燕山大学学报2011，Vol.35Issue(2)：162-166,172,6.DOI:10.3969/j.issn.1007-791X.2011.02.014
时滞反馈非线性扭振系统的稳定性与Hopf分岔研究
Study on stability and Hopf bifurcation of a nonlinear torsional system with time-delay feedback
摘要
Abstract
The stability and Hopf bifurcation of two inertia nonlinear torsional vibration with duffing-van der pol oscillators and time-delay characteristics are studied.The equation of two inertia nonlinear torsional vibration system is established.The controlled torsional vibration system is constituted by devising the time-delay feedback controller of linear displacement and velocity.The relation of limit amplitude and time-delay parameters is deduced by the method of multiple scales.Based on the analysis of the system's stability of zero solution, the condition of Hopf bifurcation is obtained.According to the research of the system's Hopf bifurcation and limit amplitude by numerical methods, two conclusions are verified: the controller of time-delay feedback not only controls the amplitude of limit but also controls the condition of the Hopf bifurcation.关键词
扭振/Hopf分岔/极限环/时滞反馈控制Key words
torsional vibration/ Hopf bifurcation/ limit cycle/ time-delay feedback control分类
数理科学引用本文复制引用
时培明,刘彬,韩东颖,朱占龙,侯东晓..时滞反馈非线性扭振系统的稳定性与Hopf分岔研究[J].燕山大学学报,2011,35(2):162-166,172,6.基金项目
国家自然科学基金资助项目(51005196) （51005196）
河北省自然科学基金资助项目(F2010001317) （F2010001317）
秦皇岛市科学技术研究与发展计划项目(201001A085) （201001A085）
