Analysis of the High Order Terms on Periodic Solution Bifurcations of the Generalized Duffing Systems

Shi Dong Chen; Zhi Qiang Wu

doi:10.4028/www.scientific.net/AMR.718-720.1705

Paper Titles

Optimal Vacuum Calculation and Analysis of Composite-Cycle Air-Cooling System
p.1687

Research for High-Voltage Nanosecond Rectangular Pulse Generator
p.1691

The Effect of High Temperature Environment on the Main Circuit of the Small Wind Power Generation System
p.1696

Sliding Mode Control of Brushless DC Motor with Feed-Forward Exponential Reaching Law
p.1700

Analysis of the High Order Terms on Periodic Solution Bifurcations of the Generalized Duffing Systems
p.1705

A Method of Calculating Attenuation Factor Based on RFID
p.1711

A 1V 2.52-kS/s 367nW Rail-to-Rail 10-Bit Successive Approximation ADC
p.1717

Finite Element Convergence Analysis of Two-Scale Non-Newtonian Flow Problems
p.1723

Piezoelectric Actuators Used for Helicopter Vibration Reduction
p.1729

HomeAdvanced Materials ResearchAdvanced Materials Research Vols. 718-720Analysis of the High Order Terms on Periodic...

Analysis of the High Order Terms on Periodic Solution Bifurcations of the Generalized Duffing Systems

Abstract:

This paper focuses on the effectsof the high order term in Duffing equation. Firstly the averaging equation andthe bifurcation equation are deduced through the multiple scale method.Secondly, the transition sets and several different bifurcation diagrams areobtained based on the singularity theory. The result shows that the high order term induces richer bifurcationcharacteristics.

You might also be interested in these eBooks

View Preview

Info:

Periodical:

Advanced Materials Research (Volumes 718-720)

Pages:

1705-1710

DOI:

https://doi.org/10.4028/www.scientific.net/AMR.718-720.1705

Citation:

Cite this paper

Online since:

July 2013

Authors:

Shi Dong Chen, Zhi Qiang Wu

Keywords:

Bifurcation, Duffingsystem, Stability, Transition Sets

Export:

RIS, BibTeX

Price:

Permissions CCC:

Request Permissions

Permissions PLS:

Request Permissions

Сopyright:

Citation:

References

[1] A. H. Nayfeh and D. T. Mook, Nonlinear Oscillations, Wiley-Interscience, New York 1979.

Google Scholar

[2] Y. S. Chen, Bifurcation of nonlinear vibration systems and chaos theory(Higher Education press, Beijing 1993).

Google Scholar

[3] J. G. Lin, High accuracy of approximate solutions of nonlinear duffing equation, Mechanics in Engineering, Vol. 21(1999)No. 5, pp.39-41(in Chinese).

Google Scholar

[4] S. K. Lai, C. W. Lim, B. S. Wu, "Newton-Harmonic balancing approach for accurate solutions to nonlinear cubic-quintic Duffing oscillators", Applied Mathematical Modelling, Vol. 33(2009) No. 2, p.852–866.

DOI: 10.1016/j.apm.2007.12.012

Google Scholar

[5] Y. Y. Cao, The Weighted Residual Method for Stability of the Periodic Solution of Duffing Equation in the System of Nonlinear Vibration, Journal of Changsha Railway Institute, Vol. 4(1986)No. 2, pp.75-78(in Chinese).

Google Scholar

[6] J. H. He, Variational iteration method: a new method for nonlinear analysis , Shanghai Journal of mechanics, Vol. 19(1998)No. 3, pp.260-264(in Chinese).

Google Scholar

[7] W. D. Li, X. Y. Wang, Duffing equation simulation analy-sis and chaos control, Journal of Dalian Jiaotong University, Vol. 30(2009)No. 5, pp.67-69(in Chinese).

Google Scholar

[8] H. L. Wang, H. Y. Hu, Z. H. Wang, Global Dynamics of Duffing Oscillator with Delayed Displacement Feedback, International Journal of Bifurcation and Chaos, Vol. 14(2004)No. 8, p.2753–2775.

DOI: 10.1142/s0218127404010990

Google Scholar

[9] W. J. Tao, S Huan, X. Y. Li, Duffing isolation system in the study of chaotic characteristics, Journal of Guangzhou University, Vol. 9(2010)No. 6, pp.69-71 (in Chinese).

Google Scholar

[10] L. X. Gao, J. Q. He, Y. G. Xu, The application of duffing oscillator in the fault diagnosis, Mechanical design and manufacture, Vol. 20(2009)No.3, pp.77-79 (in Chinese).

Google Scholar

[11] Y. N. Ye, L. Z. Wang, Weak periodic signal detection under the background of the noise based on Duffing oscillator, Mechanical & Electrical Engineering Magazine, Vol. 26(2009)No. 4, pp.97-100 (in Chinese).

Google Scholar