Analytical Solution of Whirl Speed and Mode Shape for Rotating Shafts PUBLIC ACCESS

[+] Author Affiliations
S. M. Yang, G. J. Sheu, C. D. Yang

National Cheng Kung University, Taiwan, R.O.C.

Paper No. 96-GT-264, pp. V005T14A023; 8 pages
  • ASME 1996 International Gas Turbine and Aeroengine Congress and Exhibition
  • Volume 5: Manufacturing Materials and Metallurgy; Ceramics; Structures and Dynamics; Controls, Diagnostics and Instrumentation; Education; General
  • Birmingham, UK, June 10–13, 1996
  • Conference Sponsors: International Gas Turbine Institute
  • ISBN: 978-0-7918-7876-7
  • Copyright © 1996 by ASME


The analytical solution of whirl speed and mode shape of a rotating shaft in six boundary conditions is presented in this paper. The shaft is modelled by a Rayleigh beam with rotatory inertia and gyroscopic effects, and the boundary conditions are (1) short-short, (2) long-long, (3) long-free, (4) free-free, (5) long-short, and (6) short-free bearings. It is shown that the whirl speed can be written analytically by a function of the whirl ratio (λ) defined by the rotating speed over the whirl speed and the slenderness ratio (l) defined by the length of the shaft over its radius. The number of whirl speeds, contrary to common belief, is finite when λ > 1/2. For the first time, the rotating system’s unbalanced response can be written analytically in an exact form by a finite number of vibration modes with the corresponding generalized coordinates.

Copyright © 1996 by ASME
Topics: Whirls , Mode shapes
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