Snap-through and indirect reduced-order modelling

Snap-through is a nonlinear jump phenomenon that is increasingly being designed into engineering structures. The rich and varied dynamics of snap-through present a significant bottleneck in the design process as costly dynamic simulations are required to ensure predictable behaviour. The purpose of this research is to investigate the use of a recent projection-based, reduced-order modelling technique, namely, implicit condensation and expansion with inertial compensation, to reproduce the snap-through behaviours found in bistable finite element systems in analogous models with minimal degrees of freedom. In this work, the free response of a simple mass-spring oscillator is used to differentiate different types of snap-through. This provides a framework for discussing the dynamics of a family of buckled beams. The ability of the reduced-order models to faithfully reproduce these dynamics is investigated by testing the existence and stability of predicted periodic orbits. It is shown that the minimum projection basis required to capture snap-through accurately can be found through considering the minimum energy required for different types of snap-through. For bistable beams, this can be further simplified to just requiring an eigenvalue analysis at the most unstable equilibrium.