Analytical solution of the forced Duffing's oscillator

Journal of Sound and Vibration

Volumn 194, Issue 4, 1996, Pages 513-520

  Qaisi, M I ^a  

^a UNIVERSITY OF JORDAN   (Jordan)

Author keywords

[No Author keywords available]

Indexed keywords

DIFFERENTIAL EQUATIONS; FREQUENCIES; HARMONIC ANALYSIS; MATHEMATICAL TRANSFORMATIONS; NUMERICAL METHODS; PERTURBATION TECHNIQUES;

ANALYTICAL SOLUTION; DUFFING OSCILLATOR; HAMILTON PRINCIPLE; HARMONIC BALANCE SOLUTIONS; POWER SERIES METHOD; TIME VARIABLE;

OSCILLATORS (MECHANICAL);

EID: 0030192254     PISSN: 0022460X     EISSN: None     Source Type: Journal    
DOI: 10.1006/jsvi.1996.0375     Document Type: Article

References (10)

1. Y. UEDA 1980 in New Approaches to Nonlinear Problems in Dynamics (editor P. J. Holmes); Pennsylvania: SIAM. Steady motions exhibited by Duffing's equation: a picture book of regular and chaotic motions.
2. A. H. NAYFEH and D. T. MOOK 1979 Nonlinear Oscillations. New York: John Wiley.
3. M. N. HAMDAN and T. D. BURTON 1993 Journal of Sound and Vibration 166, 255-266. On the steady state response and stability of nonlinear oscillators using harmonic balance.
4. A. HASSAN 1989 Ph.D. Thesis, Washington State University. On the periodic and chaotic response of Duffing's oscillator.
5. W. SZEMPLINSKA-STUPNICKA 1988 International Journal of Nonlinear Mechanics 23, 257-277. Bifurcation of harmonic solutions leading to chaotic motion in the softening type Duffing's oscillator.
6. J. G. MARGALLO and J. B. BEJARANO 1987 Journal of Sound and Vibration 116, 591-595. A generalization of the method of harmonic balance.
7. A. HASSAN 1994 Journal of Sound and Vibration 178, 1-19. Use of transformation with higher order method of multiple scales to determine the steady state periodic response of harmonically excited nonlinear oscillators, part I: Transformation of Derivatives.
8. W. F. AMES 1968 Nonlinear Ordinary Differential Equations in Transport Processes. New York: Academic Press.
9. W. KAPLAN 1958 Ordinary Differential Equations. U.S.A.: Addison-Wesley Company.
10. E. T. WHITTAKER 1965 A Treatise on the Analytical Dynamics of Particles and Rigid Bodies. Cambridge University Press.