Crack damage detection of structures using spectral transfer matrix

A novel spectral transfer matrix for a cracked beam element is developed in this article and the same is used to identify the crack parameters on the beam structures. Spectral transfer matrix is developed from trigonometric functions based on the theory of fracture mechanics. This matrix determines the natural frequencies of a structure with crack with better accuracy than any other transfer matrices in the literature. The state vector at a node on the structure is formed which includes the displacement, rotation, internal and external forces, and moments at that node. When the state vector is multiplied with the transfer matrix, the state vector at the adjacent node is obtained. Each element is assumed to have a single open breathing crack with unknown depth and location. Initially, the developed spectral transfer matrix is used to determine the natural frequencies of a known cantilever, and after successful validation, the same is used for crack damage detection. By an inverse approach, crack parameters in each element are identified. The state vector at one node on the structure is obtained by measurement of input and out responses which is known as the initial state vector. Acceleration responses at selected nodes on the structure are measured and the state vectors at those nodes are predicted using spectral transfer matrices. The mean square error between measured and simulated responses is minimized using a heuristic optimization algorithm, with crack depth and location in each element as the optimization variables. Spectral transfer matrix method is applied to two numerical problems with single crack in each element; later, this method is successfully validated experimentally with structures having different boundary conditions. The accuracy in identified crack parameters and the applicability to sub-structures of a large structure are the important aspects of this method.