Asymmetric limit cycle oscillations in systems with symmetric freeplay

In this paper, a simple 2D aeroelastic system with degrees of freedom in pitch, plunge and control surface deflection is investigated with freeplay in the pitch degree of freedom. It is shown that this system features a fixed point at the origin as well as two anti-symmetric fixed points. Asymmetric limit cycles that span only two of the three piecewise linear subdomains of the phase plane can orbit these anti-symmetric fixed points. A single three-domain symmetric cycle and two two-domain cycles appear as a result of a grazing bifurcation occurring at the flutter speed of the underlying linear system. The two-domain cycles can undergo further fold, period doubling and torus bifurcations. They can cause both periodic and aperiodic oscillations, including highly chaotic responses at parameter values where they interact strongly.