Global behavior of nonlinear aeroelastic systems

This paper investigates the effects of nonlinearities on the dynamics of flat panels in supersonic flow. Modern dynamical systems techniques such as normal forms and global bifurcation theory are employed to detect largescale phenomena and symmetry-breaking bifurcations. The first part of this paper deals with modeling unsteady aerodynamic forces and moments acting on flat panels undergoing arbitrary motion in supersonic flow. This modeling also considers the structural nonlinearities inherent in panels. In the absence of dissipative terms the nonlinear system is reversible, which provides near integrable structure in the governing equations. Thus certain analytical methods are used to study the bifurcation behavior of the system near critical points. The normal form associated with the reversible systems can be obtained as a special case from the general normal form equations obtained previously. The linear operator is assumed to have a generic nonsemisirnple structure, and the system is simplified considerably by reducing it to the corresponding four-dimensional normal form. The local and global behavior of the equilibrium solutions is studied along with their stability properties.