An accurate closed-form approximate solution for the quintic Duffing oscillator equation

Mathematical and Computer Modelling

Volumn 52, Issue 3-4, 2010, Pages 637-641

  Belendez A ^a   Bernabeu, G ^a   Frances J ^a   Mendez D I ^a   Marini, S ^a  

^a UNIVERSITY OF ALICANTE   (Spain)

Author keywords

Approximate solutions; Chebyshev polynomials; Nonlinear oscillator; Quintic Duffing equation

Indexed keywords

APPROXIMATE SOLUTION; CHEBYSHEV POLYNOMIALS; DUFFING EQUATIONS; NON-LINEAR OSCILLATORS; QUINTIC;

APPROXIMATION ALGORITHMS; DIFFERENTIAL EQUATIONS; OSCILLATORS (MECHANICAL); POLYNOMIALS;

NONLINEAR EQUATIONS;

EID: 77954863397     PISSN: 08957177     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.mcm.2010.04.010     Document Type: Article

References (10)

1. Nayfeh A.H. Problems in Perturbations 1985, Wiley, New York.
2. Mickens R.E. Oscillations in Planar Dynamics Systems 1996, World Scientific, Singapore.
3. Lai S.K., Lim C.W., Wu B.S., Wang C., Zeng Q.C., He X.F. Newton-harmonic balancing approach for accurate solutions to nonlinear cubic-quintic Duffing oscillators. Appl. Math. Modelling 2009, 33:852-866.
4. Ramos J.I. On Lindstedt-Poincaré techniques for the quintic Duffing equation. Appl. Math. Comput. 2007, 193:303-310.
5. Lim C.W., Xu R., Lai S.K., Yu Y.M., Yang Q. Nonlinear free vibration of an elastically restrained beam with a point mass via the Newton-harmonic balancing approach. Int. J. Nonlinear Sci. Numer. Simul. 2009, 10:661-674.
6. Denman J.H. An approximate equivalent linearization technique for nonlinear oscillations. J. Appl. Mech. 1969, 36:358-360.
7. Jonckheere R.E. Determination of the period of nonlinear oscillations by means of Chebyshev polynomials. ZAMM Z. Angew. Math. Mech. 1971, 55:389-393.
8. Bravo Yuste S. Cubication of non-linear oscillators using the principle of harmonic balance. Int. J. Non-Linear Mech. 1992, 27:347-356.
9. Beléndez A., Álvarez M.L., Fernández E., Pascual I. Cubication of conservative nonlinear oscillators. Eur. J. Phys. 2009, 30:973-981.
10. Beléndez A., Méndez D.I., Fernández E., Marini S., Pascual I. An explicit approximate solution to the Duffing-harmonic oscillator by a cubication method. Phys. Lett. A 2009, 373:2805-2809.