An analytical method for diagnosis of cracks in thick-walled pipes with a circular hollow section is investigated in this study. In the proposed method, the defect is assumed to be a non-leaking crack, which is modeled by a massless linear spring with infinitesimal length at the crack location. In order to find the cracks in the pipe, the vibration-based method related to the modal properties of the pipe is utilized. In the modal analysis, the mass and stiffness matrices influence the dynamic

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... operties of the pipe. It is assumed that the mass matrix remains unchanged after the crack initiation, while the corresponding stiffness matrix changes. The stiffness matrix of a cracked element can be formulated by the finite element method with two unknown parameters: location and depth of the crack. Using the eigensolution for an undamped dynamic system to formulate the objective function yields to a complicated optimization problem, which can be solved by an iterative numerical optimization method. Among the optimization approaches, the Artificial Bee Colony (ABC) algorithm is a simple and flexible technique for minimizing the objective function. In this paper, the analytical model is utilized to find the size and position of cracks in a pipe using the ABC algorithm and subsequently some numerical examples are examined in order to assess the accuracy of the method. The results show that the proposed method is able to acceptably estimate the location and depth of multiple cracks in the straight pipes as well as curved ones.