The Fourier Coefficient Method for Damage Detection in Beams

In this paper it is shown that natural frequency and antiresonant frequency shifts induced by a damage contain information on certain generalized Fourier coefficients of the stiffness variation caused by the damage itself in a vibrating beam. Under the assumption that the damaged beam is a perturbation of the undamaged one, a reconstruction procedure based on an iterative algorithm is proposed. The theoretical results are confirmed by a comparison with dynamic measurements on steel beams with localized damages, either under axial or bending vibration.