The existence of periodic solution of the fourth ordinary nonlinear differential equation caused by flow-induced vibration (Q1333812)

In this paper the authors consider a system of two mutual coupled second order nonlinear differential equations, describing the vortex induced vibration problem. By using a method based on Schauder's fixed point principle, the existence of \(2 \pi\)-periodic solutions is studied. A further analysis about conditions ensuring the existence of periodic solutions of any period is also given. Finally, in the last part of the paper, a very brief numerical application is considered.