Hopf bifurcation of an oscillator with quadratic and cubic nonlinearities and with delayed velocity feedback

被引：0
作者：
Wang, Huailei [1 ]
Wang, Zaihua [2 ]
Hu, Haiyan [1 ]
机构：
[1] Inst. of Vibration Eng., Nanjing Univ. of Aero. and Astron.
[2] Inst. of Sci., PLA Univ. of Sci. and Technol.
来源：
Acta Mechanica Sinica/Lixue Xuebao | 2004年 / 20卷 / 04期
基金：
中国国家自然科学基金;
关键词：
Delay differential equation; Fredholm alternative; Stability switches; Supercritical Hopf bifurcation;
D O I：
10.1007/bf02489381
中图分类号：
学科分类号：
摘要：
This paper studies the local dynamics of an SDOF system with quadratic and cubic stiffness terms, and with linear delayed velocity feedback. The analysis indicates that for a sufficiently large velocity feedback gain, the equilibrium of the system may undergo a number of stability switches with an increase of time delay, and then becomes unstable forever. At each critical value of time delay for which the system changes its stability, a generic Hopf bifurcation occurs and a periodic motion emerges in a one-sided neighbourhood of the critical time delay. The method of Fredholm alternative is applied to determine the bifurcating periodic motions and their stability. It stresses on the effect of the system parameters on the stable regions and the amplitudes of the bifurcating periodic solutions.
引用
收藏
页码：426 / 434
页数：8
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