Vv. Bolotin et al., SECONDARY BIFURCATIONS AND GLOBAL INSTABILITY OF AN AEROELASTIC NONLINEAR-SYSTEM IN THE DIVERGENCE DOMAIN, Journal of sound and vibration, 191(3), 1996, pp. 431-451
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