Elliptic harmonic balance method for two degree-of-freedom self-excited oscillators

Communications in Nonlinear Science and Numerical Simulation

Volumn 14, Issue 3, 2009, Pages 916-922

  Chen, Y M ^a   Liu, J K ^a  

^a SUN YAT SEN UNIVERSITY   (China)

Author keywords

Elliptic function; Harmonic balance; Limit cycle; Self excited oscillator

Indexed keywords

DEGREES OF FREEDOM (MECHANICS); HARMONIC FUNCTIONS; NUMERICAL METHODS; OSCILLATORS (MECHANICAL);

ANALYTICAL METHOD; ELLIPTIC-FUNCTION; HARMONIC BALANCE; HARMONIC BALANCE METHOD; HARMONIC BALANCING; LIMIT-CYCLE; NON-LINEAR OSCILLATORS; SELF-EXCITED OSCILLATORS; SINGLE DEGREE OF FREEDOMS; TWO-DEGREE-OF-FREEDOM;

HARMONIC ANALYSIS;

EID: 50249175067     PISSN: 10075704     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.cnsns.2007.11.008     Document Type: Article

References (21)

1. Davis H.T. Introduction to nonlinear differential equations (1962), Dover, New York
2. Barkham P.G.D., and Soudack A.C. An extension to the method of Kryloff and Bogoliuboff. Int J Control 10 (1969) 377-392
3. Qiao Z.C., and Dai S.Q. Limit cycle analysis of a class of strongly nonlinear oscillation equation. Nonlinear Dyn 10 (1996) 221-233
4. Chen S.H., and Cheung Y.K. An elliptic perturbation method for certain strongly nonlinear oscillators. J Sound Vib 192 2 (1996) 453-464
5. Chen S.H., and Cheung Y.K. An elliptic Lindstedt-Poincaré method for certain strongly non-linear oscillators. Nonlinear Dyn 12 (1997) 199-213
6. Belhqa M., Fiedler B., and Lakrad F. Homoclinic connections in strongly self-excited nonlinear oscillators: the Melnikov function and the flliptic Lindstedt-Poincaré method. Nonlinear Dyn 23 (2000) 67-86
7. Waluya S.B., and Van Horssen W.T. On approximation of first integral for strongly nonlinear oscillators. Nonlinear Dyn 32 (2003) 109-141
8. Cveticanin L. Vibrations of a coupled two-degree-of-freedom system. J Sound Vib 247 2 (2001) 279-292
9. Yu Y.X., Wang Q., and Zhang H.Q. The extension of the Jacobi elliptic function rational expansion method. Commun Nonlinear Sci Numer Simulat 12 (2007) 702-713
10. Zhang H.Q. Extended Jacobi elliptic function expansion method and its applications. Commun Nonlinear Sci Numer Simulat 12 (2007) 627-635
11. Yuste S.B., and Bejarano J.D. Construction of approximate analytical solutions of a new class of non-linear oscillator equations. J Sound Vib 110 2 (1986) 347-350
12. Margallo J.G., Bejarano J.D., and Yuste S.B. Generalized Fourier series for the study of limit cycles. J Sound Vib 125 1 (1988) 13-21
13. Yuste S.B. Cubication of non-linear oscillators using the principle of harmonic balance. Int J Nonlinear Mech 27 3 (1992) 347-356
14. Margallo J.G., and Bejarano J.D. Generalized Fourier series and limit cycles of generalized van der Pol oscillators. J Sound Vib 136 3 (1990) 453-466
15. Margallo J.G., and Bejarano J.D. The limit cycles of the generalized Rayleigh-Lienard oscillator. J Sound Vib 125 1 (1992) 13-21
16. Alex E.Z. Application of Jacobian elliptic functions to the analysis of the steady-state solution of the damped Duffing equation with driving force of elliptic type. Nonlinear Dyn 42 (2005) 175-184
17. Alex E.Z. A general solution of the Duffing equation. Nonlinear Dyn 45 (2006) 227-235
18. Belhaq M., and Lakrad F. On the elliptic harmonic balance method for mixed parity nonlinear oscillators. J Sound Vib 233 5 (2000) 935-937
19. Zhao L.C., and Yang Z.C. Chaotic motions of an airfoil with nonlinear stiffness in incompressible flow. J Sound Vib 138 2 (1989) 245-254
20. Liu J.K., and Zhao L.C. Bifurcation analysis of airfoils in incompressible flow. J Sound Vib 154 1 (1991) 117-124
21. Liu L.P., and Dowell E.H. The secondary bifurcation of an aeroelastic airfoil motion: effect of high harmonics. Nonlinear Dyn 37 (2004) 31-49