Damage detection and generalized Fourier coefficients

This paper deals with damage identification in a vibrating beam, either under axial or bending vibration, based on measurement of damage-induced changes in natural frequencies. It is found that frequency shifts contain information on certain generalized Fourier coefficients of the stiffness variation caused by the damage. Under the assumptions that the damaged beam is a perturbation of the undamaged one and the damage belongs to a half of the beam, 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.