Periodic solutions for a weakly dissipated hybrid system

Abstract : We consider the motion of a stretched string coupled with a rigid body at one end and we study the existence of periodic solution when a periodic force $f$ acts on the body. The main difficulty of the study is related to the weak dissipation that characterizes this hybrid system, which does not ensure a uniform decay rate of the energy. Under additional regularity conditions on $f$, we use a perturbation argument in order to prove the existence of a periodic solution. In the last part of the paper we present some numerical simulations based on the theoretical results.
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Submitted on : Wednesday, February 23, 2011 - 1:36:05 PM
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Nicolae Cindea, Sorin Micu, Ademir Pazoto. Periodic solutions for a weakly dissipated hybrid system. Journal of Mathematical Analysis and Applications, Elsevier, 2012, 385 (1), pp.399-413. ⟨10.1016/j.jmaa.2011.06.049⟩. ⟨hal-00568704⟩

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