Limit cycles in nonlinear vibrating systems excited by a nonideal energy source with a large slope characteristic

详细信息    查看全文

• 作者：Javier González-Carbajal ; Jaime Domínguez
• 关键词：Nonideal excitation ; Unbalanced motor ; Hopf bifurcation ; Limit cycle
• 刊名：Nonlinear Dynamics
• 出版年：2017
• 出版时间：January 2017
• 年：2017
• 卷：87
• 期：2
• 页码：1377-1391
• 全文大小：
• 刊物类别：Engineering
• 刊物主题：Vibration, Dynamical Systems, Control; Classical Mechanics; Mechanical Engineering; Automotive Engineering;
• 出版者：Springer Netherlands
• ISSN：1573-269X
• 卷排序：87

文摘

This study is the natural continuation of a previous paper of the authors González-Carbajal and Domínguez in J. Sound Vib. (Under revision), where the possibility of finding Hopf bifurcations in vibrating systems excited by a nonideal power source was addressed. Herein, some analytical tools are used to characterize these Hopf bifurcations, deriving a simple rule to classify them as supercritical or subcritical. Moreover, we find conditions under which the averaged system can be proved to be always attracted by a limit cycle, irrespective of the initial conditions. These limit cycle oscillations in the averaged system correspond to quasiperiodic motions of the original system. To the authors’ knowledge, limit cycle oscillations have not been addressed before in the literature about nonideal excitations. Through supporting numerical simulations, we also investigate the global bifurcations destroying the limit cycles. The analytical results are verified numerically.