Non-linear vibrations and stability of an axially moving beam with time-dependent velocity

Öz H., Pakdemirli M., Boyaci H.

International Journal of Non-Linear Mechanics, vol.36, no.1, pp.107-115, 2001 (SCI-Expanded, Scopus) identifier identifier

  • Publication Type: Article / Article
  • Volume: 36 Issue: 1
  • Publication Date: 2001
  • Doi Number: 10.1016/s0020-7462(99)00090-6
  • Journal Name: International Journal of Non-Linear Mechanics
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.107-115
  • Keywords: non-linear vibrations, axially moving material, perturbation methods
  • Manisa Celal Bayar University Affiliated: Yes

Abstract

Non-linear vibrations of an axially moving beam are investigated. The non-linearity is introduced by including stretching effect of the beam. The beam is moving with a time-dependent velocity, namely a harmonically varying velocity about a constant mean velocity. Approximate solutions are sought using the method of multiple scales. Depending on the variation of velocity, three distinct cases arise: (i) frequency away from zero or two times the natural frequency, (ii) frequency close to zero, (iii) frequency close to two times the natural frequency. Amplitude-dependent non-linear frequencies are derived. For frequencies close to two times the natural frequency, stability and bifurcations of steady-state solutions are analyzed. For frequencies close to zero, it is shown that the amplitudes are bounded in time.