Determination of global stability of steady-state solutions of a beam system with discontinuous support using manifolds

This paper deals with the global stability of the long term dynamics of nonlinear mechanical systems under periodic excitation. Generally, the boundaries of the basins of attraction are formed by the stable manifolds of unstable periodic solutions. These stable manifolds are the set of initial conditions of trajectories which approach an unstable periodic saddle solution. Because these are the only trajectories which do not approach an attractor, in general the stable manifolds are the boundaries of the basins of attraction. In this paper manifolds are calculated of a beam system supported by a one-sided spring in order to identify the global stability of the coexisting attractors. The numerical results are compared with experimental results.