Abstract
The in-plane vibrations of regular polygonal rings composed of rigid segments joined by torsional springs are studied for the first time. The nonlinear dynamical difference equations are formulated and solved by perturbation about the equilibrium state. As the number of segments increase, the frequencies, if aptly normalized, converge to the classical vibration frequencies of a continuous elastic ring. The vibration mode shapes are illustrated. The tiling of many identical polygons is discussed. Possible applications include the vibrations of space structures and graphene sheets.
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