Detection of cracks in beam structures using measurements of natural frequencies

A method based on measurements of natural frequencies of structures has been developed for the detection of crack location and quantification of damage magnitude in a uniform beam under simply supported or cantilever boundary conditions. The method adopts rotational massless springs in the beam element as a mechanical model to represent the local flexibility introduced by a crack. For a given natural frequency and a damage location, the characteristic equation can be solved to provide numerical value of the stiffness of the rotational spring. The intersection points of the values of the normalized crack stiffness K at various natural frequencies omega sub i along the axial direction of the beam represent the possible locations of the crack. Furthermore, the numerical value K has been shown to be directly related to the damage magnitude as DeltaI/I, where DeltaI is the reduction of section modulus and I is the original undamaged section modulus. Two numerical case studies are given to demonstrate the validity of the method.