Two-to-one internal resonances in continuous systems with arbitrary quadratic nonlinearities

Pakdemirli M., Özkaya E.

Arabian Journal for Science and Engineering, cilt.29, sa.1 C, ss.99-112, 2004 (SCI-Expanded, Scopus) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 29 Sayı: 1 C
  • Basım Tarihi: 2004
  • Dergi Adı: Arabian Journal for Science and Engineering
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.99-112
  • Anahtar Kelimeler: vibrations, continuous systems, internal resonances
  • Manisa Celal Bayar Üniversitesi Adresli: Evet

Özet

Vibrations of a general continuous system with arbitrary quadratic nonlinearities are considered. The nonlinearities are expressed in terms of arbitrary quadratic operators. The two-to-one internal resonance case is considered. A general approximate solution is presented for the system. Amplitude and phase modulation equations are derived. Steady state solutions and their stability are discussed in the general sense. The sufficiency condition for such resonances to occur is derived. Finally the algorithm is applied to a specific problem.