Limitation of application of the center manifold reduction in aeroelasticity

In this paper, the method of center manifold reduction is applied to the limit cycle calculations of a three-dimensional thin airfoil placed in an incompressible flow. Limit cycle oscillations are caused by a cubic structural restoring force corresponding to the aileron rotation. The equation of motion is written as an integro-differential equation and also as an approximate set of ordinary differential equations. Two different implementations of the method of center manifold reduction for these two cases are briefly outlined. It is emphasized, that the formal power series expansions used in the method of center manifold reduction typically diverge and cause the method not to give satisfactory results. An example is presented, when the method of center manifold reduction cannot even qualitatively predict the occurrence of a stable limit cycle of a small amplitude.