The equivalent linearization method （ELM） is modified to investigate the nonlinear flut- ter system of an airfoil with a cubic damping. After obtaining the linearization quantity of the cubic nonlinearity by the ELM, an equivalent system can be deduced and then investigated by linear flut- ter analysis methods. Different from the routine procedures of the ELM, the frequency rather than the amplitude of limit cycle oscillation （LCO） is chosen as an active increment to produce bifurca- tion charts. Numerical examples show that this modification makes the ELM much more efficient. Meanwhile, the LCOs obtained by the ELM are in good agreement with numerical solutions. The nonlinear damping can delay the occurrence of secondary bifurcation. On the other hand, it has marginal influence on bifurcation characteristics or LCOs.
An optimization approach based on Artificial Bee Colony(ABC)algorithm is proposed for structural local damage detection in this study.The objective function for the damage identification problem is established by structural parameters and modal assurance criteria(MAC).The ABC algorithm is presented to solve the certain objective function.Then the Tournament Selection Strategy and chaotic search mechanism is adopted to enhance global search ability of the certain algorithm.A coupled double-beam system is studied as numerical example to illustrate the correctness and efficiency of the propose method.The simulation results show that the modified ABC algorithm can identify the local damage of the structural system efficiently even under measurement noise,which demonstrates the proposed algorithm has a higher damage diagnosis precision.
