Decomposition of governing equations in the analysis of resonant response of a nonlinear and non-ideal vibrating system

The dynamic response of a nonlinear system with three degrees of freedom in resonance that is loaded, inter alia, with a non-ideal excitation is investigated. A direct current motor (DC motor) with an eccentrically mounted rotor serves as a non-ideal source of energy. The general coordinate corresponding to the rotor dynamics steadily increases as a result of rotational motion. The decomposition of the equations of motion proposed in the paper allows us to separate the vibration of rotor from its rotations. The presented approach can be used to separate the vibration from rotations in many other mechanical and mechatronic systems. The behaviour of the considered non-ideal system near two simultaneously occurring resonances is examined using the Krylov-Bogolyubov averaging method. The stability analysis of the resonant response is also carried out.