SECONDARY BIFURCATIONS AND GLOBAL INSTABILITY OF AN AEROELASTIC NON-LINEAR SYSTEM IN THE DIVERGENCE DOMAIN

The behaviour of dissipative non-linear systems is studied in the instability region of the trivial (zero) solution. The study is motivated by the classical problem of stability of an initially flat elastic panel subjected to the combination of a supersonic gas flow and a quasistatic compression that may produce buckling. This allows one to investigate various types of instabilities such as primary flutter and divergence as well as secondary, tertiary, etc., instability phenomena. Three items are analyzed in detail in this paper: (1) the local (Lyapunov) stability of a buckled panel, with special attention paid to the influence of the damping distribution between particular modes; (2) the stable flutter-like vibrations of the buckled panel in the domains of its Lyapunov instability; (3) the stable flutter-like vibrations in the domain where the buckled mode of the panel is stable in Lyapunov sense. The case of damping distributed non-uniformly among the vibration modes is studies in detail. It is shown that a region of secondary flutter exist in the divergence domain. The secondary flutter responses are asymmetric with respect to the initial plane of the panel, and the structure of their attraction basins is rather complicated. Global flutter-like responses in the divergence?!domain are observed. The hysteretic properties of these responses are studied by numerical simulation.