Abstract Rotating the clamped ends of a buckled arch induces a snap-through instability. Predicting the limit point and determining the equilibria at the start and end of the snap are routine computations in the quasistatic setting. The instability itself, however, is dynamic and quite violently so. We propose an energy-preserving nonlinear single-degree-of-freedom model for this dynamic phenomenon in the case of a symmetrically deforming arch idealized as an elastica. The model hinges on a surprising observation relating elastica profiles during the free dynamic snap to a specific sequence of geometrically constrained elastic energy-minimizing configurations. We corroborate this phenomenological observation over a significant range of arch depths through experiments and finite element simulations. The resulting model does not rely on modal expansions, explicit slowness assumptions, or linearization of the arch’s kinematics. Instead, the model is effective because its solutions approximate the action integral well. The model provides distinctive computational benefits that can be leveraged in applications. Equally significantly, it reveals interesting observations and poses new questions on the dynamic snap-through phenomenon.
Bhattacharyya et al. (Fri,) studied this question.