Synchronization of three non-identical coupled exciters with the same rotating directions in a far-resonant vibrating system

The aim of this paper, is to investigate the synchronization of three non-identical coupled exciters, rotating with the same directions, in a far-resonant vibrating system of plane motion. By deducing the dimensionless coupling equations of three exciters, the synchronization problem is reduced to an existence and stability problems of finding the zero solutions for the averaged differential equations. By introducing the dimensionless coupling torques and the characteristics of the corresponding limited functions, the synchronization criterion for three exciters is obtained. The stability criterion of synchronous states is derived, it satisfies automatically the criterions of the generalized Lyapunov and Routh–Hurwitz. The diversity feature of the vibrating system is discussed numerically. Both numerical and simulation results show that the structural parameters of the vibrating system can ensure the stability criterion of its synchronous operation.