Load carrying capacity of systems within a global safety perspective. Part II. Attractor/basin integrity under dynamic excitations

Abstract

The effects of the dynamic excitation on the load carrying capacity of mechanical systems are investigated with reference to the archetypal model addressed in Part I, which permits to highlight the main ideas without spurious mechanical complexities. First, the effects of the excitation on periodic solutions are analyzed, focusing on bifurcations entailing their disappearance and playing the role of Koiter critical thresholds. Then, attractor robustness (i.e., large magnitude of the safe basin) is shown to be necessary but not sufficient to have global safety under dynamic excitation. In fact, the excitation strongly modifies the topology of the safe basins, and a dynamical integrity perspective accounting for the magnitude of the solely compact part of the safe basin must be considered. By means of extensive numerical simulations, robustness/erosion profiles of dynamic solutions/basins for varying axial load and dynamic amplitude are built, respectively. These curves permit to appreciate the practical reduction of system load carrying capacity and, upon choosing the value of residual integrity admissible for engineering design, the Thompson practical stability. Dwelling on the effects of the interaction between axial load and lateral dynamic excitation, this paper supports and, indeed, extends the conclusions of the companion one, highlighting the fundamental role played by global dynamics as regards a reliable estimation of the actual load carrying capacity of mechanical systems.