Limit cycles in the dynamics of an elastically mounted aerodynamic pendulum

The dynamics of a elastically mounted single-link aerodynamic is considered. The unsteady aerodynamic action is modeled using an attached oscillator. It is assumed that the stiffness of the mounting spring contains cubic term, in addition to the linear one. Equilibrium positions of the pendulum and their stability are investigated. It is shown, in particular, that at certain values of the parameters of the system, the “weather vane” equilibrium position becomes unstable, and an attracting limit cycle arises. Approximate formulas for the frequency and amplitude of this cycle are obtained. It is shown that, in a wide range of parameter values, its frequency practically does not depend on the coefficient of stiffness of the fastening spring and on the moment of inertia of the pendulum. The amplitude of the cycle increases with an increase in the moment of inertia and decreases with an increase in the stiffness coefficient.