Effect of damping on the postcritical behaviour of autonomous non-conservative systems

Abstract Postcritical behavior of non-linear autonomous non-conservative systems is studied with special attention to the effects produced by the damping forces non-uniformly distributed among the natural modes (or the degrees of freedom). The objective is to find out, to what degree the well-known destabilization effect of damping primarily observed in linear systems affects the postcritical behaviour of a system if non-linearities are taken into account. As a bench model, an initially planar elastic panel is considered subjected to the supersonic gas flow. However, the qualitative conclusions may be extrapolated upon a wide class of phenomena in non-linear autonomous non-conservative systems such as airfoils and panel flutter, instabilities induced by the jet thrust or jet pressure, etc. The main conclusion confirms the already formulated statement that, from the rigorous viewpoint, all these phenomena are to be treated taking into account the initial complete positive damping, however small. There are no “paradoxes” neither in the linear nor the non-linear statement of a problem under the condition that the concept of stability is used in the proper sense. On the other hand, a strong effect is demonstrated by the ratio of partial damping factors on the postcritical behaviour. In general, the ratio of these factors influences the postcritical behaviour to a higher degree that their absolute magnitudes, at least if the latter are small or moderate.