Necessary and sufficient conditions of existence of periodical motions in the model of a hinge mechanism in a flow. (2017) - Klimina, Liubov; Lokshin, Boris; Selyutskiy, Yury; Garziera, Rinaldo
Abstract: Mathematical model of a one-degree-of-freedom hinge mechanism (wind power unit) interacting with a wind flow is introduced. Equations of motion of this device represent a second order system of autonomous ordinary differential equations. The common factor at terms corresponding to aerodynamic forces is assumed to be a small parameter. Thus, the system is close to a Hamiltonian one. Both Hamiltonian and non-conservative parts of the system are essentially nonlinear. The Poincare-Pontryagin approach is used in order to obtain necessary and sufficient conditions of existence and orbital stability of periodic trajectories of the system. Attracting periodic trajectories correspond to operation modes of the wind power unit. Estimation of the trapped power for these regimes is obtained, and bifurcation diagrams of this power are constructed depending on parameters of the system.