Effect of external excitations on a nonlinear system with time delay

Nonlinear Dynamics

Volumn 41, Issue 4, 2005, Pages 385-402

  Ji, J C ^a   Hansen, Colin H ^a   Li, Xinye ^b  

^a UNIVERSITY OF ADELAIDE   (Australia)

^b HEBEI UNIVERSITY OF TECHNOLOGY   (China)

Author keywords

Coexistence of stable motions; Hopf bifurcation; Non resonances; Quasi periodic motions; Super harmonic resonances; Time delay; Two degree of freedom nonlinear system

Indexed keywords

BIFURCATION (MATHEMATICS); DEGREES OF FREEDOM (MECHANICS); ELECTRIC EXCITATION; OSCILLATIONS; RESONANCE;

EXTERNAL EXCITATION; HOPF BIFURCATION; NON-RESONANCES; QUASI-PERIODIC MOTIONS; SUPER HARMONIC RESONANCES; TIME DELAY; TWO DEGREE-OF-FREEDOM NONLINEAR SYSTEM;

NONLINEAR SYSTEMS;

EID: 23944482916     PISSN: 0924090X     EISSN: None     Source Type: Journal    
DOI: 10.1007/s11071-005-0418-2     Document Type: Article

References (17)

1. Gilsinn, D.E., 'Estimating critical Hopf bifurcation parameters for a second-order delay differential equation with application to machine tool chatter', Nonlinear Dynamics 30, 2002, 103-154.
2. Kalmar-Nagy, T., Stepan, G., and Moon, F. C., 'Subcritical Hopf bifurcation in the delay equation model for machine tool vibrations', Nonlinear Dynamics 26, 2001, 121-142.
3. Raghothama, A. and Narayanan, S., 'Periodic response and chaos in nonlinear systems with parametric excitation and time delay', Nonlinear Dynamics 27, 2002, 341-365.
4. Ji, J. C. and Leung, A. Y. T., 'Resonances of a non-linear SDOF system with two time-delays in linear feedback control', Journal of Sound and Vibration 253, 2002, 985-1000.
5. Maccari, A., 'The resonances of a parametrically excited van der Pol oscillator to a time delay state feedback', Nonlinear Dynamics 26, 2001, 105-119.
6. Hu, H. Y., Dowell, E. H., and Virgin, L. N., 'Resonances of a harmonically forced Duffing oscillator with time delay state feedback', Nonlinear Dynamics 15, 1998, 311-327.
7. Plaut, R. H. and Hsieh, J. C., 'Non-linear structural vibrations involving a time delay in damping', Journal of Sound and Vibration 117, 1987, 497-510.
8. Wirkus, S. and Rand, R., 'The dynamics of two coupled van der Pol oscillators with delay coupling', Nonlinear Dynamics 30, 2002, 205-221.
9. Ji, J. C. and Hansen, C. H., 'Hopf bifurcation of a magnetic bearing system with time delay', ASME Journal of Vibration and Acoustics, in press.
10. Hale, J., Theory of Functional Differential Equations, Springer-Verlag, New York, 1977.
11. Hale, J. K. and Verduyn Lunel, S. M., Introduction to Functional Differential Equations, Springer-Verlag, New York, 1993.
12. Halanay, A., Differential Equations, Stability, Oscillations, Time Lags, Academic Press, New York, 1966.
13. Yu,P, 'Computation of normal forms via a perturbation technique', Journal of Sound and Vibration 211, 1998, 19-38.
14. Nayfeh, A. H. and Mook, D. T., Nonlinear Oscillations, Wiley-Interscience, New York, 1979.
15. Yu, P., Taneri, U., and Huseyin, K., 'Forced oscillations, bifurcations and stability of a molecular system (part I): Non-resonance', International Journal of Systems Science 27, 1996, 1339-1350.
16. Yu, P., Taneri, U., and Huseyin, K., 'Forced oscillations, bifurcations and stability of a molecular system (part II): Resonances', International Journal of Systems Science 27, 1996, 1351-1361.
17. Hairer, E., Norsett, S. P., and Wanner, G., Solving Ordinary Differential Equations I. Nonstiff Problems, 2nd revised edn., Springer-Verlag, Berlin, 1993.