Non linear vibrations of stepped beam system under different boundary conditions

Özkaya E., TEKİN A. R.

Structural Engineering and Mechanics, cilt.27, sa.3, ss.333-345, 2007 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 27 Sayı: 3
  • Basım Tarihi: 2007
  • Doi Numarası: 10.12989/sem.2007.27.3.333
  • Dergi Adı: Structural Engineering and Mechanics
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.333-345
  • Anahtar Kelimeler: stepped beam, nonlinear vibration, perturbation method
  • Manisa Celal Bayar Üniversitesi Adresli: Evet

Özet

In this study, the nonlinear vibrations of stepped beams having different boundary conditions were investigated. The equations of motions were obtained using Hamilton's principle and made non dimensional. The stretching effect induced non-linear terms to the equations. Forcing and damping terms were also included in the equations. The dimensionless equations were solved for six different set of boundary conditions. A perturbation method was applied to the equations of motions. The first terms of the perturbation series lead to the linear problem. Natural frequencies for the linear problem were calculated exactly for different boundary conditions. Second order non-linear terms of the perturbation series behave as corrections to the linear problem. Amplitude and phase modulation equations were obtained. Non-linear free and forced vibrations were investigated in detail. The effects of the position and magnitude of the step, as well as effects of different boundary conditions on the vibrations, were determined.