Bifurcations of equilibria at bimodal branching points in potential systems are investigated. General formulas describing postbuckling paths and conditions for their stability are derived in terms of the original potential energy. Formulas describing unfolding of bimodal branching points due to a change of system parameters are given. A full list of possible cases for postbuckling paths, their stability, and unfolding depending on three system coefficients is presented. In order to calculate these coefficients, one needs the derivatives of the potential energy and eigenvectors of the linearized problem taken at the bifurcation point. The presented theory is illustrated by a mechanical example on stability and postbuckling behavior of an articulated elastic column having four degrees of freedom and depending on three problem parameters (stiffness coefficients at the hinges). For some of the bimodal critical points, numerical results are obtained illustrating influence of parameters on postbuckling paths, their stability, and unfolding. A surprising phenomenon that a symmetric bimodal column loaded by an axial force can buckle with a stable asymmetric mode is recognized. An example with a constrained sum of the stiffnesses of the articulated column shows that the maximum critical load (optimal design) is attained at the bimodal point.
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e-mail: mailybaev@imec.msu.ru
e-mail: seyran@imec.msu.ru
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March 2008
Research Papers
Bifurcations of Equilibria in Potential Systems at Bimodal Critical Points
Alexei A. Mailybaev,
Alexei A. Mailybaev
Institute of Mechanics,
e-mail: mailybaev@imec.msu.ru
Moscow State Lomonosov University
, Michurinsky prospect 1, 119192 Moscow, Russia
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Alexander P. Seyranian
Alexander P. Seyranian
Institute of Mechanics,
e-mail: seyran@imec.msu.ru
Moscow State Lomonosov University
, Michurinsky prospect 1, 119192 Moscow, Russia
Search for other works by this author on:
Alexei A. Mailybaev
Institute of Mechanics,
Moscow State Lomonosov University
, Michurinsky prospect 1, 119192 Moscow, Russiae-mail: mailybaev@imec.msu.ru
Alexander P. Seyranian
Institute of Mechanics,
Moscow State Lomonosov University
, Michurinsky prospect 1, 119192 Moscow, Russiae-mail: seyran@imec.msu.ru
J. Appl. Mech. Mar 2008, 75(2): 021016 (11 pages)
Published Online: February 26, 2008
Article history
Received:
December 25, 2006
Revised:
August 20, 2007
Published:
February 26, 2008
Citation
Mailybaev, A. A., and Seyranian, A. P. (February 26, 2008). "Bifurcations of Equilibria in Potential Systems at Bimodal Critical Points." ASME. J. Appl. Mech. March 2008; 75(2): 021016. https://doi.org/10.1115/1.2793136
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