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Three-dimensional postbuckling and vibration of vertical half-loop under self-weight

Publication ,  Journal Article
Plaut, RH; Virgin, LN
Published in: International Journal of Solids and Structures
January 1, 2004

The stability and vibration characteristics of a flexible and inextensible half-loop are investigated. The loop is fixed at two base points, which are separated by a specified distance, and is only subjected to gravity loading. If the length of the loop is sufficiently small, the loop stands upright in a vertical plane. If the length is increased past a critical value, the planar equilibrium shape becomes unstable and the loop droops to one side (i.e., laterally). This out-of-plane displacement may occur smoothly (supercritical bifurcation), or the loop may suddenly jump to a severely-drooped configuration (subcritical bifurcation), depending on the constitutive law. Linearly-elastic and softening materials are considered. Prebuckled and postbuckled equilibrium states are determined numerically with the use of a shooting method. Droop caused by an applied torsional moment is also analyzed. Then small vibrations about the prebuckled (planar) states are studied. Three basic types of vibration modes occur: in-plane, out-of-plane (symmetric), and twist about a vertical axis through the center of the loop. Experiments on a fiber-optic rod and a curtain wire are carried out to qualitatively verify the numerical results for both types of constitutive laws. © 2004 Elsevier Ltd. All rights reserved.

Duke Scholars

Published In

International Journal of Solids and Structures

DOI

ISSN

0020-7683

Publication Date

January 1, 2004

Volume

41

Issue

18-19

Start / End Page

4975 / 4988

Related Subject Headings

  • Mechanical Engineering & Transports
  • 40 Engineering
  • 09 Engineering
 

Citation

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Plaut, R. H., & Virgin, L. N. (2004). Three-dimensional postbuckling and vibration of vertical half-loop under self-weight. International Journal of Solids and Structures, 41(18–19), 4975–4988. https://doi.org/10.1016/j.ijsolstr.2004.03.014
Plaut, R. H., and L. N. Virgin. “Three-dimensional postbuckling and vibration of vertical half-loop under self-weight.” International Journal of Solids and Structures 41, no. 18–19 (January 1, 2004): 4975–88. https://doi.org/10.1016/j.ijsolstr.2004.03.014.
Plaut RH, Virgin LN. Three-dimensional postbuckling and vibration of vertical half-loop under self-weight. International Journal of Solids and Structures. 2004 Jan 1;41(18–19):4975–88.
Plaut, R. H., and L. N. Virgin. “Three-dimensional postbuckling and vibration of vertical half-loop under self-weight.” International Journal of Solids and Structures, vol. 41, no. 18–19, Jan. 2004, pp. 4975–88. Scopus, doi:10.1016/j.ijsolstr.2004.03.014.
Plaut RH, Virgin LN. Three-dimensional postbuckling and vibration of vertical half-loop under self-weight. International Journal of Solids and Structures. 2004 Jan 1;41(18–19):4975–4988.
Journal cover image

Published In

International Journal of Solids and Structures

DOI

ISSN

0020-7683

Publication Date

January 1, 2004

Volume

41

Issue

18-19

Start / End Page

4975 / 4988

Related Subject Headings

  • Mechanical Engineering & Transports
  • 40 Engineering
  • 09 Engineering