Synchronization and Stability of a Nonlinear Vibrating Mechanical System Characterized by Asymmetrical Piecewise Linearity

Abstract

Abstract In previous studies about the synchronization of vibrators, the restoring forces of springs are mainly treated as linear directly, whereas the nonlinear features are rarely considered in vibrating systems. To make up this drawback, a dynamical model of a nonlinear vibrating mechanical system with double rigid frames (RFs), driven by two vibrators, is proposed to explore the synchronization and stability of the system. In this paper, the nonlinearity is reflected in nonlinear restoring forces of springs characterized by asymmetrical piecewise linear, where the nonlinear stiffness of springs is linearized equivalently using the asymptotic method. Based on the average method and Hamilton’s principle, the theory conditions to achieve synchronization and stability of two vibrators are deduced. After the theory analyses, some numerical qualitative analyses are given to reveal the coupling dynamical characteristics of the system and the relative motion properties between two RFs. Besides, some experiments are carried out to examine the validity of the theoretical results and the correctness of the numerical analyses results. Based on the comparisons of the theory, numeric and experiment, the ideal working regions of the system are suggested. Based on the present work, some new types of vibrating equipment, such as vibrating discharging centrifugal dehydrators/conveyers/screens, can be designed.

Keywords

• Synchronization
• Stability
• Nonlinear vibrating system
• Vibrators
• Asymmetrical piecewise linearity