Study On Nonlinear Characteristics Of Aerodynamic Forces In Typical Deck Sections Of Long-Span Bridges

As the bridge discipline develops towards lightweight,large span,high strength and diversity of structural forms,the bridge is much more sensitive to the wind,and the wind-induced vibration response is more and more remarkable.Flutter is a form of vibration that must be eliminated,and with the development of wind engineering of bridge,flutter has been studied for many decades,but the traditional linear self-excited aerodynamic force model can not reflect the nonlinear characteristics of aerodynamic forces,nor can it meet the needs of wind-resistant design of today’s long-span bridges.The study in nonlinear characteristics of selfexcited aerodynamic forces are significant.The main work in this paper includes:(1)The theoretical research status of linear as well as nonlinear self-excited forces and the existing selfexcited force models were expounded,pointing out that the existing models had not considered bendingtorsional coupling effect,and they were difficult to determine aerodynamic parameters,and not practical enough.(2)The reliability of the CFD method was verified in the calculation of the ideal plate flutter derivative.The grids independence of the CFD calculation domain for the main beam section of the Forth Nanjing Yangtze River Bridge was verified.According to the inlet wind speed,the vibration frequency and the empirical formula,the calculation domain size,near-wall grid heights and grid sizes were reasonably selected.(3)The CFD calculations of vertical and torsional single-degree-of-freedom forced vibrations of the main beam section of the Nanjing Yangtze River Fourth Bridge was carried out.It was found that the selfexcited forces contained the fundamental vibration frequency components as well as the double and triple frequency components,so there was a multiple frequency phenomenon in the aerodynamic forces of the streamlined box girder.(4)In order to explore the flow field mechanism when nonlinear features generated,single-degree-offreedom forced vibration calculations with different vertical and torsional amplitude conditions were carried out.The generation,distribution,motion trace and interaction of the vortices around the main beam section of Nanjing Fourth Yangtze River Bridge were observed under different amplitude conditions.Combined with the vortex morphology observed from the streamline diagrams and the wind pressure distributions on the surface of the main beam,the reasons for appearance of multiple frequency in the wind pressure spectrum were analyzed.(5)The two-degree-of-freedom coupled forced vibration calculations with separate bending and torsion frequencies were carried out.It was found that in addition to the multiple frequency phenomenon,there was a coupling frequency phenomenon existing in coupled vibration calculations.Based on these nonlinear characteristics,a nonlinear self-excited aerodynamic force model with 24 sub-items was proposed.The subitems in the model were derived,and the nonlinear self-excited force model was expressed as a functional form associated with the motion state of α,α?,?,??.(6)The practical transformation of the nonlinear self-excited force model was carried and it was discribled as a function of magnitudes and phases.In order to find out the variation law of magnitudes and phases of each frequency component with the change of amplitude,the calculations of single-degree-offreedom and two-degree-of-freedom bending-torsional coupled forced vibrations were carried out,and the amplitude correlation formulas were curve-fitted to modify the nonlinear aerodynamic force model.The nonlinear model was validated by three kinds of coupled vibration conditions of small,medium and large amplitudes.It was found that the nonlinear model results fitted well with the CFD results.Finally,the nonlinear self-excited force model was simplified and derived when the inlet wind speed was approaching the critical wind speed of flutter,and the bending and torsion frequencies tended to be equal,which expanded the applicable range of the model.(7)The methods of solving the free vibration response by CFD and the nonlinear aerodynamic force model in Matlab were introduced.The response calculations were carried out by both two methods and the critical wind speeds of flutter were found.Soft-type flutter phenomenon was not observed in both cases,and the possible reasons were analyzed.