Principal parametric resonances of a general continuous system with cubic nonlinearities

ÖZHAN B. B., Pakdemirli M.

Applied Mathematics and Computation, cilt.219, sa.5, ss.2412-2423, 2012 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 219 Sayı: 5
  • Basım Tarihi: 2012
  • Doi Numarası: 10.1016/j.amc.2012.08.048
  • Dergi Adı: Applied Mathematics and Computation
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.2412-2423
  • Anahtar Kelimeler: Nonlinear vibrations, Method of multiple scales, Viscoelastic pipe, Pipe conveying fluid, Principal parametric resonance
  • Manisa Celal Bayar Üniversitesi Adresli: Evet

Özet

A generalized vibrational model of cubic nonlinear continuous system with arbitrary parametric excitation is considered. The method of multiple scales (a perturbation method) is used to find an approximate analytical solution. The primary parametric resonance of the parametric excitation is considered. The amplitude and phase modulation equations are derived. Steady state solutions and their stability are discussed. The solution algorithm is applied to the problem of nonlinear vibrations of viscoelastic pipes conveying fluids. Natural frequencies of viscoelastic pipes are found. Frequency response curves and bifurcation points are drawn. Stable and unstable regions of trivial and nontrivial solutions are obtained. © 2012 Elsevier Inc. All rights reserved.