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TECHNICAL PAPERS

Nonlinear Vibration of Parametrically Excited, Viscoelastic, Axially Moving Strings

[+] Author and Article Information
Eric M. Mockensturm, Jianping Guo

Department of Mechanical and Nuclear Engineering, Pennsylvania State University, 157 Hammond Building, University Park, PA 16802

J. Appl. Mech 72(3), 374-380 (May 06, 2005) (7 pages) doi:10.1115/1.1827248 History: Received June 06, 2003; Revised November 03, 2004; Online May 06, 2005
Copyright © 2005 by ASME
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References

Zhang,  L., and Zu,  J. W., 1999, “Nonlinear Vibration of Parametrically Excited Viscoelastic Moving Belts, Part I: Dynamic Response,” J. Appl. Mech., 66, pp. 396–402.
Zhang,  L., and Zu,  J. W., 1999, “Nonlinear Vibration of Parametrically Excited Viscoelastic Moving Belts, Part II: Stability Analysis,” J. Appl. Mech., 66, pp. 403–409.
Jha,  R. K., and Parker,  R. G., 2000, “Spatial Discretization of Axially Moving Media Vibration Problems,” J. Vibr. Acoust., 122, pp. 290–294.
Oz,  H. R., 2001, “On the Vibrations of an Axially Travelling Beam on Fixed Supports With Variable Velocity,” J. Sound Vib., 239, pp. 556–564.
Oz,  H. R., Pakdemirli,  M., and Boyaci,  H., 2001, “Nonlinear Vibrations and Stability of an Axially Moving Beam With Time-Dependent Velocity,” Int. J. Non-Linear Mech.,36, pp. 107–115.
Parker,  R. G., 1999, “Supercritical Speed Stability of the Trivial Equilibrium of an Axially-Moving String on an Elastic Foundation,” J. Sound Vib., 221, pp. 205–219.
Parker,  R. P., 1998, “On the Eigenvalues and Critical Speed Stability of Gyroscopic Continua,” J. Appl. Mech., 65, pp. 134–140.
Pakdemirli,  M., and Ulsoy,  A. G., 1997, “Stability Analysis of an Axially Accelerating String,” J. Sound Vib., 203, pp. 815–832.
Lengoc,  L., and McCallion,  H., 1996, “Transverse Vibration of a Moving String: A Comparison Between the Closed-Form Solution and the Normal-Mode Solution,” J. Syst. Eng., 6, pp. 72–78.
Mockensturm,  E. M., Perkins,  N. C., and Ulsoy,  A. G., 1996, “Stability and Limit Cycles of Parametrically Excited, Axially Moving Strings,” J. Vibr. Acoust., 118, pp. 346–351.
Zhang,  L., and Zu,  J. W., 1999, “Nonlinear Vibration of Parametrically Excited Moving Belts, Part I: Dynamic Response,” J. Appl. Mech., 66, pp. 396–402.
Chen,  L. Q., Zhang,  N. H., and Zu,  J. W., 2003, “The Regular and Chaotic Vibrations of an Axially Moving Viscoelastic String Based on Fourth Order Galerkin Truncation,” J. Sound Vib., 261, pp. 764–773.
Zhang,  L., and Zu,  J. W., 1998, “Nonlinear Vibrations of Viscoelastic Moving Belts, Part I: Free Vibration Analysis,” J. Sound Vib., 216, pp. 75–91.
Zhang,  L., and Zu,  J. W., 1998, “Nonlinear Vibrations of Viscoelastic Moving Belts, Part II: Forced Vibration Analysis,” J. Sound Vib., 216, pp. 93–105.
Chen,  L. Q., Zhang,  N. H., and Zu,  J. W., 2002, “Bifurcation and Chaos of an Axially Moving Viscoelastic String,” Mech. Res. Commun., 29, pp. 81–90.
Hou,  Z. C., and Zu,  J. W., 2002, “Nonlinear Free Oscillations of Moving Viscoelastic Belts,” Mech. Mach. Theory, 37, pp. 925–940.
Wickert,  J. A., and Mote,  C. D., 1990, “Classical Vibration Analysis of Axially Moving Continua,” J. Appl. Mech., 57, pp. 738–744.

Figures

Grahic Jump Location
Stability boundaries of the first combination parametric resonance (n=1,l=2) obtained with (a) and without (b) steady state dissipation with ζ=10 and φ=400
Grahic Jump Location
The amplitude of the nontrivial limit cycles in the first combination parametric resonance (n=1 and l=2) for c=0.5, ζ=10, and φ=400. Inset shows solution neglecting steady state dissipation.
Grahic Jump Location
Stability boundaries of the first principle parametric resonance (n=l=1) obtained with (a) and without (b) steady state dissipation with ζ=10 and φ=400
Grahic Jump Location
The amplitude of the nontrivial limit cycles in the first principle parametric resonance (n=l=1) for c=0.5, ζ=10, and φ=400. Inset shows solution neglecting steady state dissipation.
Grahic Jump Location
Stability boundaries of the second principle parametric resonance (n=l=2) obtained with (a) and without (b) steady state dissipation with ζ=10 and φ=400
Grahic Jump Location
The amplitude of the nontrivial limit cycles in the second principle parametric resonance (n=l=2) for c=0.25, ζ=10, and φ=400. Inset shows solution neglecting steady state dissipation.

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