Aerodynamic flutter and limit cycle analysis for a 2-D wing with pitching freeplay in the supersonic flow

The problem of flutter and limit cycle oscillation (LCO) for two-degrees-of freedom airfoil with structural and aerodynamic nonlinearities is addressed in this paper. The model which includes freeplay in pitching is established using the Lagrange equation. The aerodynamic lift and moment are derived in terms of the 3rd-order piston theory. The forth order Runge-Kutta method is employed to solve the nonlinear dynamic equations numerically. Period response, multi-periodic response and chaotic motion are observed after investigating the phase plane and power spectral density diagrams. Bifurcation diagram of the pitching is obtained with gradually increasing values of the dimensionless air speed. The results indicate that the critical flutter speed is lower than that of the system without freeplay. It can be also concluded from the simulation that the initial value and the magnitude of the freeplay have significant effects on the dynamic motion of the system in both regions of stable and LCO. The dimensionless air speed region in which the system behaves chaotic motion is wider than that reported in the existing literature.