| FUNDAMENTAL AREAS OF PHENOMENOLOGY(INCLUDING APPLICATIONS) |
|
|
|
|
Vibrational Resonance in Fractional-Order Anharmonic Oscillators |
| YANG Jian-Hua** |
School of Mechanical and Electrical Engineering, China University of Mining and Technology, Xuzhou 221116
|
|
| Cite this article: |
|
YANG Jian-Hua 2012 Chin. Phys. Lett. 29 104501 |
|
|
|
|
Abstract The phenomenon of vibrational resonance in fractional-order anharmonic oscillators is investigated. Based on the method of separating slow and fast motions, the approximate solution of the response amplitude is obtained. Both analytical and numerical results show that not only the high-frequency signal but also the fractional-order damping can induce vibrational resonance. The present results provide a new way to control periodical signals in coupled systems.
|
|
|
Received: 04 May 2012
Published: 01 October 2012
|
|
| PACS: |
45.10.Hj
|
(Perturbation and fractional calculus methods)
|
| |
33.20.Tp
|
(Vibrational analysis)
|
| |
05.45.Xt
|
(Synchronization; coupled oscillators)
|
|
|
|
|
|
[1] Yang F and Zhu K Q 2011 Theor. Appl. Mech. Lett. 1 012007
[2] Mainardi F 2010 Fractional Calculus and Waves in Linear Viscoelasticity: An Introduction to Mathematical Models (London: Imperial College Press)
[3] Merala F C, Roystona T J and Maginb R 2010 Commun. Nonlinear Sci. Numer. Simul. 15 939
[4] Chen Y, Sun R, Zhou A and Zaveri N 2008 J. Vib. Control 14 1443
[5] Oldham K B 2010 Adv. Eng. Softw. 41 9
[6] Magin R L and Ovadia M 2008 J. Vib. Control 14 1431
[7] Magin R L 2010 Comput. Math. Appl. 59 1586
[8] Carpinteri A and Mainardi F 1997 Fractals and Fractional Calculus in Continuum Mechanics (New York: Springer)
[9] Rossikhin Y A and Shitikova M V 2010 Appl. Mech. Rev. 63 010801
[10] Vinagre B M, Petrá? I, Podlubny I and Chen Y Q 2002 Nonlinear Dyn. 29 269
[11] Agrawal O P 2004 Nonlinear Dyn. 38 323
[12] Ozaktas H M, Zalevsky Z and Kutay M A 2001 The Fractional Fourier Transform: with Applications in Optics and Signal Processing (New York: Wiley)
[13] Das S and Pan I 2011 Fractional Order Signal Processing: Introductory Concepts and Applications (Berlin: Springer)
[14] Kusnezov D, Bulgac A and Dang G D 1999 Phys. Rev. Lett. 82 1136
[15] Monje C A, Chen Y, Vinagre B M, Xue D and Feliu V 2010 Fractional-order Systems and Controls (London: Springer)
[16] Yang J H and Zhu H 2012 Chaos 22 013112
[17] Landa P S and McClintock P V E 2000 J. Phys. A 33 L433
[18] Jeyakumari S, Chinnathambi V, Rajasekar S and Sanjuan M A F 2009 Phys. Rev. E 80 046608
[19] Jeyakumari S, Chinnathambi V, Rajasekar S and Sanjuan M A F 2009 Chaos 19 043128
[20] Wang C J 2011 Chin. Phys. Lett. 28 090504
[21] Chizhevsky V N, Smeu E and Giacomelli G 2003 Phys. Rev. Lett. 91 220602
[22] Yang J H and Liu X B 2010 J. Phys. A 43 122001
[23] Yang J H and Liu X B 2010 Chaos 20 033124
[24] Jeevarathinam C, Rajasekar S and Sanjuan M A F 2011 Phys. Rev. E 83 066205
[25] Deng B, Wang J, Wei X, Tsang K M and Chan W L 2010 Chaos 20 013113
[26] Qin Y M, Wang J, Men C, Deng B and Wei X L 2011 Chaos 21 023113
[27] Yao C and Zhan M 2010 Phys. Rev. E 81 061129
[28] Yang J H and Liu X B 2011 Phys. Scr. 83 065008
[29] Gandhimathi V M, Rajasekar S and Kurths J 2006 Phys. Lett. A 360 279
[30] Fang C J and Liu X B 2012 Chin. Phys. Lett. 29 050504
[31] Blekhman I I 2000 Vibrational Mechanics (Singapore: World Scientific) |
|
Viewed |
|
|
|
Full text
|
|
|
|
|
Abstract
|
|
|
|
|
