Point attractors and dynamic buckling of autonomous systems under step loading

In this study the dynamic response of autonomous mainly dissipative multi D .O.F. systems under step loading is re-examined. Based on the geometrical p oint of view of the theory of non-linear dynamical systems and the rapidly developing theory of attractors, the investigation focuses on limit point l ike systems, with snapping as their salient feature. It is found that dynam ic buckling (through a saddle or its neighborhood), although leading to a l arge amplitude motion, may be associated with a point attractor response on the prebuckling fixed point, depending on the amount of damping considered in close conjunction with the motion channel geometry and the total potent ial characteristics of all (stable and complementary) equilibria. For such systems, only a straightforward fully non-linear dynamic analysis can provi de valid information on the global dynamic stability, since the shape of th e total potential hypersurface may become very complicated, rendering energ y aspects practically not applicable. A 2-D.O.F. model, simulating an asymm etric suspended roof is comprehensively analyzed to capture the above findi ngs, and a parametric investigation is carried out, revealing a variety of new dynamic response types and leading to a more accurate insight of the st ability of motion in the large. (C) 1999 Elsevier Science Ltd. All rights r eserved.