Modelling and formulation of equations of motion for cracked rotating shafts

Abstract The dynamics of a cracked, distributed parameter rotor component is studied. The proposed model is a rotating Timoshenko shaft which is also flexible in extension and torsion. Two uniform fields are connected by a local, complex spring element with reduced stiffness and damping simulating an open crack. The modification describing a closed crack is introduced, and the open/close condition is formulated. The governing boundary value problem is then derived. Finally, a special approach prepares the obtained set of equations for application of direct variational methods in a simplified form replacing the geometric discontinuity by a load discontinuity at the crack location. A simple example, discussing the torsional vibrations of a simply supported, circular rotating shaft with a circumferential crack, emphasizes the general considerations.

[1]  I. W. Mayes,et al.  The Vibrational Behavior of a Multi-Shaft, Multi-Bearing System in the Presence of a Propagating Transverse Crack , 1984 .

[2]  Robert D. Adams,et al.  The location of defects in structures from measurements of natural frequencies , 1979 .

[3]  H. D. Nelson,et al.  The Dynamics of a Rotor System with a Cracked Shaft , 1986 .

[4]  R. Eshleman,et al.  On the Critical Speeds of a Continuous Rotor , 1969 .

[5]  B. Grabowski,et al.  The Vibrational Behavior of a Turbine Rotor Containing a Transverse Crack , 1980 .

[6]  Jörg Wauer,et al.  On the Dynamics of Cracked Rotors: A Literature Survey , 1990 .

[7]  Andrew D. Dimarogonas,et al.  Coupled Longitudinal and Bending Vibrations of a Cracked Shaft , 1988 .

[8]  Andrew D. Dimarogonas,et al.  Coupled longitudinal and bending vibrations of a rotating shaft with an open crack , 1987 .

[9]  P. Gudmundson.  The dynamic behaviour of slender structures with cross-sectional cracks , 1983 .

[10]  Jörg Wauer.  Stabilität viskoelastischer Wellen unter axialem Druck , 1985 .

[11]  Andrew D. Dimarogonas,et al.  Torsional vibration of a shaft with a circumferential crack , 1981 .

[12]  H. Petroski.  Simple static and dynamic models for the cracked elastic beam , 1981 .

[13]  Preben Terndrup Pedersen.  On forward and backward precession of rotors , 1972 .

[14]  Henry Petroski,et al.  On detecting a crack by tapping a beam , 1986 .

[15]  Andrew D. Dimarogonas,et al.  Coupling of bending and torsional vibration of a cracked Timoshenko shaft , 1987 .

[16]  Olivier Bernasconi.  Solution for torsional vibrations of stepped shafts using singularity functions , 1986 .