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Global and bifurcation analysis of a structure with cyclic symmetry

Abstract : Introducing non-linearities into models contributes towards a better reality description but leads to systems having multiple solutions. It is then legitimate to look for all the solutions of such systems, that is to have a global analysis approach. However no effective method can be found in literature for systems described by more than two or three degrees of freedom. We propose in this paper a way to find all T-periodic solutions--where T is known--of a non-linear dynamical system. This method is compared to three other approaches and is shown to be the most efficient on a Duffing oscillator. As a more complex example, a rotor model including a squeeze-film damper is studied and a second branch of solutions is exhibited.
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Submitted on : Wednesday, September 14, 2011 - 4:47:36 PM
Last modification on : Friday, August 27, 2021 - 9:38:02 AM
Long-term archiving on: : Thursday, December 15, 2011 - 2:26:27 AM

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Emmanuelle Sarrouy, Aurélien Grolet, Fabrice Thouverez. Global and bifurcation analysis of a structure with cyclic symmetry. International Journal of Non-Linear Mechanics, Elsevier, 2011, 46 (5), pp.727--737. ⟨10.1016/j.ijnonlinmec.2011.02.005⟩. ⟨hal-00623630⟩

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