The Open Mechanical Engineering Journal

2014, 8 : 314-319
Published online 2014 September 16. DOI: 10.2174/1874155X01408010314
Publisher ID: TOMEJ-8-314

Grazing and Hopf Bifurcations of a Periodic Forced System with Soft Impacts

Zhu Xifeng and Gao Quanfu
School of Mechatronic Engineering, Lanzhou Jiaotong University, Box no.406, 88 West Anning Road, Lanzhou, Gansu Province, Postcard: 730070, P.R. China.

ABSTRACT

Based on the research of a periodic forced system with soft impacts, the piecewise properties of the soft-impacts system, such as asymmetric motion and singularity, were analyzed by using the Poincaré map and Runge-Kutta numerical simulation method. The routes from periodic motions to chaos, via Hopf bifurcation and grazing bifurcation, were investigated thoroughly. In the case of large constraint stiffness, the Hopf bifurcation is observed in the periodic forced system with soft impacts. The clearances of the system are the main reasons for influencing the chaotic motion. For small clearances, the grazing bifurcations bring about asymmetric motion and singularity. The steady 1-1-1 period orbits will exist within a wideband frequency range when appropriate system parameters are chosen.

Keywords:

Grazing bifurcation, soft impacts, periodic motion, vibration.