Free vibrations of a multi-span Timoshenko beam carrying multiple spring-mass systems

Creative Commons License

YEŞİLCE Y., DEMİRDAĞ O., ÇATAL S.

SADHANA-ACADEMY PROCEEDINGS IN ENGINEERING SCIENCES, cilt.33, sa.4, ss.385-401, 2008 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 33 Sayı: 4
  • Basım Tarihi: 2008
  • Doi Numarası: 10.1007/s12046-008-0026-1
  • Dergi Adı: SADHANA-ACADEMY PROCEEDINGS IN ENGINEERING SCIENCES
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.385-401
  • Anahtar Kelimeler: free vibration, Timoshenko multi-span beam, spring-mass system, eigenvalue problem, BERNOULLI UNIFORM BEAM, ALTERNATIVE FORMULATIONS, NATURAL FREQUENCIES, RESTRAINED BEAMS, BENDING MOMENT, SHEAR FORCE, PILES, NUMBER, RODS, SOIL
  • Dokuz Eylül Üniversitesi Adresli: Evet

Özet

Structural elements supporting motors or engines are frequently seen in technological applications. The operation of a machine may introduce additional dynamic stresses on the beam. It is important, then, to know the natural frequencies of the coupled beam-mass system, in order to obtain a proper design of the structural elements. The literature regarding the free vibration analysis of Bernoulli-Euler single-span beams carrying a number of spring-mass system and Bernoulli-Euler multi-span beams carrying multiple spring-mass systems are plenty, but on Timoshenko multi-span beams carrying multiple spring-mass systems is fewer. This paper aims at determining the natural frequencies and mode shapes of a Timoshenko multi-span beam. The model allows to analyse the influence of the shear effect and spring-mass systems on the dynamic behaviour of the beams by using Timoshenko Beam Theory (TBT). The effects of attached spring-mass systems on the free vibration characteristics of the 1-4 span beams are studied. The natural frequencies of Timoshenko multi-span beam calculated by using secant method for non-trivial solution are compared with the natural frequencies of multi-span beam calculated by using Bernoulli-Euler Beam Theory (EBT) in literature; the mode shapes are presented in graphs.