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A continuous vibration theory for beams with a vertical edge crack
Behzad, M ; Sharif University of Technology | 2010
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- Type of Document: Article
- Publisher: 2010
- Abstract:
- In this paper, a continuous model for flexural vibration of beams with an edge crack perpendicular to the neutral plane has been developed. The model assumes that the displacement field is a superposition of the classical Euler-Bernoulli beam's displacement and of a displacement due to the crack. The additional displacement is assumed to be a product between a function of time and an exponential function of space. The unknown functions and parameters are determined based on the zero stress conditions at the crack faces and the concept of J-integral from fracture mechanics. The governing equation of motion for the beam has been obtained using the Hamilton principle and solved using a modified Galerkin method. The results have been compared with finite element results and an excellent agreement is observed
- Keywords:
- Cracked beam ; Continuous models ; Crack faces ; Cracked beams ; Displacement field ; Edge cracks ; Euler Bernoulli beams ; Finite Element ; Flexural vibrations ; Function of time ; Governing equations ; Hamilton principle ; J-integral ; Modified galerkin method ; Neutral plane ; Stress condition ; Vertical crack ; Vertical edges ; Vibration ; Vibration theory ; Equations of motion ; Exponential functions ; Fracture mechanics ; Galerkin methods ; Stresses ; Cracks ; Crack ; Displacement ; Finite element method ; Flexure ; Fracture mechanics ; Galerkin method ; Numerical model ; Strain ; Stress analysis ; Vibration
- Source: Scientia Iranica ; Volume 17, Issue 3 B , 2010 , Pages 194-204 ; 10263098 (ISSN)
- URL: http://www.sid.ir/en/VEWSSID/J_pdf/95520103B01.pdf