An incremental method for limit cycle oscillations of an airfoil with an external store

摘要

This paper proposes an incremental method, which is based on the harmonic balance method, to analyze the nonlinear aeroelastic problem of an airfoil with an external store. The governing equations of limit cycle oscillations (LCOs) of the airfoil are deduced by the harmonic balancing procedure. Different from usual procedures, the harmonic balance equations are not solved directly but instead transformed into an equivalent minimization problem. The minimization problem is solved using the Levenberg-Marquardt method. Numerical examples show that the LCOs obtained by the presented method are in excellent agreement with numerical solutions. The bifurcation of the LCOs is further analyzed using the Floquet theory. It is found that the LCOs exhibit saddle-node, symmetry breaking and period-doubling bifurcations with the wind speed as control parameter. Compared with the harmonic balance method, the presented method has a wider convergence region and hence makes it easier to choose a proper initial guess for iterations.