Resonant vibrations of nonlinear rotors

Abstract In this paper the primary resonance of a non-linear rotor system under the influence of monofrequency excitation is studied. The nonlinearity is caused by non-linear elastic material properties. The rotor system is a two-degree-freedom system described by a differential equation with complex deflection function. An averaging method for obtaining the amplitude and phase variation in time is developed. It is based on the method of slow varying amplitude and phase developed for one-degree-of-freedom system. The steady state solution is also considered. The method is applied for a rotor with small damping, nonlinearity and excitation function. The transient and steady state motion of the system are analyzed for various values of parameters. An experiment is carried out with shafts made of different materials. The analytical solutions are proved experimentally.