Vibrating beams are like dartboards

The upper plot in this video shows the “basins of attraction” for a bistable compressed beam as you bend its support angle from flat (0 degrees) to about 18 degrees. This beam is about 4% too large to fit in its assigned area, so the center pops up or down. From our earlier work we know that beams prefer to pop in the same direction as the supporting substrate, and we have the potential energy function that describes this behavior more quantitatively. It’s the lower plot.

When a beam is dropped into “phase space” (a plot of velocity vs position of the beam center) it will coast to one of the two minimal energy positions. The red spiral shape is the region of phase space corresponding to the higher energy state, and it shrinks as the substrate bends. When the high-energy basin of attraction goes to zero area, the beam snaps to the low-energy state if it wasn’t there already. We are looking at the area of the spiral as a way to measure the curvature of the underlying substrate through the statistics of repeated experiments. This is a “dartboard” style experiment; a smaller target should receive fewer hits than a larger one.

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