Free vibration characteristics of a 3d mixed formulation beam element with force-based consistent mass matrix

Soydas O., SARITAŞ A.

JOURNAL OF VIBRATION AND CONTROL, cilt.23, sa.16, ss.2635-2655, 2017 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 23 Sayı: 16
  • Basım Tarihi: 2017
  • Doi Numarası: 10.1177/1077546315619263
  • Dergi Adı: JOURNAL OF VIBRATION AND CONTROL
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.2635-2655
  • Anahtar Kelimeler: Beam finite element, mixed formulation, force-based formulation, free vibration, consistent mass matrix, vibration frequency, TIMOSHENKO BEAM, TRANSVERSE VIBRATIONS, 3-DIMENSIONAL VIBRATIONS, FREQUENCIES, SHEAR, BARS, RODS, END
  • Orta Doğu Teknik Üniversitesi Adresli: Evet

Özet

In this analytical study, free vibration analyses of a 3d mixed formulation beam element are performed by adopting force-based consistent mass matrix that incorporates shear and rotary inertia effects. The force-based approach takes into account the actual distribution of mass of an element in the derivation of the mass matrix. Moreover, the force-based approach enables accurate determination of free vibration frequencies of members with varying geometry and material distribution without any need for specification of different displacement shape functions for each individual case. This phenomenon is justified by comparing free vibration frequencies of cantilever beams that have circular and rectangular cross-sections and various mass distribution configurations. Vibration frequencies of the mixed formulation element are compared with the frequencies obtained from closed-form solutions and finite element analyses. Fundamental frequency is computed with only one element per member span and higher order frequencies are determined with two or four elements with considerable accuracy by employing 3d mixed element and force-based consistent mass matrix.