Response of nonlinear system to random narrow-band excitation with time delay state feedback

Zhendong Gongcheng Xuebao/Journal of Vibration Engineering

Volumn 19, Issue 1, 2006, Pages 57-64

  Sun, Zhong Kui ^a   Xu, Wei ^a   Yang, Xiao Li ^a,b  

^a NORTHWESTERN POLYTECHNICAL UNIVERSITY   (China)

^b SHAANXI NORMAL UNIVERSITY   (China)

Author keywords

Bifurcation; Nonlinear vibration; Principal resonance response; Stability; Time delay

Indexed keywords

ACTUATORS; BIFURCATION (MATHEMATICS); COMPUTER SIMULATION; CONTROL EQUIPMENT; CONTROL SYSTEMS; FEEDBACK; RESONANCE; STABILITY; VIBRATIONS (MECHANICAL);

DUFFING OSCILLATOR; NONLINEAR VIBRATION; NUMERICAL SIMULATION; PRINCIPAL RESONANCE RESPONSE; RANDOM NARROW BAND EXCITATION; TIME DELAY;

NONLINEAR SYSTEMS;

EID: 33744745361     PISSN: 10044523     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (20)

1. Hale J K, Lunel S M V. Introduction to functional differential equations[M]. New York: Springer-Verlag, 1993.
2. Kaplan J K, Yorke J A. Ordinary differential equations which yield periodic solutions of differential delay equations[J]. Journal of Mathematical Analysis and Applications, 1974, 48: 317-324.
3. Belair J, Campell S A. Stability and bifurcation of equilibria in a multiple-delayed differential equation[J]. SIAM J. Appl. Math., 1994, 54(5): 1402-1424.
4. Compell S A, Belar J, Ohira T. Complex dynamics and multistability in a damped harmonic oscillator with delayed negative feedback[J]. Chaos, 1995, 5(4): 640-645.
5. Casal A, Freeman M A. Poincare-Lindstedt approach to bifurcation problem for differential delay equations[J]. IEEE Transactions on Automatic Control, 1980, 25: 967-973.
6. McDonald N. Harmonic balance in delay-differential equations[J]. Journal of Sound and Vibration, 1995, 186: 649-656.
7. Das S L, Chatterjee A. Multiple scales without center manifold reductions for delay differential equations near Hopf bifurcations[J]. Nonlinear Dynamics, 2002, 30: 323-335.
8. Xu J, Yu P. Delay-induced bifurcations in a nonautonomous system with delayed velocity feedbacks[J]. Int. J. Bifurcation and Chaos, 2004, 14(8): 2777-2798.
9. Xu J, Chung K W. Effects of time delayed position feedback on a van der Pol-Duffing oscillator[J]. Physica D, 2003, 180: 17-39.
10. Horsthemke W, Lefever R. Noise-induced transitions, theory and applications in physics, chemistry, and biology[M]. Springer Series in Synergetics Vol.15, New York: Springer-Verlag, 1984.
11. Longtin A. Noise-induced transitions at a Hopf bifurcation in a first-order delay-differential equation[J]. Phys. Rev. A, 1991, 44: 4801-4813.
12. Longtin A, Milton J G, Bos J E, et al. Noise and critical behavior of the pupil light reflex at oscillation onset[J]. Phys. Rev. A, 1990, 41: 6992-7005.
13. Wedig W V. Invariant measures and Lyapunov exponents for generalized parameter fluctuations[J]. Structural Safety, 1990, 8: 13-25.
14. Hu H Y, Wang Z H. Dynamics of controlled mechanical systems with delayed feedback[M]. Berlin Heidelberg: Springer-Verlag, 2002.
15. Hayfeh A H, Balakumar B. Applied nonlinear dynamics: analytical, computational, and experimental methods[M]. New York: John Wiley and Sons, 1995.
16. Nayfeh A H, Mook D T. Nonlinear oscillations[M]. New York: John Wiley and Sons, 1979.