Dynamic stiffness approach and differential transformation for free vibration analysis of a moving Reddy-Bickford beam

BOZYİĞİT B., YEŞİLCE Y.

STRUCTURAL ENGINEERING AND MECHANICS, cilt.58, sa.5, ss.847-868, 2016 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 58 Sayı: 5
  • Basım Tarihi: 2016
  • Doi Numarası: 10.12989/sem.2016.58.5.847
  • Dergi Adı: STRUCTURAL ENGINEERING AND MECHANICS
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.847-868
  • Anahtar Kelimeler: axially moving beam, Reddy-Bickford beam theory, dynamic stiffness method, differential transform method, free vibration analysis, natural frequency, SPRING-MASS SYSTEMS, ELASTIC SOIL, TIMOSHENKO BEAM, TRANSVERSE VIBRATION, NATURAL FREQUENCIES, EQUATIONS, ELEMENT, PLATES
  • Dokuz Eylül Üniversitesi Adresli: Evet

Özet

In this study, the free vibration analysis of axially moving beams is investigated according to Reddy-Bickford beam theory (RBT) by using dynamic stiffness method (DSM) and differential transform method (DTM). First of all, the governing differential equations of motion in free vibration are derived by using Hamilton's principle. The nondimensionalised multiplication factors for axial speed and axial tensile force are used to investigate their effects on natural frequencies. The natural frequencies are calculated by solving differential equations using analytical method (ANM). After the ANM solution, the governing equations of motion of axially moving Reddy-Bickford beams are solved by using DTM which is based on Finite Taylor Series. Besides DTM, DSM is used to obtain natural frequencies of moving Reddy-Bickford beams. DSM solution is performed via Wittrick-Williams algorithm. For different boundary conditions, the first three natural frequencies that calculated by using DTM and DSM are tabulated in tables and are compared with the results of ANM where a very good proximity is observed. The first three mode shapes and normalised bending moment diagrams are presented in figures.