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.
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November 2013
Research-Article
Multimode Dynamics of Inextensional Beams on the Elastic Foundation With Two-to-One Internal Resonances
Lianhua Wang,
Lianhua Wang
1
College of Civil Engineering,
Hunan University
,Changsha
,Hunan 410082
, China
Key Laboratory of Building
Safety and Energy Efficiency,
Ministry of Education,
e-mail: Lhwang@hnu.edu.cn
Safety and Energy Efficiency,
Ministry of Education,
Hunan 410082
, China
e-mail: Lhwang@hnu.edu.cn
1Corresponding author.
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Yueyu Zhao
Yueyu Zhao
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Lianhua Wang
College of Civil Engineering,
Hunan University
,Changsha
,Hunan 410082
, China
Key Laboratory of Building
Safety and Energy Efficiency,
Ministry of Education,
e-mail: Lhwang@hnu.edu.cn
Safety and Energy Efficiency,
Ministry of Education,
Hunan 410082
, China
e-mail: Lhwang@hnu.edu.cn
Jianjun Ma
e-mail: Majianjun@hnu.edu.cn
Minghui Yang
e-mail: Yamih@hnu.edu.cn
Lifeng Li
e-mail: Lilifeng@hnu.edu.cn
Yueyu Zhao
1Corresponding author.
Manuscript received December 13, 2012; final manuscript received January 23, 2013; accepted manuscript posted February 19, 2013; published online August 21, 2013. Assoc. Editor: Alexander F. Vakakis.
J. Appl. Mech. Nov 2013, 80(6): 061016 (11 pages)
Published Online: August 21, 2013
Article history
Received:
December 13, 2012
Revision Received:
January 23, 2013
Accepted:
February 19, 2013
Citation
Wang, L., Ma, J., Yang, M., Li, L., and Zhao, Y. (August 21, 2013). "Multimode Dynamics of Inextensional Beams on the Elastic Foundation With Two-to-One Internal Resonances." ASME. J. Appl. Mech. November 2013; 80(6): 061016. https://doi.org/10.1115/1.4023694
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