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Adjacent Equilibria in Highly Flexible Upright Loop on Rigid Foundation

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Abstract

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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Authors and Affiliations

  1. Department Mechanical Engineering, Duke University, Durham, NC, 27708, USA

    L.N. Virgin

  2. Department Civil and Environmental, Virginia Technology, Blacksburg, VA, 24061, USA

    R.H. Plaut

  3. Department Mathematics, Cornell University, Ithaca, NY, 14850, USA

    E.V. Cartee

Authors
  1. L.N. Virgin
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  2. R.H. Plaut
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  3. E.V. Cartee
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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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  • DOI: https://doi.org/10.1007/s11340-015-0011-7

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