A modified elliptic Lindstedt-Poincaré method for certain strongly non-linear oscillators

Journal of Sound and Vibration

Volumn 273, Issue 4-5, 2004, Pages 921-932

  Yang, C H ^a,b   Zhu, S M ^b   Chen, S H ^b  

^a CENTRAL CHINA NORMAL UNIVERSITY   (China)

^b SUN YAT SEN UNIVERSITY   (China)

Author keywords

[No Author keywords available]

Indexed keywords

APPROXIMATION THEORY; FUNCTIONS; PERTURBATION TECHNIQUES; PROBLEM SOLVING;

JACOBIAN ELLIPTIC FUNCTIONS; MULTIPLE TIME SCALES (MTS) METHOD;

NONLINEAR EQUATIONS;

EID: 2542590842     PISSN: 0022460X     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0022-460X(03)00565-0     Document Type: Article

References (11)

1. A.H. Nayfeh, Introduction to Perturbation Techniques, Wiley, New York, 1981.
2. R.E. Mickens, Nonlinear Oscillations, Cambridge University Press, New York, 1981.
3. R.E. Mickens, K. Oyedeji, Construction of approximate analytical solutions to a new class of nonlinear oscillator equations, Journal of Sound and Vibration 102 (1985) 579-582.
4. S.B. Yuste, J.D. Bejarano, Construction of approximate analytical solutions to a new class of nonlinear oscillator equations, Journal of Sound and Vibration 110 (1986) 347-350.
5. J.G. Margallo, J.D. Bejarano, S.B. Yuste, Generalized Fourier series for the study of limit cycles, Journal of Sound and Vibration 125 (1988) 13-21.
6. J.G. Margallo, J.D. Bejarano, S.B. Yuste, Generalized Fourier series and limit cycles of generalized Van der Pol oscillators, Journal of Sound and Vibration 136 (1990) 453-466.
7. S.B. Yuste, J.D. Bejarano, Extension and improvement to the 'krylov-bogoliubov methods using elliptic functions, International Journal of Control 49 (1989) 1127-1141.
8. V.T. Coppola, R.H. Rand, Averaging using elliptic functions: approximations of limit cycle, Acta Mechanica 81 (1990) 125-142.
9. S.H. Chen, Y.K. Cheung, An elliptic perturbation method for certain strongly non-linear oscillators, Journal of Sound and Vibration 192 (2) (1996) 453-464.
10. S.H. Chen, Y.K. Cheung, An elliptic Lindstedt-Poincaré method for certain strongly non-linear oscillators, Nonlinear Dynamics 12 (1997) 199-213.
11. Y.K. Cheung, S.H. Chen, S.L. Lau, A modified Lindstedt-Poincaré method for certain strongly non-linear oscillators, Nonlinear Mechanics 26 (3/4) (1991) 367-378.