## 留言板

 引用本文: 李欣业, 陈予恕, 吴志强. 双重内共振系统非线性模态分岔的奇异性分析[J]. 应用数学和力学, 2002, 23(10): 997-1007.
LI Xin-ye, CHEN Yu-shu, WU Zhi-qiang. Singular Analysis of Bifurcation of Nonlinear Normal Modes for a Class of Systems With Dual Internal Resonances[J]. Applied Mathematics and Mechanics, 2002, 23(10): 997-1007.
 Citation: LI Xin-ye, CHEN Yu-shu, WU Zhi-qiang. Singular Analysis of Bifurcation of Nonlinear Normal Modes for a Class of Systems With Dual Internal Resonances[J]. Applied Mathematics and Mechanics, 2002, 23(10): 997-1007.

• 中图分类号: O322

## Singular Analysis of Bifurcation of Nonlinear Normal Modes for a Class of Systems With Dual Internal Resonances

• 摘要: 利用多尺度法构造的一类1:2:5双重内共振系统的耦合非线性模态的分岔是一个两变量的分岔问题.利用Maple计算机代数可以通过消元将耦合的模态分岔方程分离为两个单变量的分岔方程.对分离后的单变量分岔方程进行奇异性分析,发现随着系统参数的变化,非线性模态的分岔既可以是一种模态向另一种模态的转化,也可以是一种模态的突然出现与消失.最后给出了两变量分岔问题可以利用消元后得到的单变量分岔方程和耦合方程进行处理的一种方法.
•  [1] Rosenberg R M. On normal vibration of a general class of nonlinear dual-mode systems[J]. Journal of Applied Mechanics,1961,28:275-283. [2] Atkinson C P,Beverly T. A Study of nonlinearly related modal solutions of coupled nonlinear systems by supersition technique[J]. Journal of Applied Mechanics,1965,32:359-373. [3] Jonson T L,Rand R H. On the existence and bifurcation of minimal modes[J]. International Journal of Nonlinear Mechanics,1979,14:1-12. [4] Anand G V. Nature mode of a coupled nonlinear system[J]. International Journal of Nonlinear Mechanics,1972,7:81-91. [5] Yen D. On the normal modes of nonlinear dual-mass systems[J]. International Journal of Nonlinear Mechanics,1974,9:45-53. [6] Shaw S W,Pierre C. Normal modes for nonlinear vibrating systems[J]. Journal of Sound and Vibration,1993,164(1):85-124. [7] Nayfeh A,Lacabbonara W,Chin Char-Ming. Nonlinear normal modes of buckled beams:three-to-one and one-to-one internal resonances[J]. Nonlinear Dynamics,1999,18:253-273. [8] Nayfeh A H,Chin C,Nayfeh S A. On nonlinear normal modes of systems with internal resonance[J]. Journal of Vibration and Acoustics,1994,118:340-345. [9] Caughey T K,Vakakis A F,Sivo J M. Analytical study of similar normal modes and their bifurcation in a class of strongly nonlinear system[J]. International Journal of Nonlinear Mechanics,1990,25(5):521-533. [10] King M E,Vakakis A F. An Energy-based formulation for computing nonlinear normal modes in undamped continuous systems[J]. Journal of Vibration and Acoustics,1994,116:332-340. [11] Vakakis A F,Rand R H. Normal modes and global dynamics of a two-degree-of-freedom nonlinear system-Ⅰ Low energies[J]. International Journal of Nonlinear Mechanics,1992,27(5):861-874. [12] Vakakis A F,Vakakis R H,Rand R H. Normal modes and global dynamics of a two-degree-of-freedom nonlinear system-Ⅱ High energies[J]. International Journal of Nonlinear Mechanics,1992,27(5):875-888. [13] 李欣业. 多自由度内共振系统的非线性模态及其分岔[D]. 博士论文.天津:天津大学,2000,49-59. [14] CHEN Yu-shu,Andrew Y T Leung. Bifurcation and Chaos in Engineering[M]. London:Springer-Verlag London Limited,1998,220-234. [15] 唐云. 对称性分岔理论基础[M]. 北京:科学出版社,1998,135-141. [16] 刘济科,赵令诚,方同. 非线性系统的模态分岔与模态局部化现象[J]. 力学学报,1995,27(5):614-617. [17] Rand R H. Nonlinear normal modes in a two degrees of freedom system[J]. Journal of Applied Mechanics,1971,38:561-573.

##### 计量
• 文章访问数:  2250
• HTML全文浏览量:  100
• PDF下载量:  763
• 被引次数: 0
##### 出版历程
• 收稿日期:  2001-05-08
• 修回日期:  2002-05-10
• 刊出日期:  2002-10-15

/

• 分享
• 用微信扫码二维码

分享至好友和朋友圈