Two-to-one internal resonances in a shallow curved beam resting on an elastic foundation

Öz H., Pakdemirli M.

Acta Mechanica, cilt.185, sa.3-4, ss.245-260, 2006 (SCI-Expanded, Scopus) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 185 Sayı: 3-4
  • Basım Tarihi: 2006
  • Doi Numarası: 10.1007/s00707-006-0352-5
  • Dergi Adı: Acta Mechanica
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.245-260
  • Manisa Celal Bayar Üniversitesi Adresli: Evet

Özet

Vibrations of shallow curved beams are investigated. The rise function of the beam is assumed to be small. Sinusoidal and parabolic curvature functions are examined. The immovable end conditions result in mid-plane stretching of the beam which leads to nonlinearities. The beam is resting on an elastic foundation. The method of multiple scales, a perturbation technique, is used in search of approximate solutions of the problem. Two-to-one internal resonances between any two modes of vibration are studied. Amplitude and phase modulation equations are obtained. Steady state solutions and stability are discussed, and a bifurcation analysis of the amplitude and phase modulation equations are given. Conditions for internal resonance to occur are discussed, and it is found that internal resonance is possible for the case of parabolic curvature but not for that of sinusoidal curvature.