Research on the Synchronization Theory of the Vibration System of Four Circularly Symmetrical Vibrator

Abstract

This dissertation aims to study the synchronization properties of a vibrating system consisting of four oscillators, with three located equidistantly on the same circular trajectory and the fourth exciter situated at the center. This study is divided into three stages. Firstly, by utilizing the Lagrange equation, the dynamic model is developed for the research object, and the differential equation is derived when the body runs stable. Secondly, the differential equation obtained in the previous step is solved using Hamiltonian theory, and the solution of the equation is obtained. The necessary conditions required for the vibration system to achieve stable synchronization are also deduced. Finally, the accuracy of the synchronization characteristics is verified by using simulation techniques. The findings indicate that with specific prerequisites met, four motors can achieve synchronicity while the vibration system maintains stability and elliptical motion of the system centroid. These research outcomes establish a theoretical basis for the development of similar vibrational equipment.