COEXISTING PERIODIC ORBITS IN VIBRO-IMPACTING DYNAMICAL SYSTEMS

Applied Mathematics and Mechanics (English Edition) ›› 2003, Vol. 24 ›› Issue (3): 261-273.

COEXISTING PERIODIC ORBITS IN VIBRO-IMPACTING DYNAMICAL SYSTEMS

李群宏, 陆启韶

School of Science, Beijing University of Aeronautics and Astronautics, Beijing 100083, P. R. China

收稿日期:2001-05-28 修回日期:2002-12-10 出版日期:2003-03-18 发布日期:2003-03-18
基金资助:
the National Natural Science Foundation of China(19990510, 19872010);the Doctoral Foundation of National Educational Ministry of China(98000619)

COEXISTING PERIODIC ORBITS IN VIBRO-IMPACTING DYNAMICAL SYSTEMS

LI Qun-hong, LU Qi-shao

School of Science, Beijing University of Aeronautics and Astronautics, Beijing 100083, P. R. China

Received:2001-05-28 Revised:2002-12-10 Online:2003-03-18 Published:2003-03-18
Supported by:
the National Natural Science Foundation of China(19990510, 19872010);the Doctoral Foundation of National Educational Ministry of China(98000619)

摘要/Abstract

摘要： A method is presented to seek for coexisting periodic orbits which may be stable or unstable in piecewise-linear vibro-impacting systems. The conditions for coexistence of single impact periodic orbits are derived, and in particular, it is investigated in details how to assure that no other impacts will happen in an evolution period of a single impact periodic motion. Furthermore, some criteria for nonexistence of single impact periodic orbits with specific periods are also established. Finally, the stability of coexisting periodic orbits is discussed, and the corresponding computation formula is given. Examples of numerical simulation are in good agreement with the theoretic analysis.

Abstract: A method is presented to seek for coexisting periodic orbits which may be stable or unstable in piecewise-linear vibro-impacting systems. The conditions for coexistence of single impact periodic orbits are derived, and in particular, it is investigated in details how to assure that no other impacts will happen in an evolution period of a single impact periodic motion. Furthermore, some criteria for nonexistence of single impact periodic orbits with specific periods are also established. Finally, the stability of coexisting periodic orbits is discussed, and the corresponding computation formula is given. Examples of numerical simulation are in good agreement with the theoretic analysis.

中图分类号:

O175
O322

李群宏;陆启韶. COEXISTING PERIODIC ORBITS IN VIBRO-IMPACTING DYNAMICAL SYSTEMS[J]. Applied Mathematics and Mechanics (English Edition), 2003, 24(3): 261-273.

LI Qun-hong;LU Qi-shao . COEXISTING PERIODIC ORBITS IN VIBRO-IMPACTING DYNAMICAL SYSTEMS[J]. Applied Mathematics and Mechanics (English Edition), 2003, 24(3): 261-273.

参考文献

[1] Guckenheimer J, Holmes P. Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields [M]. New York: Springer-Verlag, 1986.
[2] Wigins S. Introduction to Applied Nonlinear Dynamical Systems and Chaos [M].(Reprinted) . New York: Springer-Verlag, 1991.
[3] Wiggins S. Global Bifurcations and Chaos,Analytical Methods[M].New York: Springer-Verlag,1988.
[4] Bazejczyk-Okolewska B, Kapitaniak T. Co-existing attractors of impact oscillator[J]. Chaos, Solitons & Fractals, 1998,9(8): 1439-1443.
[5] Feudel U, Grebogi C, Poon L, Yorke J A. Dynamical properties of a simple mechanical system with a large number of coexisting periodic attractors[J]. Chaos, Solttons & Fractals, 1998,9(1/2):171-180.
[6] Whiston G S. Global dynamics of a vibro-impacting linear oscillator[J]. J Sound Vib, 1987,118(3):395-424.
[7] Shaw S W, Holmes P J. A periodically forced piecewise linear oscillator[J].J Sound Vib,1983,90(1):129-155.
[8] Ivanov A P. Stabilization of an impact oscillator near grazing incidence owing to resonance[J]. J Sound Vib, 1993,162(3): 562-565.
[9] Whiston G S. Impacting under harmonic excitation[J].J Sound Vib,1979,67(2):179-186.
[10] Whiston G S. The vibro-impact response of a harmonically excited and preloaded one-dimensional linear oscillator[J]. J Sound Vib, 1987,115(2): 303-319.
[11] Nordmark A B. Non-periodic motion caused by grazing incidence in an impact oscillator[J]. J Sound Vib, 1991,145(2):279-297.
[12] Foale S, Bishop S R. Dynamical complexities of forced impacting systems [J]. Phil Trans Royal Soc London A, 1992,338(4):547-556.
[13] Nordmark A B. Effects due to low velocity in mechanical oscillators [J]. Int ,J Bifurcation and Chaos, 1992,2(3):597-605.
[14] Shaw S W, Rand R H. The transifion to chaos in a simple mechanical system[J]. Int J Nonlinear Mech, 1989,24(1):41-56.

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COEXISTING PERIODIC ORBITS IN VIBRO-IMPACTING DYNAMICAL SYSTEMS

COEXISTING PERIODIC ORBITS IN VIBRO-IMPACTING DYNAMICAL SYSTEMS

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