A procedure for multiple crack identification in beam-like structures from natural vibration mode

This paper deals with the problem of multiple crack identification for beam-like structures from a natural vibration mode. A simplified expression for natural vibration modes of a beam with an arbitrary number of cracks has been obtained explicitly in terms of the crack parameters. The obtained solution allows not only a new form of the eigenvalue problem for a multiple cracked beam to be derived, but it is also straightforward to formulate the standard inverse problem of multi crack identification from measured mode shape. The proposed procedure in combination with the well known regularization method enables both location and size of multiple cracks to be consistently identified from the sparsely and noisy measured data. The robustness of the technique that can be called the crack scanning method has been illustrated and validated by the numerical simulation results.