Chaotic synchronization of geometric nonlinear composite beam under horizontal-vertical excitation

PDF(1483 KB)

Journal of Vibration and Shock ›› 2016, Vol. 35 ›› Issue (9) : 28-31.

WANG Long-Fei1 HAN Zhi-Jun1 YAN Xiao-Peng1 LU Guo-Yun 2

Author information +

History +

Abstract

Based on Ritz-Galerkin Method, the governing equations of composite beam with the clamped-fixed boundary conditions can be simplified to the typical formal of Duffing Equations when geometric nonlinear is taken into consideration. The Duffing-Van Der Pol System is introduced, and parameter values of two systems reaching the chaotic state commonly are obtained according to their bifurcation diagrams. The accurate synchronization among the Duffing System and the DVP System (short for Duffing-Van Der Pol) can be achieved by generalized projective synchronization method and their controller is also acquired. Finally, numerical analysis of chaotic synchronization is accomplished by Matlab and synchronous error curve diagrams, 2D-phase-trajectory diagrams, 3D-phase-trajectory diagrams can be gotten, these diagrams are used to verify the accuracy of chaotic synchronization.

Key words

composite / chaotic synchronization / DVP system / generalized projective synchronization method

Cite this article

EndNote

Ris (Procite)

Bibtex

Download Citations

WANG Long-Fei1 HAN Zhi-Jun1 YAN Xiao-Peng1 LU Guo-Yun 2 . Chaotic synchronization of geometric nonlinear composite beam under horizontal-vertical excitation[J]. Journal of Vibration and Shock, 2016, 35(9): 28-31

References

[1] Liu Yang-Zheng,Jiang Chang-Sheng. Chaos switch-synchron- ization for a class of 4-D chaoticsystems[J]. Acta Physica Sinica, 2007(2).
[2] Maggio G,Rulkov N,Reggiani L. Pseudo-chaotic time hopping
for UWB impulse radio[J]. IEEE Trans on Circuit and System,
2001,48(12):1424-1434.
[3] Fridrich J,Goljan M. Protection of digital images using self embedding[EB/OL] http://Proc of IC IP99,1999.
[4] Pecora.L.M,Carroll.T.L. Synchronization in chaotic systems [J].Physical Review Letters, 1990,64(8):821-827.
[5] L.Kocarev,U.Parlitz. General Approach for Chaotic Synchroni-zation with Applications to Communication[J], Phys.Rev.Lett,1995(74),5028-5031.
[6]   Pyragas.K. Experimental Control of Chaos by delayed
    self-controlling feedback[M]. Phys.Lett.A, 1993(181),203.
[7] Mainieri.R,Rehacek.J. Projective synchronization in three-dimensional chaotic systems[J]. Phys.Rev.Lett,1999,82(15):3042-3045.
[8] Yan J P,Li C P. Generalized projective synchronization of a unifiedchaotic system[J]. Chaos Solitons and Fractals, 2005,26(4):1119-1124.
[9] Hu Manfeng,Xu Zhenyuan.Full state hybrid projective synchro-nization in continuous-time chaotic (hyperchaotic)systems[J]. Communications in Nonlinear Science and Numerical Simula-tion, 2008,13(2):456-464.
[10] 闵富红,王执铨. 两个四维混沌系统广义投影同步[J].物理学报，2007，56(11)：6238-6244.
     Min Fuhong,Wang Zhiquan. Generalized projective synchro-nization of two four-dimensional chaotic systems[J]. ACTA PHYSICA SINICA,2007，56(11):6238-6244.
[11] 闵富红,王执铨,史国生. 新型超混沌系统的改进自适应广义投影同步[J].系统仿真学报,2008,20(14):3785-3789.
     Min Fuhong,Wang Zhiquan,Shi Guosheng.Adaptive Modified Generalized Projective Synchronization for New Hyper-cha-otic Systems[J]. Journal of System Simulation,2008,20(14):
     3785-3789.
[12] 王宇野,许红珍. 异结构不确定混沌系统的广义投影同步[J]. 系统工程与电子技术，2010(2):355-358.
     Wang Yuye, Xu Hongzhen.Generalized projective Synchron-ization between two different uncertain chaotic systems[J]. Systems Engineering and Electronics, 2010(2):355-358.
[13] 冯浩,杨洋. Chen系统和Liu系统的广义投影同步的电路仿真设计[J]. 河北北方学院学报(自然科学版)，2013,29(5):14-17.
     Feng Hao,Yang Yang.Circuit Simulation Design of Generali- zed Projective Synchronization of Chen System and Liu System[J]. Journal of Hebei North University(Natural Science
     Edition),2013,29(5):14-17.
[14] 杨洋. 混沌系统全状态混合投影同步研究[D].石家庄:河北师范大学. 2007.