Crack detection and vibration behavior of cracked beams

A theoretical and experimental dynamic behavior of different multi-beams systems containing a transverse crack is presented. The additional flexibility that the crack generates in its vicinity is evaluated using the strain energy density function given by the linear fracture mechanic theory. Based on this flexibility, a new cracked finite element stiffness matrix is deduced, which can be used subsequently in the FEM analysis of crack systems. The proposed element is used to evaluate the dynamic response of a cracked free–free beam and a U-frame when a harmonic force is applied. The resulting parametrically excited system is non-linear and the equations of motion are solved using the Hilbert, Hughes and Taylor integration method implemented using a Matlab software platform. Some useful conclusions for diagnosing cracked beams systems are proposed.