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

The behaviour of dissipative non-linear systems is studied in the inst ability region of the trivial (zero) solution. The study is motivated by the classical problem of stability of an initially flat elastic pan el subjected to the combination of a supersonic gas flow and a quasist atic compression that may produce buckling. This allows one to investi gate various types of instabilities such as primary flutter and diverg ence as well as secondary, tertiary, etc., instability phenomena. Thre e items are analyzed in detail in this paper: (1) the local (Lyapunov) stability of a buckled panel, with special attention paid to the infl uence of the damping distribution between particular modes; (2) the st able flutter-like vibrations of the buckled panel in the domains of it s 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 mo des is studies in detail. It is shown that a region of secondary flutt er exist in the divergence domain. The secondary flutter responses are asymmetric with respect to the initial plane of the panel, and the st ructure of their attraction basins is rather complicated. Global flutt er-like responses in the divergence domain are observed. The hystereti c properties of these responses are studied by numerical simulation. ( C) 1996 Academic Press Limited