Periodic solutions for a weakly dissipated hybrid system

Nicolae Cindea (1) , Sorin Micu (2) , Ademir Pazoto (3)

1 MACS - Modeling, analysis and control in computational structural dynamics
2 UCV - Department of Mathematics
3 IM / UFRJ - Instituto de Matemática da Universidade Federal do Rio de Janeiro

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.

Mots clés: Periodic solutions; Non homogeneous hyperbolic system

Domaines: Optimisation et contrôle [math.OC]

Nicolae Cindea, Sorin Micu, Ademir Pazoto. Periodic solutions for a weakly dissipated hybrid system. Journal of Mathematical Analysis and Applications, 2012, 385 (1), pp.399-413. ⟨10.1016/j.jmaa.2011.06.049⟩. ⟨hal-00568704⟩