An Unsymmetrical Motion in a Horizontal Impact Oscillator

[+] Author and Article Information
Albert C. J. Luo

Department of Mechanical and Industrial Engineering, Southern Illinois University Edwardsville, Edwardsville, IL 62034-1805, USAEmail: aluo@siue.edu

J. Vib. Acoust 124(3), 420-426 (Jun 12, 2002) (7 pages) doi:10.1115/1.1468869 History: Received February 01, 2001; Revised February 01, 2002; Online June 12, 2002
Copyright © 2002 by ASME
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Grahic Jump Location
A mechanical model of an impact oscillator under a harmonic excitation
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The P-1 motion with 2-impacts during N-periods of the base motion: (a) commutative diagram and (b) physical response
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Stability and bifurcation conditions for symmetrical and unsymmetrical period-1 motions (d=10.0, e=0.5,ω=π, N=1), and the critical points are marked by circular symbols. The dark solid, dot-dashed, dotted and dashed curves represent stable node, first saddle-node (unstable), stable focus and second saddle-node (unstable) motions, respectively.
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Regions for symmetrical and unsymmetrical period-1 motions (R-I : non-RL motion existence, R-II : symmetrical motion, R-III : unsymmetrical motion, and R-IV : period-2 motion and other motion) (d=10.0, e=0.5, N=1)
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A numerical prediction of symmetric, unsymmetrical period-1, period-2 motion of the LR-model and LLR (or RLL) periodic motion to chaos (d=10.0, e=0.5, ω=π, N=1). The circular symbols stand for saddle-node and period-doubling bifurcations.
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Symmetrical period-1 motion for LR model (A=2.2,dy0/dt=−17.8188, and φ=5.4128,d=10.0,e=0.5,ω=π,N=1)
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Unsymmetrical period-1 motion for LR model (A=4.5,dy0/dt=−24.8543, and φ=4.7607,d=10.0,e=0.5,ω=π,N=1)
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Unsymmetrical period-2 motion for LR model after period-doubling bifurcation. (A=5.45,dy0/dt=−28.2211, and φ=4.5926,d=10.0,e=0.5,ω=π,N=1)
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Unsymmetrical period-2 motion after motion model switching to the LLR model (A=5.45,dy0/dt=−28.2211, and φ=4.5926,d=10.0,e=0.5,ω=π,N=1)
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Chaotic attractors (A=5.8) relative to unsymmetrical motions (dy0/dt=−31.2003,φ=5.6848 (upper), and dy0/dt=−25.2768,φ=4.7571 (lower), d=10.0,e=0.5,ω=π,N=1)




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