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2020 Vol.11, Issue 4 Preview Page

General Article

Approximate analytical solution for free axial vibration of a cracked cantilever beam
Hillal Ayas1†
,
Mokhtar Touati2
,
Mohamed Chabaat3
1Associate Professor, Department of Civil Engineering and Hydraulics, University of Jijel, B.P. 98 Ouled Aissa Jijel, Algeria.
2Associate Professor, Built Environmental Research Lab., Dept. of Structures and Materials, Civil Engineering Faculty, University of Sciences and Technology Houari Boumediene, B. P. 32 El Alia, Bab Ezzouar, Algiers, Algeria
3Professor, Built Environmental Research Lab., Dept. of Structures and Materials, Civil Engineering Faculty, University of Sciences and Technology Houari Boumediene, B. P. 32 El Alia, Bab Ezzouar, Algiers, Algeria
*hillal.ayas@gmail.com
31 December 2020. pp. 209-221
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Abstract

In this paper, free vibration analysis of a cracked cantilever bar by an Approximate Analytical approach is investigated. The crack is modeled by an equivalent axial spring with stiffness Kx according to Castigliano’s theorem. The effect of different crack depth ratio on the longitudinal frequencies and mode shapes in the cracked bar has been analyzed. It is shown that an increase in the crack depth ratio produces a decrease in the fundamental longitudinal natural frequency of a cracked bar. On the other hand, approximate analytical results indicate that the variation of a normalized longitudinal natural frequency with respect to the crack depth ratio give comparable results with those obtained from the numerical solution of an analytical equation of a cracked beam.

Keywords
crack
free vibration
axial spring
longitudinal natural frequency
castigliano’s theorem
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Information
  • Publisher :Sustainable Building Research Center (ERC) Innovative Durable Building and Infrastructure Research Center
  • Publisher(Ko) :건설구조물 내구성혁신 연구센터
  • Journal Title :International Journal of Sustainable Building Technology and Urban Development
  • Volume : 11
  • No :4
  • Pages :209-221
  • Received Date : 2019-12-15
  • Accepted Date : 2020-12-11
  • DOI :https://doi.org/10.22712/susb.20200016
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