We consider the nonlinear nonlocal beam evolution equation introduced by Woinowsky-Krieger. We study the existence and behavior of periodic solutions: these are called nonlinear modes. Some solutions only have two active modes and we investigate whether there is an energy transfer between them. The answer depends on the geometry of the energy function which, in turn, depends on the amount of compression compared to the spatial frequencies of the involved modes. Our results are complemented with numerical experiments; overall, they give a complete picture of the instabilities that may occur in the beam. We expect these results to hold also in more complicated dynamical systems.

Energy transfer between modes in a nonlinear beam equation / Battisti, Ubertino; Berchio, Elvise; Ferrero, Alberto; Gazzola, Filippo. - In: JOURNAL DE MATHÉMATIQUES PURES ET APPLIQUÉES. - ISSN 0021-7824. - STAMPA. - 108:6(2017), pp. 885-917. [10.1016/j.matpur.2017.05.010]

Energy transfer between modes in a nonlinear beam equation

Battisti, Ubertino;Berchio, Elvise;
2017

Abstract

We consider the nonlinear nonlocal beam evolution equation introduced by Woinowsky-Krieger. We study the existence and behavior of periodic solutions: these are called nonlinear modes. Some solutions only have two active modes and we investigate whether there is an energy transfer between them. The answer depends on the geometry of the energy function which, in turn, depends on the amount of compression compared to the spatial frequencies of the involved modes. Our results are complemented with numerical experiments; overall, they give a complete picture of the instabilities that may occur in the beam. We expect these results to hold also in more complicated dynamical systems.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11583/2698384
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