The Homotopy Perturbation Method for free vibration analysis of beam on elastic foundation

ÖZTÜRK B., COŞKUN S. B.

STRUCTURAL ENGINEERING AND MECHANICS, sa.4, ss.415-425, 2011 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Basım Tarihi: 2011
  • Doi Numarası: 10.12989/sem.2011.37.4.415
  • Dergi Adı: STRUCTURAL ENGINEERING AND MECHANICS
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.415-425
  • Anahtar Kelimeler: homotopy perturbation method, beam on elastic foundation, free vibration analysis, DIFFERENTIAL TRANSFORM METHOD, CRITICAL BUCKLING LOADS, EULER COLUMNS, FLEXURAL STIFFNESS, EQUATIONS
  • Kocaeli Üniversitesi Adresli: Evet

Özet

In this study, the homotopy perturbation method (HPM) is applied to free vibration analysis of beam on elastic foundation. This numerical method is applied on three different axially loaded cases, namely: 1) one end fixed, the other end simply supported; 2) both ends fixed and 3) both ends simply supported cases. Analytical solutions and frequency factors are evaluated for different ratios of axial load N acting on the beam to Euler buckling load, N(r). The application of HPM for the particular problem in this study gives results which are in excellent agreement with both analytical solutions and the variational iteration method (VIM) solutions for all the cases considered in this study and the differential transform method (DTM) results available in the literature for the fixed-pinned case.