Subsonic flutter calculation of an aircraft with nonlinear control system based on center-manifold reduction - Grzędziński, J. (Archives of Mechanics, 1997)
The paper presents a method of calculation of limit cycle subsonic flutter oscillations caused by structural nonlinearities. Numerical examples assume the nonlinearities to be concentrated in the hinges of the aircraft control surfaces. Since nonlinear flutter is essentially the Hopf bifurcation, these oscillations tend asymptotically to a certain two-dimensional attracting subspace called the center manifold. Consequently, an asymptotic motion of the entire aircraft in the neighbourhood of bifurcation point is fully described by only two equations. The method of center-manifold reduction consists in a nonlinear change of coordinates, and transforms the initial multi-dimensional nonlinear integro-differential flutter equation into a system of two nonlinear ordinary differential equations of the first order, having phase-shift symmetry. Under the assumption that the nonlinear term has a formal power series expansion with respect to generalized coordinates (multi-variable Taylor series), the transformation can be also expressed in the form of a power series, and the limit cycle amplitude and frequency can be easily calculated.