Solution of free vibration equation of elastically supported Timoshenko columns with a tip mass by differential transform method


DEMİRDAĞ O., YEŞİLCE Y.

ADVANCES IN ENGINEERING SOFTWARE, cilt.42, sa.10, ss.860-867, 2011 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 42 Sayı: 10
  • Basım Tarihi: 2011
  • Doi Numarası: 10.1016/j.advengsoft.2011.06.002
  • Dergi Adı: ADVANCES IN ENGINEERING SOFTWARE
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.860-867
  • Anahtar Kelimeler: Free vibration, Elastic support, Timoshenko column, Differential transform method, Natural frequencies, Partial differential equation, NATURAL FREQUENCIES, TRANSVERSE VIBRATION, DYNAMIC-ANALYSIS, FINITE-ELEMENT, UNIFORM BEAM, POINT MASSES, MODE SHAPES, WEDGE BEAMS, IN-SPAN, SYSTEMS
  • Dokuz Eylül Üniversitesi Adresli: Evet

Özet

In this study free vibration analysis of a Timoshenko column with a tip mass having rotary inertia is carried out by both exact solution and differential transform method (DTM). The support of the system is modeled by an elastic spring against rotation. Fixity factor is used to define the relative stiffness of the elastic connection and the column. The governing equation of the column is solved by the separation of variables method including the rotatory inertia to get the exact solution. The same problem is also solved by DTM algorithm and the results are compared with the ones of exact solution. The comparison tables are presented in numerical analysis to show that a very good agreement is observed for DTM. (C) 2011 Elsevier Ltd. All rights reserved.