Nonlinear Analysis of a Two DOF Piecewise Linear Aeroelastic System

Abstract

The nonlinear dynamic analysis of aeroelastic systems is a topic that has been covered extensively in the literature. The two main sources of nonlinearities in such systems, structural and aerodynamic nonlinearities, have analyzed numerically, analytically and experimentally. In this research project, the aerodynamic nonlinearity arising from the stall behavior of an airfoil is analyzed. Experimental data was used to fit a piecewise linear curve to describe the lift versus angle of attack behavior for a NACA 0012 2 DOF airfoil. The piecewise linear system equilibrium points are found and their stability analyzed. Bifurcations of the equilibrium points are analyzed and applying continuation software the bifurcation diagrams of the system are shown. Border collision and rapid/Hopf bifurcations are the two main bifurcations of the system equilibrium points. Chaotic behavior represented in the intermittent route to chaos was also observed and shown as part of the system dynamic analysis. Finally, sets of initial conditions associated with the system behavior are defined. Numerical simulations are used to show those sets, their subsets and their behavior with respect to the system dynamics. Poincaré sections are produced for both the periodic and the chaotic solutions of the system. The proposed piecewise linear model introduced some interesting dynamics for such systems. The introduction of the border collision bifurcation and the existence of periodic and chaotic solutions for the system are some examples. The model also enables the understanding of the mapping of initial conditions as it defines clear boundaries with different dynamics that can be used as Poincaré sections to understand further the global system dynamics. One of the constraints of the system is its validity as it is dependent on the range of the experimental data used to generate the model. This can be addressed by adding more linear pieces to the system to cover a wider range of the dynamics.