A Continuous Vibration Theory for Beams with a Vertical Edge Crack

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.