A multiparameter, numerical stability analysis of a standing cantilever conveying fluid

Nawaf M. Bou-Rabee, Louis A. Romero, Andrew G. Salinger

Research output: Contribution to journalArticlepeer-review

14 Scopus citations


In this paper, we numerically examine the stability of a standing cantilever conveying fluid in a multiparameter space. Based on nonlinear beam theory, our mathematical model turns out to be replete with exciting behavior, some of which was totally unexpected and novel, and some of which confirm our intuition as well as the work of others. The numerical bifurcation results obtained from applying the Library of Continuation Algorithms (LOCA) reveal a plethora of one, two, and higher codimension bifurcations. For a vertical or standing cantilever beam, bifurcations to buckled solutions (via symmetry breaking) and oscillating solutions are detected as a function of gravity and the fluid-structure interaction. The unfolding of these results as a function of the orientation of the beam compared to gravity is also revealed.

Original languageEnglish (US)
Pages (from-to)190-214
Number of pages25
JournalSIAM Journal on Applied Dynamical Systems
Issue number2
StatePublished - 2002
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Analysis
  • Modeling and Simulation


  • Aero-elasticity
  • Beam flutter
  • Buckling
  • Numerical bifurcation analysis


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