Spectral and Perturbation Analysis of First-Order Beams With Notch Damage

The influence of damage on waves propagating in beam structures is investigated through a numerical model formulated by combining spectral finite elements and perturbation techniques. The resulting numerical tool allows for an efficient computation of the wave propagation response and the analysis of the effects of localized damages of various extents and locations. The dynamic behavior of damaged beams is described through a first-order model, which couples bending and axial behavior, thus allowing the prediction of mode conversion phenomena. Damage is modeled as a small, localized reduction of the beam thickness which, allows for an application of perturbation theory. Numerical examples in the time and frequency domains are presented to illustrate the model capabilities.