Periodic Solutions for a Weakly Dissipated Hybrid System

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Karami, Hamed | 2012

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Type of Document: M.Sc. Thesis
Language: Farsi
Document No: 43330 (02)
University: Sharif University of Technology
Department: Mathematical Sciences
Advisor(s): Hesaraki, Mahmoud
Abstract:
In this thesis, 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 acts on the body. In this hybrid system, there is a weak dissipation that characterizes. The main difficulty of the study is related to the weak dissipation which does not ensure a uniform decay rate of the energy. In this thesis, firstly, under the condition of 0 1 0 , we prove there exists a periodic solution. Then, we change the conditions on , Indeed, we restrict ourselves to solve the problem. In this case, under the condition of 0 2 0 , we show there is a periodic solution for rational periods. In the last part, by presenting numerical simulations, the theoretical results are confirmed
Keywords:
Periodic Solution ; Hybrid System ; Numerical Approximation

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