Detecting cracks in pipes filled with fluid from changes in natural frequencies

This paper deals with the identification of a single open crack in a straight pipe containing fluid under pressure by frequency measurements. The crack is assumed to be a transverse partial cut of the pipe wall thickness with straight front and it is simulated by an equivalent elastic spring. It is shown that the measurement of the damage-induced shifts in a pair of natural frequencies of the bending vibration can be used to formulate and solve the diagnostic problem. In particular, it is shown that the change in the first two frequencies in a simply supported uniform pipe is sufficient to localize a small crack, except for a symmetrical position, and to determine the damage severity. Closed-form expressions are provided for damage location and severity. An extension of the method to simply supported uniform pipe with two cracks of equal severity is also presented. The analysis is based on an explicit expression of the frequency sensitivity to damage and allows to consider pipes under general set of boundary conditions. Analytical results agree well with numerical tests.