Vibration analysis of beams with open and breathing cracks subjected to moving masses

This paper presents an analytical approach, as well as a calculation method for determining the dynamic response of the undamped Euler–Bernoulli beams with breathing cracks under a point moving mass using the so-called discrete element technique (DET) and the finite element method (FEM). First, the standard DET formulation is modified to consider the effects of Coriolis and centrifugal forces. Next, the formulation is extended to be able to evaluate the cases with open and breathing cracks under moving masses. The results will be validated against those reported in the literature and also compared with results from the finite element method. The effects of the moving mass velocity, location, and size of the crack on beam deflection will be investigated. Natural frequencies of the beam under the effect of crack will also be studied to compare the results with those of a beam without crack. It is observed that the presence of crack results in higher deflections and alters beam response patterns. In particular, the largest deflection in the beam for a given speed takes longer to build up, and a discontinuity appears in the slope of the beam deflected shape at the crack location. The effects of crack and load depend on speed, time, crack size, crack location, and the moving mass level.