Nonlinear reduced models for beam damage detection using data on moving oscillator–beam interactions

The problem of detecting local and/or distributed loss of stiffness in beam structures using vibration data generated by passage of a moving oscillator is considered. A time domain structural damage detection scheme, within finite element modeling framework, that takes into account time varying structural matrices, structural nonlinearities and spatial incompleteness of measured data, is developed. The damage parameters associated with changes in structural stiffness are shown to be governed by a set of overdetermined nonlinear equations which are solved iteratively. Illustrative examples on a geometrically nonlinear Euler–Bernoulli beam carrying a moving single degree of freedom oscillator are provided.