%0 Journal Article
%T A Continuous Vibration Theory for Beams with a Vertical Edge Crack
%J Scientia Iranica
%I Sharif University of Technology
%Z 1026-3098
%A Meghdari, A.
%A Behzad, M.
%A Ebrahimi, A.
%D 2010
%\ 06/01/2010
%V 17
%N 3
%P -
%! A Continuous Vibration Theory for Beams with a Vertical Edge Crack
%K Vibration
%K Cracked beam
%K Vertical crack
%K J-integral
%R
%X In this paper, a continuous model for
exural vibration of beams with an edge crack
perpendicular to the neutral plane has been developed. The model assumes that the displacement eld
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 modied
Galerkin method. The results have been compared with nite element results and an excellent agreement
is observed.
%U https://scientiairanica.sharif.edu/article_3290_17c26938a9279a203cf4d5baad242ba0.pdf