Analysis of free vibration of beam on elastic soil using differential transform method

Catal S.

STRUCTURAL ENGINEERING AND MECHANICS, vol.24, no.1, pp.51-62, 2006 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 24 Issue: 1
  • Publication Date: 2006
  • Doi Number: 10.12989/sem.2006.24.1.051
  • Journal Name: STRUCTURAL ENGINEERING AND MECHANICS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED)
  • Page Numbers: pp.51-62
  • Keywords: differential transformation method, partial differential equation, motion equation, free motion, elastic soil
  • Dokuz Eylül University Affiliated: Yes

Abstract

Differential transforin method (DTM) for free vibration analysis of both ends simply supported beam resting on elastic foundation is suggested. The fourth order partial differential equation for free vibration of the beam resting on elastic foundation subjected to bending moment, shear and axial compressive load is obtained by using Winkler hypothesis and small displacement theory. It is assumed that the material is linear-elastic, and that axial load and modulus of subgrade reaction to be constant. In the analysis, shear and axial load effects are considered. The frequency factors of the beam are calculated by using DTM due to the values of relative stifffiess; the results are presented in graphs and tables.