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Global search of non-linear systems periodic solutions: A rotordynamics application

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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https://hal.archives-ouvertes.fr/hal-00623621
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Submitted on : Wednesday, September 14, 2011 - 4:39:35 PM
Last modification on : Tuesday, June 14, 2022 - 11:31:57 AM
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Emmanuelle Sarrouy, Fabrice Thouverez. Global search of non-linear systems periodic solutions: A rotordynamics application. Mechanical Systems and Signal Processing, Elsevier, 2010, 24 (6), pp.1799-1813. ⟨10.1016/j.ymssp.2010.02.001⟩. ⟨hal-00623621⟩

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