An iteration approach to nonlinear oscillations of conservative single-degree-of-freedom systems

Acta Mechanica

Volumn 170, Issue 1-2, 2004, Pages 69-75

  Li, P S ^a,b   Wu, B S ^a,b  

^a Jilin University ^*

^b JILIN UNIVERSITY   (China)

Author keywords

[No Author keywords available]

Indexed keywords

APPROXIMATION THEORY; DEGREES OF FREEDOM (MECHANICS); DIFFERENTIAL EQUATIONS; HARMONIC ANALYSIS; ITERATIVE METHODS; NONLINEAR SYSTEMS; PERTURBATION TECHNIQUES;

EARDRUM OSCILLATION; FOURIER SERIES; NONLINEAR OSCILLATIONS; NONLINEAR RESTORING FORCE;

OSCILLATIONS;

EID: 3142746199     PISSN: 00015970     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00707-004-0112-3     Document Type: Article

References (10)

1. Nayfeh, A. H., Mook, D. T.: Nonlinear oscillations. New York: Wiley 1979.
2. Hagedorn, P.: Nonlinear oscillations. Oxford: Clarendon 1988.
3. Mickens, R. E.: Oscillations in planar dynamic systems. Singapore: World Scientific Publishing 1996.
4. Krylov, N., Bogoliubov, N.: Introduction to nonlinear mechanics. Princeton, NJ: Princeton University Press 1943.
5. Bogoliubov, N., Mitropolsky, J. A.: Asymptotic methods in the theory of nonlinear oscillations. Delhi: Hindustan Publishing 1963.
6. Mickens, R. E.: Iteration procedure for determining approximate solutions to nonlinear oscillator equations. J. Sound Vibr. 116, 185-188 (1987).
7. Mickens, R. E.: Comments on the method of harmonic-balance. J. Sound Vibr. 94, 456-460 (1984).
8. Delamotte, B.: Nonperturbative method for solving differential equations and finding limit cycles. Phys. Rev. Lett 70, 3361-3364 (1993).
9. Rao, A. V., Rao, B. N.: Some remarks on the harmonic-balance method for mixed-parity nonlinear oscillations. J. Sound Vibr. 170, 571-576 (1994).
10. Lim, C. W., Wu, B. S.: A modified Mickens procedure for certain nonlinear-linear oscillators. J. Sound Vibr. 257, 202-206 (2002).