Multimode Dynamics of Inextensional Beams on the Elastic Foundation With Two-to-One Internal Resonances

被引：9

作者：

Wang, Lianhua ^{[1
,2
]}

Ma, Jianjun ^{[1
]}

Yang, Minghui ^{[1
]}

Li, Lifeng ^{[1
]}

Zhao, Yueyu ^{[1
]}

机构：

[1] Hunan Univ, Coll Civil Engn, Changsha 410082, Hunan, Peoples R China

[2] Minist Educ, Key Lab Bldg Safety & Energy Efficiency, Changsha 410082, Hunan, Peoples R China

来源：

JOURNAL OF APPLIED MECHANICS-TRANSACTIONS OF THE ASME | 2013年 / 80卷 / 06期

关键词：

inextensional beams; elastic foundations; nonlinear interaction; internal resonances; primary resonance; NORMAL-MODES; VIBRATIONS; COLUMNS;

D O I：

10.1115/1.4023694

中图分类号：

O3 [力学];

学科分类号：

08 ; 0801 ;

摘要：

The modal interactions and nonlinear responses of inextensional beams resting on elastic foundations with two-to-one internal resonances are investigated and the primary resonance excitations are considered. The multimode discretization and the method of multiple scales are applied to obtain the modulation equations. The equilibrium and dynamic solutions of the modulation equations are examined by the Newton-Raphson, shooting, and continuation methods. Numerical simulations are performed to investigate the chaotic dynamics of the beam. It is shown that the nonlinear responses may undergo different bifurcations and exhibit rich nonlinear phenomena. Finally, the effects of the foundation models on the nonlinear interactions of the beam are examined.

引用

页数：11

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