Improvements in Convergence Robustness with a 2D–3DOF Method: Application of Genetic Algorithm to Coupled Flutter

To overcome nonconvergence in the two-dimensional–three degrees of freedom (2D–3DOF) method, the practical modal-driven flutter analysis method (PMDFA) was proposed for the coupled flutter in long span bridges that used a genetic algorithm (GA). First, formulas in the 2D–3DOF method were updated when the assumed initial displacement was expressed as an exponential form for the frequency and damping. Then, the calculation results from the modified formulas proved to be identical to the exact solution that was calculated by the complex eigenvalue analysis (CEVA). However, due to the inherent defects in the iterative equations, the original fixed-point method (FPM) failed to converge when the frequencies of heaving and torsion were close. To overcome the convergence limitations in the FPM, a powerful GA without the restrictions of the iterative equation properties was introduced into the revised 2D–3DOF method. Then, the flutter analysis of suspension bridges with a main span from 1,000 to 5,000 m was carried out, and the numerical calculation showed that the FPM failed to complete the flutter calculation in most cases; however, the GA performed the analysis. In addition, a study on a suspension bridge showed that the numerical results obtained by the PMDFA were in reasonable agreement with the experimental results. Therefore, the proposed GA-based method has advantages of high accuracy and strong robustness and has wider application prospects in the flutter analysis of super long span bridges.

Flutter instability can cause a large amplitude vibration and destroy a structure completely and it must be avoided during the service life of a structure. With an increase in the span, flutter performance has become an important index in the wind resistance design of long span bridges. The 2D–3DOF method can evaluate the flutter performance of structures effectively and establish a deep understanding between aerodynamic parameters and aerodynamic performance. Therefore, it plays an important role in the analysis of the flutter mechanism. However, due to the defect in the original convergence algorithm, sometimes it cannot calculate U_craccurately in practical engineering applications. Therefore, to overcome this problem, a GA was introduced into this paper to calculate convergence. The case study showed that the proposed GA-based method has the advantages of high accuracy and strong robustness, and could deal with the problem perfectly. In addition, the iteration problem of nonconvergence might occur in the other methods, such as the CEVA or the multimodal flutter analysis and the solution idea in this paper might have a certain reference value for the convergence calculation.