A Multiparameter, Numerical Stability Analysis of a Standing Cantilever Conveying Fluid
Abstract
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.
Additional Information
© 2002 Society for Industrial and Applied Mathematics Received by the editors January 10, 2002; accepted for publication (in revised form) by M. Dellnitz August 5, 2002; published electronically September 12, 2002. This research was supported by Sandia National Laboratories. Sandia is a multiprogram laboratory operated by Sandia Corporation, a Lockheed Martin Company, for the United States Department of Energy under contract DE-AC04-94AL85000. This work was supported by the US DOE through the MICS and ASCI programs. This work was performed by an employee of the U.S. Government or under U.S. Government contract. The U.S. Government retains a nonexclusive, royalty-free license to publish or reproduce the published form of this contribution, or allow others to do so, for U.S. Government purposes. Copyright is owned by SIAM to the extent not limited by these rights. We thank Jerry Marsden and Simon Tavener for their help with this paper. We also thank Danny Sorensen and Richard Lehoucq for making this research opportunity available to the authors.Files
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2006-01-13Created from EPrint's datestamp field
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2021-11-08Created from EPrint's last_modified field