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RESEARCH PAPERS: Vibration and Sound

Stability of Cracked Rotors in the Coupled Vibration Mode

[+] Author and Article Information
C. A. Papadopoulos, A. D. Dimarogonas

Department of Mechanical Engineering, Washington University, St. Louis, MO 63130

J. Vib., Acoust., Stress, and Reliab 110(3), 356-359 (Jul 01, 1988) (4 pages) doi:10.1115/1.3269525 History: Received June 25, 1987; Online November 23, 2009

Abstract

A transverse surface crack is known to add to a shaft a local flexibility due to the stress-strain singularity in the vicinity of the crack tip. This flexibility can be represented, in the general case by way of a 6 × 6 compliance matrix describing the local flexibility in a short shaft element which includes the crack. This matrix has off-diagonal terms which cause coupling along the directions which are indicated by the off-diagonal terms. In addition, when the shaft rotates the crack opens and closes. Then the differential equations of motion have periodically varying stiffness coefficients and the solution can be expressed as a sum of harmonic functions of time. A method for the determination of the intervals of instability of the first and of second kind is developed. The results have been presented in stability charts in the frequency vs. depth of the crack domain. The coupling effect due to the crack leads to very interesting results such as new frequencies and vibration modes.

Copyright © 1988 by ASME
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