Please wait a minute...
ZJUS-A
Journal of Zhejiang University-SCIENCE A (Applied Physics & Engineering)  2009, Vol. 10 Issue (9): 1263-1268    DOI: 10.1631/jzus.A0820651
Mechanical and Mechanics Engineering     
Solution of nonlinear cubic-quintic Duffing oscillators using He’s Energy Balance Method
D. D. GANJI, M. GORJI, S. SOLEIMANI, M. ESMAEILPOUR
Department of Mechanical Engineering, University of Mazandaran, Babol, Iran
Download:     PDF (0 KB)     
Export: BibTeX | EndNote (RIS)      

Abstract  In this study, He’s Energy Balance Method (EBM) was applied to solve strong nonlinear Duffing oscillators with cubic-quintic nonlinear restoring force. The complete EBM solution procedure of the cubic-quintic Duffing oscillator equation is presented. For illustration of effectiveness and convenience of the EBM, different cases of cubic-quintic Duffing oscillator with different parameters of α, β and γ were compared with the exact solution. We found that the solutions were valid for small as well as large amplitudes of oscillation. The results show that the EBM is very convenient and precise, so it can be widely applicable in engineering and other sciences.

Key words： Energy Balance Method (EBM)      Cubic-quintic Duffing equation      Oscillator     
Received: 08 September 2008     
CLC:  O34  
Service
E-mail this article
Add to my bookshelf
Add to citation manager
E-mail Alert
RSS
Articles by authors
D. D. GANJI
M. GORJI
S. SOLEIMANI
M. ESMAEILPOUR
Cite this article:

D. D. GANJI, M. GORJI, S. SOLEIMANI, M. ESMAEILPOUR. Solution of nonlinear cubic-quintic Duffing oscillators using He’s Energy Balance Method. Journal of Zhejiang University-SCIENCE A (Applied Physics & Engineering), 2009, 10(9): 1263-1268.

URL:

http://www.zjujournals.com/xueshu/zjus-a/10.1631/jzus.A0820651     OR     http://www.zjujournals.com/xueshu/zjus-a/Y2009/V10/I9/1263

[1] Chao-bang Yao, Wen-cai Dong. A fast integration method for translating-pulsating source Green’s function in Bessho form[J]. Journal of Zhejiang University-SCIENCE A (Applied Physics & Engineering), 2014, 15(2): 108-119.
[2] Li-jia CHEN, Hua-feng ZHANG, Jin-fang ZHOU, Kang-sheng CHEN. Efficient design of rotary traveling wave oscillator array via geometric programming[J]. Journal of Zhejiang University-SCIENCE A (Applied Physics & Engineering), 2009, 10(12): 1815-1823.
[3] Xiang-yu ZHAO, Xiao-jun JIN, Zhong-he JIN. Simulation of dual transponder carrier ranging measurements[J]. Journal of Zhejiang University-SCIENCE A (Applied Physics & Engineering), 2009, 10(10): 1395-1403.
[4] CHEN Hua-jun, ZHANG Ben-zhao, SU Xiao-yan. Low frequency oscillatory flow in a rotating curved pipe[J]. Journal of Zhejiang University-SCIENCE A (Applied Physics & Engineering), 2003, 4(4): 407-414.
[5] CHEN Jun, Eichler H.J., ZHU Qi. DIODER-PUMPED SELF-Q-SWITCHED Cr4+, Nd3+: YAG LASER WITH AMPLIFIER[J]. Journal of Zhejiang University-SCIENCE A (Applied Physics & Engineering), 2001, 2(4): 361-365.