Flutter analysis for bridges based on a hybrid firefly algorithm

When performing flutter analysis, high-order strong nonlinear equations need to be solved. For overcoming the difficulties encountered by traditional methods, a hybrid firefly algorithm was used to solve the equations. The solution of the critical flutter state problem was converted to an optimization problem by using a double-parameter optimization model. Therefore the optimization model can be employed to calculate the critical velocity and the critical frequency of two or three degrees of freedom flutter. To compensate shortcoming of the firefly algorithm, a hybrid firefly algorithm was proposed and used for searching the optimal solution of the optimization model. Finally, the reliability and the validity of the optimization model as well as its solution were confirmed by numerical and experimental examples.