Instance of hidden instability traps in intermittent transition of moving masses along a flexible beam

Abstract

The problem of an elastic beam under the periodic loading of successive moving masses is investigated as a pragmatic case for studying dynamic stability of linear time-varying systems. This model serves to highlight the odds of multi-solutions coexistence, a form of hidden instability which reveals dangerous as it may be precipitated by the slightest disturbance or variation in the model. Since no engineering model perfectly represents a physical system, such situations for which Floquet theory naively predicts stability are potentially inevitable. The harmonic balancing method is used in order to thoroughly explore the stability diagrams for detecting these instability gaps. Although this phenomenon has also been described in other physical systems, it has not been addressed for beam–moving mass systems. This result may find particular importance in applications involving self-induced vibrations of elastic structures and hence also appears of practical relevance.