Vibrations of cracked beams: Discrete mass and stiffness models

•A DEM formulation is developed for the dynamic analysis of beams with cracks.•The loss of stiffness at the crack location is based on the stress intensity factors.•The effects of the crack depth and location are investigated.

The present work aims at contributing to the characterization of the nonlinear dynamic behavior of structures incorporating cracks. With this purpose, the Discrete Element Method is adopted in conjunction with an existing result from fracture mechanics that takes into account the local flexibility of a cracked beam. The dynamic behavior of a cantilever beam and of a beam free of support conditions is studied and the effect of the presence of a crack is analyzed. When possible, the results are compared with exact solutions or with experimental data from the literature.