An integrated approach to detection of cracks using vibration characteristics

Abstract An integrated technique based on the vibration theory to nondestructively identify multiple discrete cracks in a structure is presented. Two damage modeling techniques, one involving the use of massless, infinitesimal springs to represent discrete cracks and the other one employing the continuum damage concept, are integrated to provide a crack-detection technique that utilizes the global vibration characteristics of a structure but offers local information on each individual crack, including location and extent of the cracks. In the spring model, the Castigliano's theorem and the perturbation technique are used to derive a theoretical relationship between the eigenfrequency changes and the location and extent of the discrete cracks. In the continuum damage model, the effective stress concept coupled with the Hamilton's principle are used to derive the similar relationship that is cast in a continuum form. A unified g(β) function emerges from the two model approaches. The g(β) function can be determined through the mode shapes of an intact structure by means of the modal strain energy density. In the proposed integrated approach, the continuum damage model can be used first to identify the discretizing elements of a structure that contain cracks. Then, the spring damage model can be used to quantify the location and severity of the discrete crack in each damaged element. An example of a simply-supported beam containing two discrete cracks is given to illustrate the application and accuracy of the proposed approach.