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TECHNICAL PAPERS

Nonlinear Transient Localization and Beat Phenomena Due to Backlash in a Coupled Flexible System

[+] Author and Article Information
Xianghong Ma, Alexander F. Vakakis

Department of Mechanical and Industrial Engineering, University of Illinois at Urbana-Champaign, Urbana, IL 61801

J. Vib. Acoust 123(1), 36-44 (Aug 01, 2000) (9 pages) doi:10.1115/1.1320813 History: Received October 01, 1999; Revised August 01, 2000
Copyright © 2001 by ASME
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References

Figures

Grahic Jump Location
Configuration of the coupled rod system
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(a) The displacements at the middle points, (b) The energy distribution, (c) FFT of the displacements at the middle points of rod 1 ([[dashed_line]]), rod 2 (–) when a=0.0m,b=0.0m,S=9.0 * 104N/m
Grahic Jump Location
(a) The displacements at the middle points, (b) The energy distribution, (c) FFT of the displacements at the middle points of rod 1 ([[dashed_line]]), rod 2 (–) when a=0.002m,b=0.03m,S=9.0 * 104N/m
Grahic Jump Location
(a) The displacements at the middle points, (b) The energy distribution, (c) FFT of the displacements at the middle points of rod 1 ([[dashed_line]]), rod 2 (–) when a=0.0m,b=0.0m,S=2.6 * 104N/m
Grahic Jump Location
(a) The displacements at the middle points, (b) The energy distribution, (c) FFT of the displacements at the middle points of rod 1 ([[dashed_line]]), rod 2 (–) when a=0.002m,b=0.03m,S=2.6 * 104N/m
Grahic Jump Location
(a) The displacements at the middle points, (b) The energy distribution, (c) FFT of the displacements at the middle points of rod 1 ([[dashed_line]]), rod 2 (–) when a=0.0m,b=0.0m,S=3.5 * 104N/m
Grahic Jump Location
(a) The displacements at the middle points, (b) The energy distribution, (c) FFT of the displacements at the middle points of rod 1 ([[dashed_line]]), rod 2 (–) when a=0.002m,b=0.03m,S=3.5 * 104N/m
Grahic Jump Location
(a) The first K-L mode shape of rod 1 (–), rod 2 ([[dashed_line]]), when a=0.0m,b=0.005m,S=104N/m, (b) The first K-L mode shape of rod 1 (–), rod 2 ([[dashed_line]]), when a=0.0m,b=0.037m,S=104N/m
Grahic Jump Location
(a) Numerical simulation of the time response at the middle points of rod 1 ([[dashed_line]]), rod 2 (–) when a=0.0m,b=0.001m,S=104N/m, (b) Reconstruction of the responses using 2 K-L modes
Grahic Jump Location
(a) Numerical simulation of the time response at the middle points of rod 1 ([[dashed_line]]), rod 2 (–) when a=0.0m,b=0.037m,S=104N/m, (b) Reconstruction of the responses using 2 K-L modes
Grahic Jump Location
(a) The energy transfer between the first “.-” and second “-” K-L modes with varying stiffness S, when a=0.002m,b=0.03m, (b) The energy transfer between the first “.-” and second “o-” K-L modes with varying b, when a=0.002m,S=2.6 * 104N/m
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Components of the system for constructing the 2-DOF model
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The Poincare map of the system with S=2.6 * 104N/m,a=0.002m,b=0.03m
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The time evolution of a1(t) ([[dashed_line]]) and a2(t) (–): (A) periodic orbit, (B) subharmonic orbit
Grahic Jump Location
The Poincare map of the system with S=3.5 * 104N/m,a=0.002m,b=0.03m
Grahic Jump Location
The time evolution of a1(t) ([[dashed_line]]) and a2(t) (–): (A) periodic orbit, (B) subharmonic orbit 1, (C) subharmonic orbit 2
Grahic Jump Location
The Poincare map of the system with S=9.0 * 104N/m,a=0.002m,b=0.03m
Grahic Jump Location
The time evolution of a1(t) ([[dashed_line]]) and a2(t) (–): (A) periodic orbit, (B) subharmonic orbit

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