Identification of a crack in a rod based on changes in a pair of natural frequencies

This paper deals with the identification of a single crack in a vibrating r od based on the knowledge of the damage-induced shifts in a pair of natural frequencies. The crack is simulated by an equivalent linear spring connect ing the two segments of the bar. The analysis is based on an explicit expre ssion of the frequency sensitivity to damage and enables non-uniform bars u nder general boundary conditions to be considered. The inverse problem is g enerally "ill-posed", because even if the system is not symmetrical, cracks in different locations can still produce identical changes in a pair of na tural frequencies. In spite of this, it is found that there are certain sit uations concerning uniform rods in which the effects of the non-uniqueness of the solution may be considerably reduced by means of a careful choice of the data. The theoretical results are confirmed by a comparison with dynam ic measurements on steel rods with a crack. Some of the results are also va lid for cracked beams in bending. (C) 2001 Academic Press.