The Effect of a Rotational Spring on the Global Stability Aspects of the Classical von Mises Model under Step Loading

Abstract

Abstract: The present work deals with the global sta-bility aspects of a simple two-degrees-of-freedom au-tonomous initially imperfect damped model, under step(conservative) loading. The proposed system is an ex-tension of the classical limit point one firstly introducedby von Mises, with the addition of a linear rotationalspring. The effect of its properties (stiffness and damp-ing) are fully assessed and under certain combinationsofthe parameters involved a third possibility of postbuck-ling dynamic response is revealed. This is associatedwith a point attractor response on a stable prebucklingfixed point, although dynamic buckling has already oc-curred, a finding validating new relevant phenomena re-ported recently in the literature.keyword: Modeling, dynamic buckling, point attrac-tors, global stability1 IntroductionQuite often in engineering practice simple models with afew degrees of freedom (DOFs) are used either as a pow-erful tool for the simulation of actual continuous struc-tures under various types of loading or for the compre-hensive studyof numerous instabilityphenomena as wellas for the determination of the static and dynamic stabil-ity characteristics of all kinds of distinct critical points[Gioncu and Ivan (1984), Thompson and Hunt (1984),Sophianopoulos (1996)]. Especially one and two DOFautonomous undamped/damped systems are of particu-lar interest, since their nonlinear Lagrange equations ofmotion can be rather easily treated and the resulting lo-cal as well as global dynamics may be properly classified