Sukhorukov A. L.
This paper examines the onset mechanism of self-oscillations of mast hoisting gears (MHG) related to their non-linear hydrodynamic characteristics as well as the action of external periodic forces on this self-oscillating system caused by the vortex separation similar to the Karman vortex street type. MHG oscillation equations under determinated and random hydrodynamic actions are presented. Provision for numerical determination at initial design stages of unsteady forces acting on MHG is demonstrated and comparison with experimental data is provided. On the basis of averaging method relationships were obtained for the determination of amplitudes of steady-state oscillations under the action of external periodic forces on the self-oscillating system due to vortex separation. When the coefficient of side force due to attack angle is approximated by the third-order polynomial, this relationship will be a cubic equation relative to the squared steady-state amplitude but when the same is approximated by the fifth-order polynomial, this relationship will be a quintic equation. Stability conditions of steady-state oscillation modes were obtained for various options of approximation of MHG hydrodynamic characteristics. It is shown that in the autonomous system with a cubic approximation of the side force versus attack angle relationship, amplitudes increase infinitely, if instability appears. To eliminate this effect the fifth-order polynomial approximation of the side force versus at-tack angle relationship is required. With an actual MHG structure being taken as an example, MHG amplitude-frequency characteristics in the resonant area were plotted using the above-mentioned relationships.