Dynamics of a nonlinear electromagnetic system

An experiment with a test rig consisting of a symmetric rotor suspended by a spring device and excited by a series of nonlinear electromagnetic forces has been performed by Chang and Tung [Sound & Vib. 214 (1998) 853], to investigate the effects of an electromagnet processing highly nonlinear characteristics on general mechanical systems. A nonlinear mathematical model has been obtained by applying a modified conventional identification technique based on the principle of harmonic balance. In this study, analytical work is carried out on this identified nonlinear model by applying the first-harmonic approximation solution and the Floquet theory. The resulting criteria for bifurcations can be used to evaluate the operational range of a system employing such a nonlinear actuator. We also employ the method of Lyapunov exponents to show the occurrence of chaotic motion and to verify the above analyses. A comparison of the analytical results with those of the experimemt shows that the identified nonlinear model obtained from the experiment can predict and characterize the dynamics of a real electromagnetic system.