PL EN


Preferencje help
Widoczny [Schowaj] Abstrakt
Liczba wyników
Czasopismo
2013 | 11 | 6 | 792-798
Tytuł artykułu

Numerical solution of fractionally damped beam by homotopy perturbation method

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
This paper investigates the numerical solution of a viscoelastic continuous beam whose damping behaviours are defined in term of fractional derivatives of arbitrary order. The Homotopy Perturbation Method (HPM) is used to obtain the dynamic response. Unit step function response is considered for the analysis. The obtained results are depicted in various plots. From the results obtained it is interesting to note that by increasing the order of the fractional derivative the beam suffers less oscillation. Similar observations have also been made by keeping the order of the fractional derivative constant and varying the damping ratios. Comparisons are made with the analytic solutions obtained by Zu-feng and Xiao-yan [Appl. Math. Mech. 28, 219 (2007)] to show the effectiveness and validation of this method.
Wydawca

Czasopismo
Rocznik
Tom
11
Numer
6
Strony
792-798
Opis fizyczny
Daty
wydano
2013-06-01
online
2013-10-09
Twórcy
  • Department of Mathematics, National Institute of Technology, Rourkela Odisha, 769 008, India, diptiranjanb@gmail.com
  • Department of Mathematics, National Institute of Technology, Rourkela Odisha, 769 008, India, sne_chak@yahoo.com
Bibliografia
  • [1] A. Arikoglu, I. Ozkol, Chaos Soliton. Fract. 34, 1473 (2007) http://dx.doi.org/10.1016/j.chaos.2006.09.004[Crossref]
  • [2] A.K. Golmankhaneh, Investigations in Dynamics: With Focus on Fractional Dynamics (Academic Publishing, Lap Lambert, 2012)
  • [3] A.K. Golmankhaneh, T. Khatuni, N.A. Porghoveh, D. Baleanu, Cent. Eur. J. Phys. 10, 966 (2012) http://dx.doi.org/10.2478/s11534-012-0038-7[Crossref]
  • [4] A. Shokooh, L.E. Suarez, J. Vib. Control 5, 331 (1999) http://dx.doi.org/10.1177/107754639900500301[Crossref]
  • [5] A. Yildirim, Int. J. Nonlin. Sci. Numer. Simul. 10, 445 (2009)
  • [6] D. Baleanu, J.A.T. Machado, A.C.J. Luo, Fractional Dynamics and Control (Springer, 2012) http://dx.doi.org/10.1007/978-1-4614-0457-6[Crossref]
  • [7] D. Baleanu, K. Diethelm, E. Scalas, J. J. Trujillo, Fractional Calculus: Models and Numerical Methods (World Scientific Publishing Company, 2012)
  • [8] I. Podlubny, Fractional Differential Equations (Academic Press, New York, 1999)
  • [9] J.H. He, Appl. Math. Comput. 135, 73 (2003) http://dx.doi.org/10.1016/S0096-3003(01)00312-5[Crossref]
  • [10] J.H. He, Comput. Meth. Appl. Mech. Eng. 178, 257 (1999) http://dx.doi.org/10.1016/S0045-7825(99)00018-3[Crossref]
  • [11] J.H. He, Int. J. Nonlin. Mech. 35, 37 (2000) http://dx.doi.org/10.1016/S0020-7462(98)00085-7[Crossref]
  • [12] J.H. He, Int. J. Nonlin. Sci. Numer. Simul. 6, 207 (2005)
  • [13] J.H. He, Phys. Lett. A 350, 87 (2006) http://dx.doi.org/10.1016/j.physleta.2005.10.005[Crossref]
  • [14] K.B. Oldham, J. Spanier, The Fractional Calculus (Academic Press, New York, 1974)
