Self-synchronization characteristics of a class of nonlinear vibration system with asymmetrical hysteresis

Abstract

The self-synchronization characteristics of the two excited motors for the nonlinear vibration system with the asymmetrical hysteresis have been proposed in the exceptional circumstances of cutting off the power supply of one of the two excited motors. From the point of view of the hysteretic characteristics with the asymmetry, a class of nonlinear dynamic model of the self-synchronous vibrating system is presented for the analysis of the hysteretic characteristics of the soil, which is induced by the relation between the stress and the strain in the soil. The periodic solutions for the self-synchronous system with the asymmetrical hysteresis are investigated using nonlinear asymptotic method. The synchronization condition for the self-synchronous vibrating pile system with the asymmetrical hysteresis is theoretical analyzed using the rotor-rotation equations of the two excited motors. The synchronization stability condition also is theoretical analyzed using Jacobi matrix of the phase difference equation of the two excited motors. Using Matlab/Simlink, the synchronous operation of the two excited motors and the synchronous stability operation of the self-synchronous system with the asymmetrical hysteresis are analyzed through the selected parameters. Various synchronous phenomena are obtained through the difference rates of the two excited motors, including the different initial phase and the different initial angular velocity, and so on. Especially, when there is a certain difference in the two excited motors, the synchronous operation of the two excited motors and the synchronous stability operation of the self-synchronous vibrating system with the asymmetrical hysteresis can still be achieved after the power supply of one of the two excited motors has been disconnected. It has been shown that the research results can provide a theoretical basis for the research of the vibration synchronization theory.

Synchronization characteristics in a vibrator-pendulum coupling system with spatial motion

“…From the recently published works concerning the synchronization of vibrators (Chen et al, 2016; Cieplok and Wojcik, 2020; Lyan et al, 2021; Zhang 2020; Zhang et al, 2020, 2021; Zhao et al, 2010), the dynamic model become more closely related to the actual vibrating machines including vibrating conveyor, vibrating screen, and vibrating mill, and so on. Besides, although the control synchronization (Fang et al, 2021; Fradkov et al, 2021; Huang et al, 2021; Jia et al, 2019; Li et al, 2022), multiple-frequency synchronization (Li and Chen, 2019; Zou et al, 2021), and composite synchronization (Kong and Wen, 2018) have also been investigated, the self-synchronization theory was still the most typical synchronization strategy used in engineering.…”

Dynamics features of a resonant vibromachine with self-synchronizing inertial vibroexciters in the presence of vibration limiter

“…In this work, to ensure the stability of vibration modes and vibroexciter self-synchronization in the resonant frequency range, the possibility of using an additional non-linear element -elastic limiter mounted with a certain initial clearance to the machine working element is considered. Note, that the issues of vibroexciter self-synchronization in the systems with nonlinear elastic elements are considered, for example, in [15][16][17][18][19][20]. However, in the majority of mentioned above works, these issues are considered when oscillations are excited far from resonances.…”