Periodic and torus motions of a two-degree-of-freedom dry friction vibration system

Frontiers in Physics

Physics

Yong Guo¹ 

[1] null;

关键词: dry friction;    normal form;    bifurcation;    equilibrium;    periodic motion;    torus motion;   

DOI  :  10.3389/fphy.2023.1188002

 received in 2023-03-16, accepted in 2023-04-11,  发布年份 2023

来源: Frontiers

【 摘 要 】

Vibration induced by dry friction is ubiquitous in various engineering fields. To explore the vibration characteristics for further studies and/or controls, it is of great theoretical and practical significances to investigate the non-linear dynamic behaviors of the friction systems. This study considers the slight vibration of a two-degree-of-freedom non-linear dry friction excitation system. The differential equations of system motion are established according to Newton’s law of motion. Moreover, the system’s non-linear dynamic is studied when the block velocity is always less than the friction surface velocity. The results indicate that the linearized matrix of the vibration system has a pair of purely imaginary eigenvalues for some critical values of the relevant parameters. The Poincaré-Birkhoff normal forms are utilized to simplify the motion equation under the non-resonant assumption to obtain a simplified equation with only the resonant terms. Furthermore, the truncated part of the simplified equation is analyzed in the case of only linear terms degeneration. Finally, numerical simulations reflect some qualitative conclusions about the system’s local dynamic properties, including equilibrium point, periodic motion, torus motion, and their stability.

【 授权许可】

Unknown   
Copyright © 2023 Guo.