Analytical solution to nonlinear oscillation system of the motion of a rigid rod rocking back using max-min approach

Applied Mathematical Modelling

Volumn 34, Issue 9, 2010, Pages 2676-2684

  Ganji, S S ^a   Ganji, D D ^b   Davodi, A G ^c   Karimpour, S ^d  

^a ISLAMIC AZAD UNIVERSITY   (Iran)

^b BABOL NOSHIRVANI UNIVERSITY OF TECHNOLOGY   (Iran)

^c SHAHROOD UNIVERSITY OF TECHNOLOGY   (Iran)

^d SEMNAN UNIVERSITY   (Iran)

Author keywords

Max min approach (MMA); Motion of a rigid rod rocking back; Nonlinear oscillations

Indexed keywords

ANALYTICAL SOLUTIONS; EXACT RESULTS; MAX-MIN; NON-LINEARITY; NONLINEAR OSCILLATION; NONLINEAR OSCILLATION SYSTEMS; OSCILLATION PROBLEMS; OSCILLATION SYSTEM; PERIODIC BEHAVIOR; PERIODIC SOLUTION; RIGID RODS;

DECENTRALIZED CONTROL;

OSCILLATORS (MECHANICAL);

EID: 77952543371     PISSN: 0307904X     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.apm.2009.12.002     Document Type: Article

References (18)

1. Nayfeh A.H., Mook D.T. Nonlinear Oscillations 1979, Wiley, New York.
2. Hagedorn P. Non-linear Oscillations 1988, Clarendon, Oxford, Translated by Wolfram Stadler.
3. He Ji-Huan Some asymptotic methods for strongly nonlinear equations. Int. J. Mod. Phys. B 2006, 10:1141.
4. Ji-Huan He, Non-perturbative Methods for Strongly Nonlinear Problems, Dissertation, de-Verlag im Internet GmbH, 2006.
5. He Ji-Huan Variational iteration method: a kind of nonlinear analytical technique: some examples. Int. J. Nonlinear Mech. 1999, 34(4):699-708.
6. He Ji-Huan Homotopy perturbation technique. Comput. Method Appl. Mech. Eng. 1999, 178(3/4):257-262.
7. He Ji-Huan Modified straightforward expansion. Meccanica 1999, 34(4):287-289.
8. He Ji-Huan Modified Lindstedt-Poincare methods for some strongly nonlinear oscillations. Part I: a new transformation. Int. J. Nonlinear Mech. 2002, 37:315.
9. He Ji-Huan Iteration perturbation method for strongly nonlinear oscillations. J. Vib. Control 2001, 7(5):631-642.
10. He Ji-Huan Bookkeeping parameter in perturbation methods. Int. J. Nonlinear Sci. Numer. Simul. 2001, 2(3):257-264.
11. He Ji-Huan Preliminary report on the energy balance for nonlinear oscillations. Mech. Res. Commun. 2002, 29:107-111.
12. He Ji-Huan Some asymptotic methods for strongly nonlinear equations. Int. J. Mod. Phys. B 2006, 20:1141-1199.
13. He Ji-Huan Max-min approach to nonlinear oscillators. Int. J. Nonlinear Sci. Numer. Simul. 2008, 9(2):207-210.
14. He Ji-Huan He Chengtian's inequality and its applications. Appl. Math. Comput. 2004, 151(3):887-891.
15. Mickens R.E. Oscillations in Planar Dynamics Systems 1996, World Scientific, Singapore.
16. Mickens R.E. Iteration procedure for determining approximate solutions to non-linear oscillator equation. J. Sound Vib. 1987, 116:185-188.
17. Lim C.W., Wu B.S. A new analytical approach to the Duffing-harmonic oscillator. Phys. Lett. A 2003, 311:365.
18. Wu B.S., Lim C.W., He L.H. A new method for approximate analytical solutions to nonlinear oscillations of nonnatural systems. Nonlinear Dynam. 2003, 32:1.