Coupled Longitudinal and Bending Vibrations of a Cracked Shaft

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Abstract
This paper describes the coupling of bending and longitudinal vibration of a stationary cracked shaft with an open crack. The crack is modeled by way of a 2×2 local flexibility matrix with coupling terms. The elements of this matrix are obtained analytically. One of the elements compares well with experimental data of other investigators. The free vibration of the shaft, and the influence of the crack on the vibrational behavior of the shaft is studied. The relation of the eigenvalues of the system and the crack depth as functions of the slenderness ratio are presented. The forced vibration of the shaft is also studied and the coupling of the vibration modes is verified analytically and experimentally. The applicability of the method as a crack identification tool is demonstrated.

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