Abstract
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.
Highlights
With the increase of the bridge span, especially the longspan suspension bridge, the structure tends to soften
Is is a structural instability where the equilibrium state of the structure begins to lose its stability under the action of external forces, and a slight disturbance, which is practically unavoidable, gradually increases the deformation and causes the structure to break down. e instability of the bridge system at the critical state of flutter is Hopf bifurcation; when wind speed exceeds it, there will be a phenomenon such as the Tacoma Narrows Bridge and the finiteamplitude periodic vibration that occurrs in the wind tunnel test, that is, the limit cycle oscillations (LCOs)
Effect of Damping Ratio and Cubic Stiffness on Bifurcation and LCOs. It is known from the previous section that a suspension bridge system with strong nonlinearity undergoes a supercritical Hopf bifurcation in the flutter critical state and has LCOs appeared on the right side, while the damping and nonlinear stiffness coefficients of the system may affect the bifurcation and LCOs
Summary
With the increase of the bridge span, especially the longspan suspension bridge, the structure tends to soften. When the bridge deck is subjected to torsional displacement, the change in the magnitude and direction of the elastic force of the hanger leads to geometric nonlinearity of torsion Based on this system, the authors studied the bifurcation and LCOs of this kind of two-degree bridge deck model [15,16,17,18,19,20,21]. The flutter and LCOs beyond critical flutter speed of a long-span suspension bridge deck with cubic nonlinear torsional stiffness will be studied. Considering the cubic torsional stiffness and the vibration frequency of a long-span suspension bridge, nonlinear flutter equations of Nizhou Waterway Bridge were established by referring the plane wings flutter model. On the right side of the equations are the flutter self-excited forces which are put forward by Scanlan [1]. e torsional stiffness term on the left side of the equations is written as a cubic function of torsional displacement, which means that the nonlinear cubic stiffness is related to torsional displacement:
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