AN ASYMPTOTIC SOLUTION FOR WEAK NONLINEAR VIBRATIONS OF THE ROTOR

In the paper an asymptotic solution for nonlinear vibrations of the ro tor, which is under action of normal and tangential forces, is obtaine d. The procedure is based on the well-known methods of linear vibratio ns and the asymptotic method of Bogolubov-Mitropolski. The Bogolubov-M itropolski method is adopted for a differential equation with complex function and small nonlinearity. As a special case, dynamics of the ro tor under influence of hydrodynamic force is analyzed. The comparison between obtained results for the following force types: (a) weak and l inear, (b) strong linear and (c) weak nonlinear is given. The influenc e of nonlinearity is significant.