On the experimental identification of unstable static equilibria.


Journal Article

This paper shows how the presence of unstable equilibrium configurations of elastic continua is reflected in the behaviour of transients induced by large perturbations. A beam that is axially loaded beyond its critical state typically exhibits two buckled stable equilibrium configurations, separated by one or more unstable equilibria. If the beam is then loaded laterally (effectively like a shallow arch) it may snap-through between these states, including the case in which the loading is applied dynamically and of short duration, i.e. an impact. Such impacts, if applied at random locations and of random strength, will generate an ensemble of transient trajectories that explore the phase space. Given sufficient variety, some of these trajectories will possess initial energy that is close to (just less than or just greater than) the energy required to cause snap-through and will have a tendency to slowdown as they pass close to an unstable configuration: a saddle point in a potential energy surface, for example. Although this close-encounter is relatively straightforward in a system characterized by a single degree of freedom, it is more challenging to identify in a higher order or continuous system, especially in a (necessarily) noisy experimental system. This paper will show how the identification of unstable equilibrium configurations can be achieved using transient dynamics.

Full Text

Duke Authors

Cited Authors

  • Wiebe, R; Virgin, LN

Published Date

  • June 2016

Published In

Volume / Issue

  • 472 / 2190

Start / End Page

  • 20160172 -

PubMed ID

  • 27436986

Pubmed Central ID

  • 27436986

Electronic International Standard Serial Number (EISSN)

  • 1471-2946

International Standard Serial Number (ISSN)

  • 1364-5021

Digital Object Identifier (DOI)

  • 10.1098/rspa.2016.0172


  • eng