Stability and Sommerfeld Effect of a Vibrating System With Two Vibrators Driven Separately by Induction Motors

Abstract

The previous studies on the vibrating system with vibrators are mainly focused on existence and stability problems for the synchronous solutions of dynamical systems from the point of view of mathematics and mechanics, whereas the Sommerfeld effect and electromechanical coupling characteristics are less considered, especially less validated by experiment. In this article, we take a dynamical model with two rigid frames driven by two vibrators, for example, where vibrators are powered by induction motors separately. The synchronous and stable states of the system are studied first. Then, the Sommerfeld effect is further revealed to study what happened around the natural frequency of the system. Based on the average method, the criteria of synchronization of two vibrators and that of the stability are discussed in theory and numeric. Under the precondition of implementing synchronization, the Sommerfeld effect is given by establishing the electromechanical coupling model, in which the jump phenomena at the resonant point for the rotational velocities and the vibration amplitude of the system are explained. The synchronization and the coupling characteristics of the considered system are examined by the experiment. Finally, a type of vibrating centrifugal dehydrator has been successfully applied in engineering according to this article.