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.
In this paper, authors present the study of free vibration of bending multiple cracked functionally graded material (FGM) beam. Vibration equations of multiple cracked FGM beam were established by using the rotational spring model of cracks, dynamic stiffness method (DSM) and actual position of neutral plane. The frequency equation obtained was in a simple form, that provides an effective approach to study not only free vibration of the beams but also inverse problems like identification of material and crack parameters in structure. The obtained numerical results show good agreement with other previous published results. Thence, numerical computation has been carried out to investigate the effect of each crack, the number of cracks, material and geometric parameters on the natural frequencies of multiple cracked Timoshenko FGM beams.
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