driving geometric nonlinearity to reduce the steady-state amplitude was clarified;The behavior of main girder being lifted vertically caused by geometric nonlinear effect was analyzed;Finally,the phenomenon of modal branch competition in nonlinear flutter was revealed.