Identification of a finite number of small cracks in a rod using natural frequencies

• A method for identification of cracks in a rod by natural frequencies is developed.
• Inverse problems for rods are considered for several types of end conditions.
• Numerical examples illustrating efficiency of the developed method are considered.
• Sensibility of the results to the noise in data is studied.

A problem of identification of a finite number of small cracks in a rod by means of natural frequencies corresponding to longitudinal vibration is considered. The cracks are simulated by massless translational springs. It is known, that generally for unique identification of multiple cracks in a rod it is necessary to know two spectra. An algorithm is developed enabling in case of small cracks to extract an important information about the possible number of cracks, their positions and the flexibilities of the corresponding springs by means of only one spectrum. The developed method is extended for identification small multiple cracks in a simply supported beam.