SLOW AND FAST INVARIANT-MANIFOLDS, AND NORMAL-MODES IN A 2 DEGREE-OF-FREEDOM STRUCTURAL DYNAMICAL SYSTEM WITH MULTIPLE EQUILIBRIUM STATES

Many problems in structural dynamics involve coupling between a stiff( high frequency) linear structure and a soft (low frequency) non-linear structure with multiple static equilibrium states. In this work, we a nalyze the slow and fast motions of a conservative structural system c onsisting of a non-linear oscillator with three equilibrium states cou pled to a stiff linear oscillator. We combine analysis (singular pertu rbations) with geometry (manifolds) and computation to show that the s ystem possesses invariant manifolds supporting either slow or fast mot ions. In particular, under appropriate conditions, a global slow invar iant manifold passes through the three static equilibrium states of th e system. The slow manifold is non-linear, orbitally stable, and it ca rries a continuum of in-phase periodic motions, including a homoclinic motion. We generalize the classical notion of vibrations-in-union to include systems with multiple equilibria, and thus identify the slow i nvariant manifold with a slow, non-linear normal mode of vibration. (C ) 1997 Published by Elsevier Science Ltd.