The Effect of Cubic Damping on Geometric Nonlinear Flutter in Long-Span Suspension Bridges

This study investigates the wind-induced flutter phenomenon of long-span suspension bridges. A mathematical model is established using the energy method, considering the nonlinear aeroelastic behavior of a bridge deck constrained by vertical suspenders under cubic nonlinear damping. The aerodynamic self-excited force is obtained using the Scanlan flutter theory. The critical state of flutter and the relationship between the amplitude and parameters of the limit cycle oscillation (LCO) are obtained by solving the nonlinear flutter equation using the average perturbation method. The Hopf bifurcation is confirmed to occur in the critical state of the nonlinear motion model using the Jacobian matrix. The results are verified using the Runge-Kutta numerical method, and it is found that the nonlinear response of the flutter LCO is in general agreement with the numerical solution. The study also shows that the degenerate Hopf bifurcation appears at the critical state under the condition of lower cubic damping coefficient, and the nonlinear flutter bifurcation changes from a degenerate Hopf bifurcation to a supercritical Hopf bifurcation as the cubic damping coefficient grows.