Vibration analysis of a cracked beam using the finite element method

This study is motivated by the condition monitoring and fault diagnostics of structural beams used in large-scale vibrating screens for the mining industry. For the purpose of developing a reliable model-based approach, a new stiffness matrix of a three-dimensional finite element is proposed for modelling a beam with a breathing crack. Using the obtained stiffness matrix, a finite element model was derived for a cracked beam subjected to a bidirectional base excitation. With the model, a computer simulation was conducted to examine the influence of the crack depth on the natural frequencies of the beam. The numerical results show that the crack influences mainly the natural frequencies of the bending modes in the direction of the crack's growth. The simulation also investigates the responses of the beam subjected to a harmonic base excitation in two directions. The numerical results show that the responses of the cracked beam contain several superharmonic components, and the amplitude of superharmonic components increases with the increase in crack depth. Experiments are conducted to validate the proposed dynamic model using both impact testing and forced testing.