A complex variable description of planar motion incorporates directivity as inherent information which is therefore very convenient in vibration analysis of rotors. This paper proposes to use the directional information explicitly when the equation of motion of a rotor is formulated in complex variables. It is shown that the free vibration solution to the equation of motion formulated as such can be defined as the directional natural mode because it describes not only the shape and frequency but also the direction of the free vibration response. The directional frequency response functions (dFRFs) that have been used recently are obtained as the solution to the forced vibration solution to the equation of motion. Symmetric and anti-symmetric motions of a geometrically symmetric rigid rotor are used as examples to explain these concepts and their practical significances. The proposed approach allows clear understanding and definitions of some unique characteristics of rotor vibrations, such as the forward and backward modes, and forward and backward critical speeds, which have been often used in confusing or incorrect ways.
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July 2002
Technical Papers
Vibration Analysis of Rotors Utilizing Implicit Directional Information of Complex Variable Descriptions
C. Kessler,
C. Kessler
United States Air Force Research Laboratory, AFRL/PRPG Bldg 18A Rm 231, 1950 Fifth Street, Wright-Patterson AFB, OH 45433-7251
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J. Kim
J. Kim
Structural Dynamics Research Laboratory, Mechanical Engineering, University of Cincinnati, Cincinnati, OH 45221-0072
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C. Kessler
United States Air Force Research Laboratory, AFRL/PRPG Bldg 18A Rm 231, 1950 Fifth Street, Wright-Patterson AFB, OH 45433-7251
J. Kim
Structural Dynamics Research Laboratory, Mechanical Engineering, University of Cincinnati, Cincinnati, OH 45221-0072
Contributed by the Technical Committee on Vibration and Sound for publication in the JOURNAL OF VIBRATION AND ACOUSTICS. Manuscript received May 2001; Revised January 2002. Associate Editor: G. Flowers.
J. Vib. Acoust. Jul 2002, 124(3): 340-349 (10 pages)
Published Online: June 12, 2002
Article history
Received:
May 1, 2001
Revised:
January 1, 2002
Online:
June 12, 2002
Citation
Kessler, C., and Kim, J. (June 12, 2002). "Vibration Analysis of Rotors Utilizing Implicit Directional Information of Complex Variable Descriptions ." ASME. J. Vib. Acoust. July 2002; 124(3): 340–349. https://doi.org/10.1115/1.1467649
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