Small-Amplitude free vibrations of straight beams subjected to large displacements and rotation


Eroglu U., Tüfekci E.

APPLIED MATHEMATICAL MODELLING, cilt.53, ss.223-241, 2018 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 53
  • Basım Tarihi: 2018
  • Doi Numarası: 10.1016/j.apm.2017.08.028
  • Dergi Adı: APPLIED MATHEMATICAL MODELLING
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.223-241
  • Anahtar Kelimeler: Geometrically exact beam theory, Curved beam, Vibration, Stability, Variational iterational method, Differential quadrature method, VARIATIONAL ITERATION METHOD, FINITE-ELEMENT FORMULATION, DIFFERENTIAL QUADRATURE METHOD, SINGULAR INEXTENSIBLE LIMIT, INPLANE FREE-VIBRATION, POST-BUCKLED RODS, CURVED BEAMS, TRANSVERSE VIBRATIONS, LARGE-DEFORMATION, TIMOSHENKO BEAMS
  • İstanbul Teknik Üniversitesi Adresli: Evet

Özet

In this study, a systematic approach to study small-amplitude vibrations of large deflected straight beams is presented. The differential equation system of small-amplitude free vibrations about the deflected configuration is presented considering the effects of axial extension, shear deformation, and rotatory inertia. It is shown that in the absence of axial, and shear forces, the differential equation system of small-amplitude vibrations of the deflected beam becomes identical to that of an initially curved beam. To solve the differential equation system of the large deflection problem, Variational Iterational Method is used. Free vibration analysis around the deflected configuration is performed by using Differential Quadrature Method. Several numerical examples are solved to show the versatility of the presented approach. (C) 2017 Elsevier Inc. All rights reserved.