Model Reduction of Nonlinear Aeroelastic Systems Experiencing Hopf Bifurcation

摘要

In this paper, we employ the normal form to derive a reducedud-udorder model that reproduces nonlinearuddynamical behavior of aeroelastic systems that undergo Hopf bifurcation.udAs an example, we consider a rigidudtwoud-uddimensional airfoil that is supported byudnonlinear springs in the pitch and plunge directions andudsubjected to nonlinear aerodynamic loads.udWe apply the center manifold theorem on the governing equationsudto derive its normaludform that constitutes a simplified representation of the aeroelastic sysudtem near flutterudonsetud(manifestation of Hopf bifurcation). Then, we use the normal form to identify a selfud-udexcitedudoscillatorudgoverned by a timeud-uddelay ordinary differential equation that approximates the dynamical behavior whileudreducing the dimension ofudthe original system. Results obtained fromudthis oscillator show a great capability toudpredict properly limit cycle oscillations that takeudplace beyond and above flutter as compared with theudoriginaludaeroelastic system.