Vibration Analysis of a Cracked Shaft Using FEM

Abstract

A strong interest has developed within the past several years in the dynamic behavior of turbo machinery with cracked shafts. An excellent review of the field of the dynamics of cracked rotors and of different detection procedures to diagnose fracture damage has been presented by Wauer . Vibration investigation of a damaged structure is one approach for fault diagnosis. Vibration diagnosis, as a non-destructive detection technique, has recently become of greater importance.
A crack on a beam element introduces considerable local flexibility due to the strain energy concentration in the vicinity of the crack tip under load. The vibrational characteristics of a cracked Timoshenko shaft were investigated by Rajab and Sabeeh . They presented analytical expressions and derived curves relating the crack depth and location on the shaft
to changes in the first few natural frequencies of the shaft. The element stiffness matrix of a beam with a crack was derived froman integration of the stress intensity factors and then a finite element model (FEM) of a cracked beam was established in reference . A similar approach based on the flexibility matrix developed by Papado-poulos and Dimarogonas is dealt with by using FEM in the present study for crack detection.