| In this thesis, we consider a two-dimensional airfoil oscillating in pitch and plunge with subsonic aerodynamics and with cubic, freeplay, and hysteresis structural nonlinearities. Some analytical techniques—center manifold theory, the principle of normal form, the perturbation method, and the point transformation method—were used to investigate the effects of the structural nonlinearities on flutter. For a self-excited aeroelastic system with cubic hard springs, the amplitudes and frequencies of limit cycle oscillations in the post-Hopf bifurcation can be predicted analytically. An excellent agreement was found between the results of numerical simulations and analytical predictions. For an aeroelastic system with freeplay and hysteresis models, convergent motions, period-one and period-two stable limit cycle oscillations, and chaotic motions are detected and the amplitudes and frequencies of limit cycle oscillations are predicted for the velocity below the linear flutter speed. Although time-integration numerical methods have often been used to study the response of an aeroelastic system with structural nonlinearities, the importance and necessity of analytical techniques are addressed through a detailed study of the numerical errors resulting from the Rungs-Kutta method. The analytical techniques developed in this thesis are suitable for many other non-aeroelastic systems: the center manifold theory and the principle of normal form can be generalized for nonlinear systems of ordinary differential equations with polynomial nonlinearities; the point transformation method can be extended for general piecewise linear systems. (Abstract shortened by UMI.)... |
