A Continuous Vibration Theory for Beams with a Vertical Edge Crack


Department of Mechanical Engineering,Sharif University of Technology


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 modi ed
Galerkin method. The results have been compared with nite element results and an excellent agreement
is observed.