Generalized Fourier coefficients and applications to damage detection in rods

In this paper it is shown that eigenvalue shifts contain information on certain generalized Fourier coefficients of the stiffness variation caused by damage in a vibrating rod. Under the assumptions that the damaged rod is a perturbation of the undamaged one and the damage belongs to a half of the rod, a reconstruction procedure based on an iterative algorithm is proposed. The theoretical results are confirmed by a comparison with dynamic measurements on steel rods with localized damage.