PL EN


Preferencje help
Widoczny [Schowaj] Abstrakt
Liczba wyników
Czasopismo
2015 | 13 | 1 |
Tytuł artykułu

Response of a fractional nonlinear system to harmonic excitation by the averaging method

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
In this work, we consider a fractional nonlinear vibration system of Duffing type with harmonic excitation by using the fractional derivative operator -∞−1Dαt and the averaging method. We derive the steady-state periodic response and the amplitude-frequency and phase-frequency relations. Jumping phenomena caused by the nonlinear term and resonance peaks are displayed, which is similar to the integer-order case. It is possible that a minimum of the amplitude exists before the resonance appears for some values of the modelling parameters, which is a feature for the fractional case. The effects of the parameters in the fractional derivative term on the amplitude-frequency curve are discussed.
Wydawca

Czasopismo
Rocznik
Tom
13
Numer
1
Opis fizyczny
Daty
otrzymano
2014-11-06
zaakceptowano
2014-12-11
online
2015-02-16
Twórcy
  • School of Sciences,
    Shanghai Institute of Technology, Shanghai 201418, P.R. China
autor
  • School of Mechanical Engineering, Shanghai
    Institute of Technology, Shanghai 201418, P.R. China
autor
  • School of Mechanical Engineering, Shanghai
    Institute of Technology, Shanghai 201418, P.R. China
Bibliografia
  • [1] I. Podlubny, Fractional Differential Equations (Academic, SanDiego, 1999)
  • [2] A. A. Kilbas, H. M. Srivastava, J. J. Trujillo, Theory and Applicationsof Fractional Differential Equations (Elsevier, Amsterdam,2006)
  • [3] F. Mainardi, Fractional Calculus and Waves in Linear Viscoelasticity(Imperial College, London, 2010)
  • [4] D. Băleanu, K. Diethelm, E. Scalas, J. J. Trujillo, Fractional CalculusModels and Numerical Methods, Series on Complexity, Nonlinearityand Chaos (World Scientific, Boston, 2012)
  • [5] J. T.Machado, V. Kiryakova, F.Mainardi,Commun. Nonlinear Sci.Numer. Simulat. 16, 1140 (2011)[Crossref]
  • [6] G. W. Scott-Blair, J. Scientific Instruments 21, 80 (1944)
  • [7] G. W. Scott-Blair, J. Colloid Sciences 2, 21 (1947)[Crossref]
  • [8] G. W. Scott-Blair, Survey of General and Applied Rheology (Pitman,London, 1949)
  • [9] R. C. Koeller, J. Appl. Mech. 51, 299 (1984)[Crossref]
  • [10] Y. A. Rossikhin, M. V. Shitikova, Appl. Mech. Rev. 50, 15 (1997)[Crossref]
  • [11] V. M. Zelenev, S. I. Meshkov, Yu. A. Rossikhin, J. Appl. Mech.Tech. Phys. 11, 290 (1970)[Crossref]
  • [12] M. Y. Xu, W. C. Tan, Sci. China Ser. G 46, 145 (2003)
  • [13] W. Chen, J. Vib. Control 14, 1651 (2008)[Crossref]
  • [14] R. L. Bagley, P. J. Torvik, Shock Vib. Bull. 49, 135 (1979)
  • [15] H. Beyer, S. Kempfle, ZAMM-Z. Angew Math. Mech. 75, 623(1995)[Crossref]
  • [16] R. Gorenflo, F. Mainardi, In: A. Carpinteri, F. Mainardi (Eds.),Fractals and Fractional Calculus in Continuum Mechanics(Springer-Verlag, Wien/New York, 1997) 223
  • [17] D. R. Bland, The Theory of Linear Viscoelasticity (Pergamon, Oxford,1960)[WoS]
  • [18] M. Caputo, Geophys. J. R. Astr. Soc. 13, 529 (1967)
  • [19] F. Mainardi, Chaos Solitons Fractals 7, 1461 (1996)[Crossref]
  • [20] B. N. N. Achar, J.W. Hanneken, T. Clarke, Phys. A 309, 275 (2002)
  • [21] M. Li, S. C. Lim, S. Chen, Math. Probl. Eng. 2011, Article ID657839 (2011)
  • [22] S. C. Lim, M. Li, L. P. Teo, Fluct. Noise Lett. 7, L169 (2007)[Crossref]
  • [23] S. C. Lim, L. P. Teo, J. Phys. A: Math. Theor. 42, 065208 (2009)[Crossref]
  • [24] Z. H. Wang, H. Y. Hu, Sci. China Ser. G 53, 345 (2010)
  • [25] Z. H. Wang, M. L. Du, Shock Vib. 18, 257 (2011)[Crossref]
  • [26] Y. J. Shen, S. P. Yang, H. J. Xing, Acta Phys. Sin. 61, 110505 (2012)
  • [27] Y. Shen, S. Yang, H. Xing, G. Gao, Commun. Nonlinear Sci. Numer.Simulat. 17, 3092 (2012)[Crossref]
  • [28] C. P. Li, W. H. Deng, D. Xu, Phys. A 360, 171 (2006)
  • [29] W. Zhang, S. K. Liao, N. Shimizu, J. Mech. Sci. Tech. 23, 1058(2009)[Crossref]
  • [30] C. Li, Y. Ma, Nonlinear Dynam. 71, 621 (2013)[Crossref]
  • [31] M. S. Tavazoei, M. Haeri, M. Attari, S. Bolouki, M. Siami, J. Vib.Control 15, 803 (2009)[Crossref]
  • [32] C. M. A. Pinto, J. A. T.Machado, Nonlinear Dynam. 65, 247 (2011)[Crossref]
  • [33] A. H. Bhrawy, Y. A. Alhamed, D. Baleanu, A. A. Al-Zahrani, Fract.Calc. Appl. Anal. 17, 1137 (2014)
  • [34] H. Jafari, H. Tajadodi, D. Baleanu, J. Comput. Nonlinear Dynam.9, 021019 (2014)[Crossref]
  • [35] J. S. Duan, R. Rach, D. Baleanu, A. M. Wazwaz, Commun. Fract.Calc. 3, 73 (2012)
  • [36] D. Baleanu, G. C. Wu, J. S. Duan, In: J. A. T. Machado,D. Baleanu, A. C. J. Luo (Eds.), Discontinuity and Complexity inNonlinear Physical Systems (Springer, Cham/Heidelberg/NewYork/Dordrecht/London, 2014) 35
  • [37] G. Wang, S. Liu, D. Baleanu, L. Zhang, Abstr. Appl. Anal. 2014,932747 (2014)
  • [38] J. S. Duan, Z. Wang, S. Z. Fu, Cent. Eur. J. Phys. 11, 799 (2013)
  • [39] J. S. Duan, Z. Wang, Y. L. Liu, X. Qiu, Chaos Solitons Fractals 46,46 (2013)[Crossref]
  • [40] E. Kaslik, S. Sivasundaram, Nonlinear Anal.: Real World Appl.13, 1489 (2012)
  • [41] B. Davies, Integral Transforms and Their Applications, 3rd edition(Springer-Verlag, New York, 2001)
  • [42] L. Debnath, D. Bhatta, Integral transforms and their applications,2nd edition (Chapman & Hall/CRC, Boca Raton, 2006)
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.-psjd-doi-10_1515_phys-2015-0020
JavaScript jest wyłączony w Twojej przeglądarce internetowej. Włącz go, a następnie odśwież stronę, aby móc w pełni z niej korzystać.