Linear dynamical analysis of fractionally damped beams and rods

DÖNMEZ DEMİR D., Bildik N., SINIR B. G.

Journal of Engineering Mathematics, cilt.85, sa.1, ss.131-147, 2014 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 85 Sayı: 1
  • Basım Tarihi: 2014
  • Doi Numarası: 10.1007/s10665-013-9642-9
  • Dergi Adı: Journal of Engineering Mathematics
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.131-147
  • Anahtar Kelimeler: Fractional damping, Method of multiple scales, Perturbation method, Viscoelastic beam
  • Manisa Celal Bayar Üniversitesi Adresli: Evet

Özet

The aim of this study is to develop a general model for beams and rods with fractional derivatives. Fractional time derivatives can represent the damping term in dynamical models of continuous systems. Linear differential operators with spatial derivatives make it possible to generalize a wide range of problems. The method of multiple scales is directly applied to equations of motion. For the approximate solution, the amplitude and phase modulation equations are obtained in terms of the operators. Stability boundaries are derived from the solvability condition. It is shown that a fractional derivative influences the stability boundaries, natural frequencies, and amplitudes of vibrations. The solution procedure may be applied to many problems with linear vibrations of continuous systems. © 2013 Springer Science+Business Media Dordrecht.