Influence of transient escape and added load noise on the dynamic integrity of multistable systems

Abstract

Concepts and tools of global dynamics play a meaningful role in enhancing the engineering design and safety of multistable structural systems in a dynamic environment. Basins of attraction topology can vary meaningfully as a function of system parameters, and the basin boundaries can be smooth or fractal. Fractal boundaries have important practical consequences as they lead to uncertainty with respect to the outcome of a given initial condition, thus reducing the system safety, which can be quantified through different dynamic integrity measures and their variation with a control parameter. In the present paper two key issues influencing the integrity measures and basins’ erosion profiles are addressed: transient escape and added random noise. Transient escape is a significant issue in many structural systems since it may lead to unwanted stresses and strains or exceed some safe design requirements in terms of maximum displacements and velocities. In turn, the random noise may increase the uncertainty of the systems, thus decreasing their practical safety and escape load. As a case study, the bistable von Mises truss is considered and the effects of transient escape and added random noise on the global dynamics of the harmonically excited truss are investigated in detail, clarifying their influence on the system safety as evaluated with different integrity measures.