Synchronization and stability of a vibrating system with two rigid frames driven by two groups of coaxial rotating exciters

Abstract

This article explores the synchronization, stability and motion characteristics of the generalized dynamical model with two rigid frames (RFs) driven by two groups (even number) of coaxial rotating exciters. In light of this system’s generalized coordinates, we use Lagrange’s equations to derive the generalized differential equation of motion. The responses of absolute and relative motion of the generalized system are obtained using the transfer function method. The synchronization and stability criteria of multiple exciters are derived using the average method and Hamilton’s theory, respectively. Taking a dynamical model driven by two pairs of exciters as an example, the localized studies of generalized results are carried out. The stable synchronous solutions for phase differences and excitation frequency, the stability ability coefficient curves and the response curves are graphically presented considering the effect of two crucial dimensionless parameters on the stable synchronous states. The simulation results of the specific system are obtained using the fourth-order Runge-Kutta algorithms and compared with the numerical qualitative analysis results to reveal the high consistency between them and clarify the used methods’ effectiveness. The strength of this work stems from its use in the field of high power and large scale self-synchronization vibrating machines.

Keywords

• Synchronization
• Stability
• Exciters
• Generalized dynamical model
• Resonance regions