Wed June 5th 2024
16:00 – 17:00
Seminar Symmetry or no symmetry? A surprise in snap-through instability
Andrea Giudici


A snap-through instability occurs when a bistable structure loses one of its stable states and moves rapidly to the remaining one. For example, a symmetric buckled arch with symmetric clamps can snap between an inverted and a natural state as its ends are moved apart. A standard linear stability analysis suggests that the arch always becomes unstable to asymmetric modes. However, our experiments show that this is not always the case: symmetric transitions are also observed. This is surprising! Using experiments, numerics, and a simple toy model, we show that the symmetry of the transition depends on the rate at which the ends are moved apart, with only sufficiently fast loading leading to symmetric snap-through. Our toy model reveals that this behavior is caused by a region of the system's state space in which any initial asymmetry is amplified. The system may not traverse this region at all when loaded fast, thus remaining symmetric, but will traverse it for some interval of time when loaded slowly, causing a transient amplification of asymmetry. Our toy model also suggests that the observed behavior is not unique to snapping arches, but is a general phenomenon that can be observed in dynamic systems where both a saddle-node and a pitchfork bifurcation occur in close proximity.
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