Summary
Differently from linear dynamical systems, the analysis of global dynamics is crucial for ensuring the safety of nonlinear systems due to potential phenomena of multi-stability. Trajectories of transient motions in the phase space contain significant information about global dynamics. However, extracting this information is challenging, leading to its frequent oversight. In this study, we demonstrate how transient trajectories can provide valuable information about nearby regions in the parameter and phase space. Specifically, an irregular decay rate may indicate the presence of a fold bifurcation. By measuring this decay rate, we can extract information that can be used to predict the occurrence of fold bifurcations. It is important to note that fold bifurcations are practically significant as they often delineate regions of multi-stability. The proposed method is initially validated numerically on a mass-on-moving-belt model, a van der Pol-Duffing oscillator with an attached tuned mass damper, and a pitch-and-plunge airfoil undergoing flutter instability. Subsequently, the method is experimentally validated on a towed wheel experiencing shimmy vibrations.
