Asymptotic nonlinear behaviors in transverse vibration of an axially accelerating viscoelastic string

Li Qun Chen, Jun Wu, Jean W. Zu

Research output: Contribution to journalArticlepeer-review

36 Scopus citations

Abstract

This paper investigates longtime dynamical behaviors of an axially accelerating viscoelastic string with geometric nonlinearity. Application of Newton's second law leads to a nonlinear partial-differential equation governing transverse motion of the string. The Galerkin method is applied to truncate the partial-differential equation into a set of ordinary differential equations. By use of the Poincare maps, the dynamical behaviors are presented based on the numerical solutions of the ordinary differential equations. The bifurcation diagrams are presented for varying one of the following parameter: the mean transport speed, the amplitude and the frequency of transport speed fluctuation, the string stiffness or the string dynamic viscosity, while other parameters are fixed.

Original languageEnglish
Pages (from-to)347-360
Number of pages14
JournalNonlinear Dynamics
Volume35
Issue number4
DOIs
StatePublished - Mar 2004

Keywords

  • Axially accelerating string
  • Bifurcation diagram
  • Galerkin method
  • Poincare map
  • Viscoelasticity

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