Insight into the intrinsic time-varying aerodynamic properties of a truss girder undergoing a flutter with subcritical Hopf bifurcation

In this study, the investigation on the intrinsic time-varying nonlinear aerodynamic properties and actual energy feedback mechanism of limit cycle oscillation (LCO) and subcritical Hopf bifurcation, which is of great importance of the flutter design of bridges, but once rarely be conducted, was comprehensively carried out. The response characteristics of the nonlinear flutter were experimentally investigated. The dynamic mechanism of the subcritical Hopf bifurcation was firstly introduced in terms of the equivalent modal damping ratio as a function of amplitude. Further, a modified nonlinear self-excited force model was proposed to investigate the intrinsic time-varying characteristics of the aerodynamic properties and the real energy feedback mechanism of the subcritical Hopf bifurcation. Based on the model, the characteristics of nonlinear self-excited forces and nonlinear aerodynamic damping coefficients, as well as their contribution to the energy exchange behaviors, were studied. Subsequently, the energy feedback mechanisms of LCO and subcritical Hopf bifurcation were qualitatively discussed in detail considering the hysteresis loop of nonlinear self-excited forces (NSEF), which highlighted the important role of the linear self-excited-moment (including damping and stiffness) in the generation of a subcritical Hopf bifurcation, and the higher-order force components on the generation of stable LCO. Finally, the driving mechanisms of LCO and subcritical Hopf bifurcation were also quantitatively explained via an energy budget analysis, wherein the total work applied by structural and aerodynamic forces was presented as a function of amplitude and time.