Global Nonlinear Dynamics: Challenges in the Analysis and Safety of Deterministic or Stochastic Systems

The chapter provides a state-of-the-art, qualitative and application-oriented overview of topics in the global nonlinear dynamics of mechanical systems and structures. Models, methods, phenomena, practical examples are addressed with the aim of highlighting the enormous potential of global analysis as regards in-depth description and understanding of systems’ nonlinear dynamics, and a reliable assessment of their actual load carrying capacity. Challenges and prospects are outlined, as mostly occurring when moving from the low-order, deterministic, models mostly dealt with so far within the underlying scientific community, to the multi-dimensional, non-deterministic, systems and structures encountered in engineering and characterizing the real world. General items addressed include fundamentals of global dynamics, use of dynamical integrity as a reliable and effective computational-geometrical tool for investigating and controlling response robustness, computational challenges for multi-dof systems, need for refined reduced order modeling, influence of parametric uncertainty and noise.