Stability of stationary regimes in nonlinear systems: analytical and numerical approaches

Abstract

A stability of stationary regimes in the form of nonlinear normal modes (NNMs) with rectilinear or nearrectilinear trajectories is analysed by using the Ince algebraization when a variable associated with the vibration mode is chosen as the new independent argument. In this case the variational equations are transformed to equations with singular points. Other approach is realized for NNMs with regular or chaotic behavior in time. Namely, a test which is a consequence of the well-known Lyapunov criterion of stability is used. Both approaches are also used in analysis of stability of other stationary regimes, namely, standing or traveling nonlinear waves.