A discrete model of a vibrating beam using a time-stepping approach

A time-stepping model of a transversely vibrating, simply supported beam wh ich allows the inclusion of non-linear damage such as a breathing crack is presented. It is based on the approximation that the mass and inertia of th e beam may be lumped at points along the beam and the beam flexibility may be represented by discrete springs between rigid blocks. The advantage of a time-stepping approach over other models reported is that it enables the f lexibility of the springs to be altered at any time during the analysis all owing the modelling of non-linear damage. The natural frequencies and mode shapes predicted by the model for an undamaged beam are validated against t heoretical values and the representation of a non-linear mechanism in the m odel is compared with experimental data. The model predictions are shown to be accurate for both the undamaged and the non-linear cases. (C) 2001 Acad emic Press.