Nonlinear dynamics and Gaussian white noise excitation effects in a model of flow-induced oscillations of circular cylinder

In this paper, we investigated the dynamical behavior of the circular cylinder subjected to a uniform cross flow. The mathematical model of the scheme for non-turbulent flow were derived. The method of multiple time scale is used to determine the steady states responses. Amplitude equations as well as external force-response and frequency-response curves are obtained. We show that lock-in phenomena appear in the structure. The dynamic of the system is presented, plotting bifurcation diagram, power spectral density and phase portrait. These results are confirmed by using 0-1 test. Then, we investigated the behavior of the system under Gaussian white noise using probabilistic approach. A stochastic averaging method is applied in this system in the aim to build the Ito Stochastic differential equations. From these equations, the Fokker-Planck Equations (FPE) of the system is constructed whose the solution at the stationary state is a probability density. We find that under the influence of this king of noise, the dynamic of the nonlinear system can be well characterized through the concept of stochastic bifurcation, worked by a qualitative change of the stationary probability distribution. Whose the solution at the stationary state is probability density. The analytical results agree very well with numerical simulation.