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From:
“Dynamics of Snapping Beams and Jumping Poppers”, A. Pandey, D.E. Moulton, D. Vella, and D.P. Holmes,
(from Holmes’ website: http://www2.esm.vt.edu/~dpholmes/ EPL (Europhysical Letters), Vol. 105, 24001, 2014)
ABSTRACT: We consider the dynamic snapping instability of elastic beams and shells. We show that the stretchability of the arch plays a critical role in determining not only the post-buckling mode of deformation, but also the timescale of snapping, and the frequency of the arch's vibrations about its final equilibrium state. We show that the growth rate of the snap-through instability, and its subsequent ringing frequency, can both be interpreted physically as the result of a sound wave in the material propagating over a distance comparable to the radius of curvature of the arch. Finally, we extend our analysis of the ringing frequency of indented arches to understand the 'pop' heard when everted shell structures snap-through to their stable state. Remarkably, we find that not only are the scaling laws for the ringing frequencies in these two scenarios identical, but also the respective prefactors are numerically close; this allows us to develop a master curve for the frequency of ringing in snapping beams and shells.
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