Grazing and chaos in a periodically forced, piecewise linear system

Journal of Vibration and Acoustics

Volumn 128, Issue 1, 2006, Pages 28-34

  Luo, Albert C J ^a  

^a SOUTHERN ILLINOIS UNIVERSITY EDWARDSVILLE   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

BIFURCATION (MATHEMATICS); FORECASTING; MATHEMATICAL MORPHOLOGY; MATHEMATICAL TECHNIQUES;

ANALYTIC PREDICTION; FRAGMENTIZED STRANGE ATTRACTOR; GRAZING BIFURCATION; GRAZING MANIFOLDS; MATHEMATICAL STRUCTURE; NONSMOOTH DYNAMICAL SYSTEMS; PIECEWISE LINEAR SYSTEM;

LINEAR SYSTEMS;

EID: 33645729668     PISSN: 10489002     EISSN: None     Source Type: Journal    
DOI: 10.1115/1.2149390     Document Type: Article

References (15)

1. Hartog, J. P. D., and Mikina, S. J., 1932, "Forced Vibrations With Non-linear Spring Constants," ASME J. Appl. Mech., 58, pp. 157-164.
2. Timoshenko, S., Young, D. H., and Weaver, W., 1974, "Piecewise Linear Systems," in Vibration Problems in Engineering, 4th ed., Van Nostrand, New York, pp. 186-201.
3. Shaw, S. W., and Holmes, P. J., 1983, "A Periodically Forced Piecewise Linear Oscillator," J. Sound Vib., 90(1), pp. 121-155.
4. Natsiavas, S., 1989, "Periodic Response and Stability of Oscillators With Symmetric Trilinear Restoring Force," J. Sound Vib., 134(2), pp. 315-331.
5. Kleczka, M., Kreuzer, E., and Schiehlen, W., 1992, "Local and Global Stability of a Piecewise Linear Oscillator," Philosophical Transactions: Physical Sciences and Engineering, Nonlinear Dynamics of Engineering Systems, 338(1651), pp. 533-546.
6. Theodossiades, S., and Natsiavas, S., 2000, "Non-linear Dynamics of Gearpair Systems With Periodic Stiffness and Backlash," J. Sound Vib., 229(2), pp. 287-310.
7. Li, G. X., Rand, R. H., and Moon, F. C., 1990, "Bifurcation and Chaos in a Forced Zero-stiffness Impact Oscillator," Int. J. Non-Linear Mech., 25(4), pp. 414-432.
8. Nordmark, A. B., 1991, "Non-periodic Motion Caused by Grazing Incidence in an Impact Oscillator," J. Sound Vib., 145, pp. 279-297.
9. di Bernardo, M., Budd, C. J., and Champneys, A. R., 2001, "Normal Form Maps for Grazing Bifurcation in n-Dimensional Piecewise-smooth Dynamical Systems," Physica D, 1(60), pp. 222-254.
10. di Bernardo, M., Kowalczyk, P., and Nordmark, A. B., 2002, "Bifurcation of Dynamical Systems With Sliding: Derivation of Normal Form Mappings," Physica D, 170, pp. 175-205.
11. Ivanov, A. P., 1993, "Analytical Methods in the Theory of Vibro-impact Systems," J. Appl. Math. Mech., 57, pp. 221-236.
12. Luo, A. C. J., and Menon, S., 2004, "Global Chaos in a Periodically Forced, Linear System With a Dead-zone Restoring Force," Chaos, Solitons Fractals, 1(9), pp. 1189-1199.
13. Dankowicz, H., and Zhao, X., 2005, "Local Analysis of Co-dimension-one and Co-dimension-two Grazing Bifurcations in Impacting Microactuators," Physica D, 2(02), pp. 238-257.
14. Filippov, A. F., 1988, Differential Equations with Discontinuous Righthand Sides, Kluwer Academic Publishers, Dordrecht.
15. Luo, A. C. J., 2005, "A Theory for Non-smooth Dynamical Systems on Connectable Domains," Commun. Nonlinear Sci. Numer. Simul., 1(0), pp. 1-55.