Free vibration analysis of beams on variable winkler elastic foundation by using the differential transform method

Alev Kacar*, H. Tugba Tan, Metin O. Kaya

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

56 Citations (Scopus)

Abstract

In this study, free vibration of an Euler-Bernoulli beam resting on a variable Winkler foundation is considered. Structures which are supported along their length such as beams or pipelines resting on elastic soil are very commonly modeled with a Winkler foundation. In this problem, the elastic coefficient of the foundation is variable along the beam major axis. Constant, linear and parabolic variations are considered. The problem is handled for three different boundary conditions: simply supported-simply supported, clamped-clamped and cantilever (clamped-free) beams. The governing differential equations of the beam are solved by using Differential Transform Method (DTM). DTM is an easy transformation technique based on Taylor expansion series, providing high accuracy.

Original languageEnglish
Pages (from-to)773-783
Number of pages11
JournalMathematical and Computational Applications
Volume16
Issue number3
DOIs
Publication statusPublished - 2011

Keywords

  • Beam
  • DTM
  • Differential transform method
  • Elastic soil
  • Pipeline
  • Vibration

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