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Adjacent Equilibria in Highly Flexible Upright Loop on Rigid Foundation


For very slender structural components, self-weight may compete with elastic flexural stiffness in determining equilibrium configurations. In cases where the inherent elastic stiffness is low (relative to self-weight) we observe a variety of types of highly nonlinear behavior in the equilibrium shapes, together with changes in the natural frequencies of small oscillations about these equilibrium configurations. This technical note describes a specific phenomenon observed in experiments on very slender polycarbonate loops. In addition to profound changes in equilibrium shapes as a function of weight-to-stiffness ratio, under some circumstances it is possible to have two adjacent, co-existing equilibrium configurations. This robust, highly nonlinear snap-through behavior is demonstrated by perturbing from one shape to the other.

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Correspondence to L.N. Virgin.

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Virgin, L., Plaut, R. & Cartee, E. Adjacent Equilibria in Highly Flexible Upright Loop on Rigid Foundation. Exp Mech 55, 1191–1197 (2015). https://doi.org/10.1007/s11340-015-0011-7

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  • Weight effects
  • Adjacent equilibria
  • Loop
  • Vibration