Large amplitude non-linear oscillations of a general conservative system

International Journal of Non-Linear Mechanics

Volumn 39, Issue 5, 2004, Pages 859-870

  Wu, B S ^a   Lim, C W ^b  

^a JILIN UNIVERSITY   (China)

^b CITY UNIVERSITY OF HONG KONG   (Hong Kong)

Author keywords

Analytical approximation; General non linearity; Large amplitude; Oscillation

Indexed keywords

NONLINEAR SYSTEMS; OSCILLATIONS; PERTURBATION TECHNIQUES;

NON-LINEAR OSCILLATIONS;

DEGREES OF FREEDOM (MECHANICS);

EID: 0141882931     PISSN: 00207462     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0020-7462(03)00071-4     Document Type: Article

References (15)

1. Mickens R.E. Oscillations in Planar Dynamic Systems. 1996;World Scientific, Singapore.
2. Nayfeh A.H., Mook D.T. Nonlinear Oscillations. 1979;Wiley, New York.
3. Hagedorn P. Non-linear Oscillations. 1988;Clarendon, Oxford. (translated by Wolfram Stadler).
4. Bogoliubov N.N., Mitropolsky J.A. Asymptotic Methods in the Theory of Nonlinear Oscillations. 1963;Hindustan Publishing Co. Delhi, India.
5. Mickens R.E. Comments on the method of harmonic-balance. J. Sound Vib. 94:1984;456.
6. Delamotte B. Nonperterbative method for solving differential equations and finding limit cycles. Phys. Rev. Lett. 70:1993;3361.
7. Seelig F.F. Unrestricted harmonic-balance - a general method to evaluate periodic structures in time and-or space of arbitrary stability for non-linear chemical-reaction and reaction-diffusion systems 1. Theory and computer-program for time-dependent systems. Z. Naturforsch. A. 35:1980;1054.
8. Mickens R.E. A generalization of the method of harmonic balance. J. Sound Vib. 111:1986;515.
9. Huseyin K., Lin R. An intrinsic multiple-scale harmonic-balance method for nonlinear vibration and bifurcation problems. Int. J. Non-Linear Mech. 26:1991;727.
10. Yuste S.B. Comments on the method of harmonic-balance in which Jacobi elliptic functions are used. J. Sound Vib. 145:1991;381.
11. Summers J.L., Savage M.D. 2 timescale harmonic-balance 1. Application to autonomous one-dimensional nonlinear oscillators. Philos. Trans. R. Soc. London A. 340:1992;473.
12. Rao A.V., Rao B.N. Some remarks on the harmonic-balance method for mixed-parity nonlinear oscillations. J. Sound Vib. 170:1994;571.
13. Agrwal V.P., Denman H. Weighted linearization technique for period approximation in large amplitude nonlinear oscillations. J. Sound Vib. 99:1985;463.
14. Wu B.S., Li P.S. A method for obtaining approximate analytical periods for a class of nonlinear oscillators. Meccanica. 36:2001;167.
15. Lim C.W., Wu B.S., He L.H. A new approximate analytical approach for dispersion relation of the nonlinear Klein-Gordon equation. Chaos. 11:2001;843.