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TECHNICAL PAPERS

Nonlinear Dynamics and Bifurcations of an Axially Moving Beam

[+] Author and Article Information
F. Pellicano

Dip. Scienze dell’lngegneria, Università di Modena e Reggio Emilia, 41100 Modena, Italy e-mail: frank@unimo.it

F. Vestroni

Dip. di Ingegneria Strutturale e Geotecnica, Università di Roma “La Sapienza,” 00184 Roma, Italy e-mail: vestroni@scilla.ing.uniroma1.it

J. Vib. Acoust 122(1), 21-30 (Aug 01, 1999) (10 pages) doi:10.1115/1.568433 History: Received August 01, 1999
Copyright © 2000 by ASME
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References

Figures

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Representation of the first four linear modes in terms of the Lagrangian coordinates qi(i=1,[[ellipsis]],8) for two speed values: v=0.3 (solid line) and v=1.0 (dotted line)
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Spatial form of the complex eigenfunctions for two speed values: v=0.3 (solid line) and v=1.0 (dotted line)
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Snapshots of the first two modes in half a period of oscillation for v=1.0
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Bifurcation diagram, qi vs v
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Stability map for the straight equilibrium position: dotted region means instability
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Real and imaginary part of the second derivative of the first mode (solid line) and approximation through a sine series expansion (dotted lines) using four (upper figures) and eight terms (lower figures)
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Phase portraits, time histories and spectra for a perturbation of the trivial fixed point above the first critical velocity (v=1.1): (a, c, e), infinitesimal perturbation, i.e., homoclinic orbit; (b, d, f ), strong perturbation
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Stable and unstable eigenmodes (a) and snapshots of the homoclinic orbit (b), v=1.1
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Representation of the homoclinic motion in modal coordinates
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Time histories and spectra for a perturbation of the trivial fixed point. Case v=1.25>v(1): (a) time history, (b) spectrum; case v=2>v(2): (c) and (e) time histories, (d) and (f ) spectra for slightly different initial conditions.
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Energy versus q1,q2 for a two-degrees-of-freedom model with vf=0.104 and (a) v=1.1>v(1), (b) v=1.25>v(2)

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