Stability and coupling dynamic characteristics of a vibrating system with double rigid body driven by two motors considering energy balance

Abstract

The present work mainly focuses the coupling dynamic characteristics and energy transfer relation of the system of double rigid bodies (RBs) driven by two motors, and then explores the ideal working state of the system. The motion differential equations of the system are established by Lagrange equation. Then the energy balance method and Hamilton's principle are employed to deduce the synchronization condition and stability criterion of the system. Then the numeric analyses are introduced to investigate the influence of excitation frequency on the amplitude, stable phase difference and energy of the system. Besides, the accuracy of theoretical research is demonstrated by the computer simulation and experiment. The research results indicate that, the anti-resonance state is the ideal working state of the proposed system; the elastic potential energy between two RBs is suddenly increased owing to the decrement of absolute value of stable phase difference of the system around anti-resonance state, which is used to magnify the relative motion between two RBs and weaken the vibration of the RB2. The results can help us understand the relationship between coupling dynamic characteristics and synchronous behaviors of the system with double RBs from the view of energy transfer.