Nonlinear Vibrations of an Inclined Cable

[+] Author and Article Information
A. Berlioz1

Laboratoire de Dynamique des Machines et des Structures CNRS UMR-5006, Institut National des Sciences Appliquées de Lyon, F69621 Villeurbanne, Franceberlioz@cict.fr

C-H. Lamarque

Laboratoire de GéoMatériaux CNRS URA-1652,  Ecole Nationale des Travaux Publics de l’Etat, F69518 Vaulx-en-Velin Cedex, Franceclaude.lamarque@entpe.fr


Now at Laboratoire de Génie Mécanique de Toulouse EA814, Université Paul Sabatier, 31062 Toulouse Cedex 4, France

J. Vib. Acoust 127(4), 315-323 (Sep 02, 2004) (9 pages) doi:10.1115/1.1924638 History: Received July 23, 2003; Revised September 02, 2004

The goal of this experimental and theoretical study is to highlight the nonlinear dynamic behavior of an inclined cable consisting of a steel wire surrounded by copper wire. Measurements around the first frequency of vibration of the cable in and out of plane and around the second harmonic of this frequency were also carried out. These experimental results are in good agreement with the numerical results obtained via the multiple scale method applied to finite (1- and 2- degree-of-freedom (DOF) models). In order to prepare further investigations related to more complicated behavior, a 4-DOF model is added.

Copyright © 2005 by American Society of Mechanical Engineers
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Figure 2

Primary resonance, amplitude at X=L∕2 versus external frequency: fitted (o-o), experimental (◆)

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Figure 3

Subsystem for initial tension force in the cable

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Figure 4

Camera sensors and cable

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Figure 5

Block diagram of the experimental setup

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Figure 6

Subharmonic resonance, amplitude at X=L∕2 versus external frequency, T0=80N, Z0=3×10−4m: analytical stable branch (+), analytical unstable branch (◻), and experimental (−)

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Figure 7

Primary resonance, amplitude at X=L∕2 versus external frequency, T0=120N, Z0=0.25mm: (a) In-plane displacement (camera 1) and (b) Out-of-plane displacement (camera 2)

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Figure 8

Combination of in-plane and out-of-plane motions. Primary resonance, large Z0. In-plane (◇), out-of-plane (∎): (a) experimental results and (b) theoretical results computed from Eqs. 26,26,26,26.

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Figure 9

Sub-harmonic resonance, amplitude at X=L∕2 versus external frequency: (a) in-plane displacement (camera 1) and (b) out-of-plane displacement (camera 2)



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