A general solution procedure for the forced vibrations of a system with cubic nonlinearities: Three-to-one internal resonances with external excitation

ÖZHAN B. B., Pakdemirli M.

Journal of Sound and Vibration, cilt.329, sa.13, ss.2603-2615, 2010 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 329 Sayı: 13
  • Basım Tarihi: 2010
  • Doi Numarası: 10.1016/j.jsv.2010.01.010
  • Dergi Adı: Journal of Sound and Vibration
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.2603-2615
  • Manisa Celal Bayar Üniversitesi Adresli: Evet

Özet

A general vibrational model of a continuous system with arbitrary linear and cubic operators is considered. Approximate analytical solutions are found using the method of multiple scales. The primary resonances of the external excitation and three-to-one internal resonances between two arbitrary natural frequencies are treated. The amplitude and phase modulation equations are derived. The steady-state solutions and their stability are discussed. The solution algorithm is applied to two specific problems: (1) axially moving Euler-Bernoulli beam, and (2) axially moving viscoelastic beam. © 2010 Elsevier Ltd. All rights reserved.