Dynamic characteristics of a simply supported elastic beam with three induction motors

In the paper, the dynamic characteristics of a three induction motor driven system on a simply supported elastic beam are studied. Firstly, a dynamic coupling model of the whole system is established according to the Hamilton principle and discretized by applying the assumed mode method. Next, the synchronization solutions containing the average rotation speeds and phase differences of three motors and their stability are calculated and analyzed by using the average perturbation method. As a result, the synchronization and stability conditions of self-synchronization of three motors are established. Finally, the feasibility of the average perturbation method is verified by comparing the theoretical results with the simulation results. The results indicate that the elastic support has a large influence on the motion states of three motors. There is the self-synchronization phenomenon of three motors on the elastic beam. There appear the Sommerfeld effect (rotational speed capture and jump phenomena) near the resonance of the beam and the synchronous states of three motors will rapidly change before and after the resonance of beam. The large changes of the motion states of three motors cause the impacts of the responses of the elastic beam structure. Additionally, the effects of the structure parameters such as unbalance mass, power frequency, beam size and vibration modes on the dynamic characteristics of the system are discussed. This paper can provide some references for the design of multi-motor systems on the elastic foundations.