Academy of Mathematics and Systems Science, CAS Colloquia & Seminars
Prof. Filippo Gazzola, Polytechnic University of Milan
Energy transfer between modes in a nonlinear nonlocal beam equation
Time & Venue:
2018.4.26 16:00-17:00 N613
We consider the nonlinear nonlocal beam evolution equation introduced by Woinowsky-Krieger and 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 and we give some possible applications to the stability of suspension bridges. The talk is based on joint works with Battisti-Berchio-Ferrero and Gasparetto.
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