Analytical Solution of Dynamic Analysis of Cracked Euler-Bernoulli Beam with Elastic Boundary Condition By G.F.M

The recognition of behavior of the cracked beam causes to find out how can use all capability of beams. Existence crack during the length of the beam makes discontinuity on the beam and leads to reduce local stiffness. This paper presents the dynamic solution of the cracked Euler-Bernoulli beam by Green Function Method (G.F.M). Green function is exhibited for the Euler-Bernoulli beam with various boundary conditions. Also, discontinuity is modeled by rotational spring in this paper. The effects of crack in different locations and depths of cracks with considering various boundary conditions are assessed. In addition, the influence of crack on natural frequency is studied. Finally, several examples are presented to compare the effect of boundary conditions on the dynamic response of the weakened Euler-Bernoulli beam.