  • [15] L. Gaul, P. Klein, S. Kemple, Mech. Res. Commun. 16, 4447 (1989) http://dx.doi.org/10.1016/0093-6413(89)90067-0[Crossref]
  • [16] L. Gaul, P. Klein, S. Kemple, Mech. Syst. Signal Process 5, 8 (1991)
  • [17] L.E. Suarez, A. Shokooh, ASME J. Appl. Mech. 64, 629 (1997) http://dx.doi.org/10.1115/1.2788939[Crossref]
  • [18] L. Yuan, O.P. Agrawal, J. Vib. Acoustics 124, 321 (2002) http://dx.doi.org/10.1115/1.1448322[Crossref]
  • [19] L. Zu-feng, T. Xiao-yan, Appl. Math. Mech. 28, 219 (2007) http://dx.doi.org/10.1007/s10483-007-0210-z[Crossref]
  • [20] M. Enelund, B.L. Josefson, AIAA J. 35, 1630 (1997) http://dx.doi.org/10.2514/2.2[Crossref]
  • [21] M. Enelund, P. Olsson, Int. J. Solids Struct. 36, 939 (1999) http://dx.doi.org/10.1016/S0020-7683(97)00339-9[Crossref]
  • [22] Miller and Ross, An Introduction to the Fractional Calculus and Fractional Differential Equations (John Wiley and Sons, New York, 1993)
  • [23] O.P. Agrawal, ASME J. Vibr. Acoust. 126, 561 (2004) http://dx.doi.org/10.1115/1.1805003[Crossref]
  • [24] Q. Wang, Appl. Math. Comput. 190, 1795 (2007) http://dx.doi.org/10.1016/j.amc.2007.02.065[Crossref]
  • [25] Q. Wang, Chaos Soliton. Fract. 35, 843 (2008) http://dx.doi.org/10.1016/j.chaos.2006.05.074[Crossref]
  • [26] R.C. Koeller, ASME J. Appl. Mech. 51, 299 (1984) http://dx.doi.org/10.1115/1.3167616[Crossref]
  • [27] R. Gorenflo, Fractional Calculus: Some Numerical Methods, Fractals and Fractional Calculus in Continuum Mechanics (Springer Verlag, New York, 1997)
  • [28] R.L. Bagley, P.J. Torvik, AIAA J. 21, 741 (1983) http://dx.doi.org/10.2514/3.8142[Crossref]
  • [29] R.L. Bagley, P.J. Torvik, J. Rheol. 27, 201 (1983) http://dx.doi.org/10.1122/1.549724[Crossref]
  • [30] S. Das, Int. J. Nonlin. Sci. Numer. Simul. 9, 361 (2008) http://dx.doi.org/10.1515/IJNSNS.2008.9.4.361[Crossref]
  • [31] S.G. Samko, A.A. Kilbas, O.I. Marichev, Fractional Integrals and Derivatives-Theory and Applications (Gordon and Breach Science Publishers, Langhorne, 1993)
  • [32] S. Momani, Appl. Math. Comput. 170, 1126 (2005) http://dx.doi.org/10.1016/j.amc.2005.01.009[Crossref]
  • [33] S. Momani, Math. Comput. Simul. 70, 110 (2005) http://dx.doi.org/10.1016/j.matcom.2005.05.001[Crossref]
  • [34] S. Momani, R. Ibrahim, Int. J. Pure Appl. Math. 37, 119 (2007)
  • [35] S. Momani, Z. Odibat, A. Alawneh, Numer. Meth. Part. Differ. Equat. 24, 262 (2008) http://dx.doi.org/10.1002/num.20247[Crossref]
  • [36] V.D. Gejji, H. Jafari, Appl. Math. Comp. 189, 541 (2007) http://dx.doi.org/10.1016/j.amc.2006.11.129[Crossref]
  • [37] V.S. Kiryakova, Generalized Fractional Calculus and Applications (Longman Scientific and Technical, Longman House, Burnt Mill, Harlow, England, 1993) 798
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.-psjd-doi-10_2478_s11534-013-0201-9
JavaScript jest wyłączony w Twojej przeglądarce internetowej. Włącz go, a następnie odśwież stronę, aby móc w pełni z niej korzystać.