Nonlinear Flutter Analysis for a Long-Span Suspension Bridge

The wind-induced flutter of the long-span suspension bridge structure is extremely harmful to the bridge. Therefore, it is necessary to study the nonlinear problem of wind-induced flutter. Here, the nonlinear flutter problem of a long-span suspension bridge with cubic torsional stiffness is analyzed by the equivalent linearization method. The system has Hopf bifurcation and limit cycle oscillations (LCOs) under critical wind speed. Replacing the nonlinear stiffness term of the original nonlinear equation with the equivalent linear stiffness, we can obtain the equivalent linearized equation of the nonlinear flutter system and the solution, critical wind speed, and flutter frequency of the suspension bridge flutter system. At the same time, the system has a limit cycle vibration, and the Hopf bifurcation point is obtained. Compared with the numerical method, the calculation results are consistent. The influence of the damping ratio on the flutter system is analyzed. Increasing the system damping ratio can increase the flutter critical wind speed and reduce the amplitude of LCOs. The influence of cubic torsional stiffness on the flutter system is analyzed. The increase of the cubic stiffness coefficient does not change the critical state of flutter, but reduces the amplitude of LCOs.