Dynamic response of a rectangular beam with a known non-propagating crack of certain or uncertain depth

In this paper the deterministic behaviour of a beam with a transverse on edge non-propagating crack is first studied. Moreover the stochastic setting pertaining the case in which the crack has an uncertain depth is investigated. The beam is discretized by finite elements 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. In the stochastic case the improved perturbation method is modified in order to solve efficiently the stochastic non-linear differential equations.