A LINE-SPRING MODEL IN FINITE ELEMENT ANALYSIS OF DYNAMIC RESPONSES OF A CRACKED BEAM

In this paper a new numerical method based on a line-spring model is developed to analyze the dynamic response of a cracked beam. A stiffness matrix of the linespring model is first derived using the energy principle in conjunchon with fracture mechanics method. A finite element model of a cracked beam is then established which enables a onedimensional analysis of a two-dimensional crack problem. The effects of natural frequencies and the corresponding mode shapes are investigated for a cracked cantilever beam with differentcrack lengths and crack positions using the model. The comparisons between the numericalresults and the available experimental data are made. It is shown that both are very agreeable when the non-dimensional lengths of crack are less than 0.6; on the contrary, there are greater discrepancies between them. The causes of the errors are interpreted.