Periodic solution for strongly nonlinear vibration systems by He's Energy balance method

Acta Applicandae Mathematicae

Volumn 106, Issue 1, 2009, Pages 79-92

  Ganji, S S ^a   Ganji, D D ^a   Ganji, Z Z ^a   Karimpour, S ^a  

^a BABOL NOSHIRVANI UNIVERSITY OF TECHNOLOGY   (Iran)

Author keywords

Energy balance method; Nonlinear oscillation; Periodic solutions

Indexed keywords

ENERGY BALANCE; HELIUM; NONLINEAR SYSTEMS; OSCILLATORS (MECHANICAL);

ENERGY BALANCE METHOD; EXACT SOLUTIONS; NON-LINEAR DIFFERENTIAL EQUATIONS; NON-LINEAR VIBRATIONS; NONLINEAR OSCILLATION; PERIODIC SOLUTIONS; STRONGLY NONLINEAR; STRONGLY NONLINEAR SYSTEMS;

NONLINEAR EQUATIONS;

EID: 62949117479     PISSN: 01678019     EISSN: 15729036     Source Type: Journal    
DOI: 10.1007/s10440-008-9283-6     Document Type: Article

References (38)

1. Fidlin, A.: Nonlinear Oscillations in Mechanical Engineering. Springer, Berlin (2006)
2. Dimarogonas, A.D., Haddad, S.: Vibration for Engineers. Prentice-Hall, Englewood Cliffs (1992)
3. He, J.H.: Non-perturbative methods for strongly nonlinear problems. Dissertation, de-Verlag im Internet GmbH, Berlin (2006)
4. J.H. He 1999 Homotopy perturbation technique, computer methods Appl. Mech. Eng. 178 257 262
5. J.H. He 2004 The homotopy perturbation method for nonlinear oscillators with discontinuities Appl. Math. Comput. 151 287 292
6. S.H. Hashemi K.H.R.M. Daniali D.D. Ganji 2007 Numerical simulation of the generalized Huxley equation by He's homotopy perturbation method Appl. Math. Comput. 192 157 161
7. D.D. Ganji A. Sadighi 2006 Application of He's homotopy-perturbation method to nonlinear coupled systems of reaction-diffusion equations Int. J. Non-Linear Sci. Numer. Simul. 7 4 411 418
8. Nayfeh, A.H.: Introduction to Perturbation Techniques. Wiley, New York (1981)
9. J.H. He 2002 Modified Lindstedt-Poincare methods for some strongly nonlinear oscillations. Part I: Expansion of a constant Int. J. Non-Linear Mech. 37 309 314
10. J.H. He 2001 Modified Lindstedt-Poincare methods for some strongly nonlinear oscillations. Part III: Double series expansion Int. J. Non-Linear Sci. Numer. Simul. 2 317 320
11. S.Q. Wang J.H. He 2008 Nonlinear oscillator with discontinuity by parameter-expansion method Chaos Solitons Fractals 35 688 691
12. J.H. He 2006 Some asymptotic methods for strongly nonlinear equations Int. J. Mod. Phys. B 20 1141 1199
13. J.H. He 1999 Some new approaches to duffing equation with strongly and high order nonlinearity (II) parameterized perturbation technique Commun. Non-Linear Sci. Numer. Simul. 4 81 82
14. J.H. He 2000 A review on some new recently developed nonlinear analytical techniques Int. J. Non-Linear Sci. Numer. Simul. 1 51 70
15. J.H. He 2006 Determination of limit cycles for strongly nonlinear oscillators Phys. Rev. Lett. 90 174 181
16. M. D'Acunto 2006 Determination of limit cycles for a modified van der Pol oscillator Mech. Res. Commun. 33 93 100
17. J.H. He 2002 Preliminary report on the energy balance for nonlinear oscillations Mech. Res. Commun. 29 107 118
18. J.H. He 1999 Variational iteration method-a kind of nonlinear analytical technique: some examples Int. J. Non-Linear Mech. 34 699 708
19. M. Rafei D.D. Ganji H. Daniali H. Pashaei 2007 The variational iteration method for nonlinear oscillators with discontinuities J. Sound Vib. 305 614 620
20. J.H. He X.H. Wu 2006 Construction of solitary solution and compaction-like solution by variational iteration method Chaos Solitons Fractals 29 108 113
21. S.M. Varedi M.J. Hosseini M. Rahimi D.D. Ganji 2007 He's variational iteration method for solving a semi-linear inverse parabolic equation Phys. Lett. A 370 275 280
22. Hashemi, S.H., Tolou, K.N., Barari, A., Choobbasti, A.J.: On the approximate explicit solution of linear and non-linear non-homogeneous dissipative wave equations. In: Istanbul Conferences. Torque, accepted (2008)
23. J.H. He 2007 Variational approach for nonlinear oscillators Chaos Solitons Fractals 34 1430 1439
24. Naghipour, M., Ganji, D.D., Hashemi, S.H., Jafari, K.: Analysis of non-linear oscillations systems using analytical approach. J. Phys. 96 (2008)
25. Y. Wu 2007 Variational approach to higher-order water-wave equations Chaos Solitons Fractals 32 195 203
26. L. Xu 2008 Variational approach to Solitons of nonlinear dispersive K(m,n) equations Chaos Solitons Fractals 37 137 143
27. Inokuti, M., et al.: General use of the Lagrange multiplier in non-linear mathematical physics. In: Nemat-Nasser, S. (ed.) Variational Method in the Mechanics of Solids, pp. 156-162. Pergamon Press, Oxford (1978)
28. H.M. Liu 2005 Generalized variational principles for ion acoustic plasma waves by He's semi-inverse method Chaos Solitons Fractals 23 2 573 576
29. J.H. He 2004 Variational principles for some nonlinear partial differential equations with variable coefficient Chaos Solitons Fractals 19 4 847 851
30. V. Marinca N. Herisanu 2006 A modified iteration perturbation method for some nonlinear oscillation problems Acta Mech. 184 231 242
31. W.P. Suna B.S. Wua C.W. Lim 2007 J. Sound Vib. 300 5-6 1042
32. S. S. Ganji D. D. Ganji H. Ganji Babazadeh S. Karimpour 2008 Variational approach method for nonlinear oscillations of the motion of a rigid rod rocking back and cubic-quintic duffing oscillators Prog. Electromagn. Res. M 4 23 32
33. S.B. Tiwari B.N. Rao N.S. Swamy K.S. Sai H.R. Nataraja 2005 Analytical study on a Duffing-harmonic oscillator J. Sound Vib. 285 1217 1222
34. R.E. Mickens 1998 Periodic solutions of the relativistic harmonic oscillator J. Sound Vib. 212 905 908
35. Y.Z. Chen X.Y. Lin 2007 A convenient technique for evaluating angular frequency in some nonlinear oscillations J. Sound Vib. 305 552 562
36. Ö. Civalek 2007 Nonlinear dynamic response of MDOF systems by the method of harmonic differential quadrature (HDQ) Int. J. Struct. Eng. Mech. 25 2 201 217
37. T.C. Fung 2001 Solving initial value problems by differential quadrature method. Part 1: First-order equations Int. J. Numer. Methods Eng. 50 1411 1427
38. T.C. Fung 2002 Stability and accuracy of differential quadrature method in solving dynamic problems Comput. Methods Appl. Mech. Eng. 191 13-14 1311 1331