Dynamic analysis of beams with a closing crack

In this gaper the deterministic and stochastic dynamic behaviour of a beam with a transverse an edge nonpropagating crack is studied. The beam is discretized by a finite element model in which a so-called closing crack model, with fully open or fully closed crack, is used to describe the damaged element. Once the mathematical model of the beam is defined, the dynamic response is evaluated by applying a numerical procedure based on the philosophy of structural systems with dynamic modification. It has been assumed that the change between fully open and fully closed takes place instantaneously giving rise to a bilinear-type stiffness non-linearity. The proposed method requires: i) the evaluation of mode shapes only at the beginning of the numerical procedure in which the crack is closed, ii) the evaluation of numerical response in modal subspace by updating the fundamental operator at each step taking into account of possible crack.