Special self-balancing behavior in a self-synchronous system with both vibration utilization and vibration suppression functions

Abstract

In spite of the abundance of literature concerning the synchronization of vibrators, scant attention has been given to effectively solving the vibration dampening of the system through the lens of self-synchronization theory. This paper delves into the realms of synchronization, stability, and self-balancing behavior of a vibrating system with multiple synchronous states driven by four bias vibrators. Utilizing the average method and Hamilton's principle, the synchronization and stability criteria of the four vibrators are deduced. Grounded on the premise of ascertaining whether the theoretical transmission of dynamic loads from the system to the foundation amount to zero, the conditions for self-balancing are explicated. A numerical study unfolds, scrutinizing the effect of bias distance, bias angle, and rotation direction of the vibrator on synchronization states, stability, and self-balancing behavior across varying resonance regions. Some simulations are provided to verify the fidelity of the numerical analyses. Ultimately, the congruence among experimental findings, numerical analyses, and simulation outcomes underscores the soundness of the aforementioned conclusions and methodology employed. These findings indicate that the motion trajectory exhibited in the system in stable states hinges on the synchronization state of the system. Whether propelled by four co-rotating vibrators or counter-rotating counterparts, anchoring the system's operative point in the first sub-resonance region not only can it achieve self-balance effectively but also enables the perfect integration of vibration utilization and vibration suppression without additional vibration isolation strategies.