Nonlinear vibrations and stability analysis of axially moving strings having nonideal mid-support conditions

YURDDAŞ A., Özkaya E., Boyaci H.

JVC/Journal of Vibration and Control, cilt.20, sa.4, ss.518-534, 2014 (Scopus) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 20 Sayı: 4
  • Basım Tarihi: 2014
  • Doi Numarası: 10.1177/1077546312463760
  • Dergi Adı: JVC/Journal of Vibration and Control
  • Derginin Tarandığı İndeksler: Scopus
  • Sayfa Sayıları: ss.518-534
  • Anahtar Kelimeler: Axially moving string vibrations, method of multiple scales, nonideal boundary conditions, nonlinear vibrations, stability analysis
  • Manisa Celal Bayar Üniversitesi Adresli: Evet

Özet

In this study, nonlinear vibrations of an axially moving string are investigated. The main difference of this study from other studies is that there is a nonideal support between the opposite sides, which allows small displacements. Nonlinear equations of motion and boundary conditions are derived using Hamilton's principle. Equations of motion and boundary conditions are converted to nondimensional form. Thus, the equations become independent from geometry and material properties. The method of multiple scales, a perturbation technique, is used. A harmonically varying velocity function is chosen for modeling the axial movement. String as a continuous medium is investigated in two regions. Vibrations are investigated for three different cases of the excitation frequency Ω. Stability analysis is carried out for these three cases, and stability boundaries are determined for the principle parametric resonance case. Thus, differences between ideal and nonideal boundary conditions are investigated. © The Author(s) 2012 Reprints and permissions: sagepub.co.uk/journalsPermissions.nav.