Design of Quasi-periodic Impact Motion of an Impact Shaker System

WU Xin, WEN Gui-lin, HE Li-ping, XU Hui-dong, WEI Ke-xiang

Abstract

The Poincaré map of periodic motion was established, and the bifurcation diagram of two parameters was obtained by using an explicit critical criterion without using eigen values when the difficulties caused by the classical Neimark-Sacker bifurcation critical criterion described by the properties of eigenvalues were considered. The bifurcation diagram helps to proactively design the quasi-periodic impact motion of the system. Then, the stability of the quasi-periodic impact motion was further analyzed by utilizing the center manifold and normal formal theory. Finally, numerical experiments verify that the stable quasi-periodic impact motion can be generated at chosen parameters points.

 

 

Keywords: shaker system,  impact vibration,  Neimark-Sacker bifurcation,  quasi-periodic impact motion,  stability


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References


WAGG D J. Periodic sticking motion in a two-degree-of-free-dom impact oscillator [J]. International Journal of Non-Linear Mechanics. 2005. 40(8): 1076-1087.

WEN G L, XIE J H. Period-doubling bifurcation and non-typical routes to chaos of a two-degree-of-freedom vibro-impact system[J]. Journal of Applied Mechanics. 2001, 68(4). 670 -674.

LUO A С J. CHEN L D. Periodic motions and grazing in a harmonically forced piecewise linear oscillator with impacts [J]. Chaos Soli tons S- Fractals. 2005, 24(2):567 —578.

AGUIAR К К. WEBER H I. Mathematical modeling and ex-perimental investigation of an embedded vibro-impact system [J]. Nonlinear Dynamics. 2011 . 65(3): 317 — 334.

LUO G W, XIE J H. Bifurcations and chaos in a system with impacts[J]. Physica D. 2001. 148(3/4): 183-200.

ZHANG Si-jin. YIN Lei-lei. WEN Gui-lin. Analysis of the global bifurcations and coexistence of multiple solutions for a general quasi-Hamiltonian vibro-impact system [J]. Journal of Hunan University: Natural Sciences.2014. 41(10): 55 —61. (In Chinese)

LUO Guan-wei. XIE Jian-hua. Stability and bifurcation of periodic motions of the inertial shakers[J]. Journal of Mechanical Engineering. 2003. 39(1): 74 —78. (In Chinese)

DING Wang-cai. XIE Jian-hua. LI Wan-xiang. Dynamics analysis of two-parameter family in a case of strong resonance of vibro-impact system [J]. Chinese Journal of Computational Mechanics. 2004. 21(6): 658 — 664. (In Chinese)

WEN G L. Criterion to identify Hopf bifurcations in maps of arbitrary dimension [J]. Physical Review E. 2005. 72 ( 2 ): 026201-026204.

LUO Guan-wei. XIE Jian-hua. Periodic motion and bifurcation of vibro-impact system[MJ. Beijing: Science Press. 2004: 187 — 188. (In Chinese)

DAMICO M B. MOIOLA J L. PAOLINI E E. Controlling bifurcations in maps via a frequency domain approach [J]. Dynamics of Continuous Discrete and Impulsive Systems Series Bapplicalions & Algorithms. 2003. 10(6): 781 — 798.

KUZNETSOV Y A. Elements of applied bifurcation theory [М]. 2nd ed. New York: Springer-Verlag. 1998: 185—187.

IOOSS G. Bifurcation of maps and applications [M]. Amsterdam: North-Holland, 1979:28 —31.


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