INFLUENCE OF INITIAL CONDITIONS ON THE POSTCRITICAL BEHAVIOR OF A NONLINEAR AEROELASTIC SYSTEM

The behavior of a nonlinear, non-Hamiltonian system in the postcritica l (Butter) domain is studied with special attention to the influence o f initial conditions on the properties of attractors situated at a cer tain point of the control parameter space. As a prototype system, an e lastic panel is considered that is subjected to a combination of super sonic gas Bow and quasistatic loading in the middle surface. A two nat ural modes approximation, resulting in a four-dimensional phase space and several control parameters is considered in detail. For two fixed points in the control parameter space, several plane sections of the f our-dimensional space of initial conditions are presented and the asym ptotic behavior of the final stationary responses are identified. Amon gst the latter there are stable periodic orbits, both symmetric and as ymmetric with respect to the origin, as well as chaotic attractors. Th e mosaic structure of the attraction basins is observed. In particular , it is shown that even for neighboring initial conditions can result in distinctly different nonstationary responses asymptotically approac h quite different types of attractors. A number of closely neighboring periodic attractors are observed, separated by Hopf bifurcations. Per iodic attractors also are observed under special initial conditions in the domains where chaotic behavior is usually expected.