A DISCRETE MODEL OF A VIBRATING BEAM USING A TIME-STEPPING APPROACH

A time-stepping model of a transversely vibrating, simply supported beam which 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 the 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 flexibility of the springs to be altered at any time during the analysis allowing the modelling of non-linear damage. The natural frequencies and mode shapes predicted by the model for an undamaged beam are validated against theoretical values and the representation of a non-linear mechanism in the model is compared with experimental data. The model predictions are shown to be accurate for both the undamaged and the non-linear cases.