0
TECHNICAL PAPERS

Natural Frequencies of Rotating Uniform Beams with Coriolis Effects

[+] Author and Article Information
S. M. Hashemi, M. J. Richard

Department of Mechanical Engineering, Laval University, Québec, Canada G1K 7P4

J. Vib. Acoust 123(4), 444-455 (Apr 01, 2001) (12 pages) doi:10.1115/1.1383969 History: Received March 01, 2000; Revised April 01, 2001
Copyright © 2001 by ASME
Your Session has timed out. Please sign back in to continue.

References

Figures

Grahic Jump Location
An example of a spinning two-dimensional frame
Grahic Jump Location
An individual member of a frame
Grahic Jump Location
The domain, discretized by a number of 2-node elements
Grahic Jump Location
Rotating uniform beam geometry
Grahic Jump Location
Comparison of spin-induced effects for α=90 deg; the FREQUENCY RATIO- (first lead-lag mode (ωx)/ωx0 vs SPIN RATIO-Ω/ωz0;—, preload plus centripetal and Coriolis Accelerations included; — * —, only the centripetal Acceleration included: —+—, only the Coriolis Acceleration included; —□—, only the preload included
Grahic Jump Location
Comparison of spin-induced effects for α=90 deg; the FREQUENCY RATIO- (first flapping mode (ωz)/ωz0 vs SPIN RATIO- Ω/ωz0; —, preload plus centripetal and Coriolis Acceleration included; — * —, only the centripetal Acceleration included; —+—, only the Coriolis Acceleration included; —□—, only the preload included
Grahic Jump Location
A cantilever uniform radial beam
Grahic Jump Location
The basis functions (Pifz,i=1,2,3,4) for in-plane (lead-lag) flexural vibration of a uniform beam rotating in horizontal plane; E=1 GPa, A=1 m2 , L=1 m, ρ=1 kg/m3 , and l=1 m4 . (a) Standard (static) cubic basis functions; (b) dynamic basis functions for a nonrotating beam; (c) dynamic basis function for a rotating beam and λ=Ω.l2.m/E.I=12; —, P1; —○—, P2; —+—, P3; —⋆–, P4.  
Grahic Jump Location
The variation of the dynamic in-plane (lead-lag) flexural shape functions Ni vs frequency changes for a uniform beam rotating in horizontal plane; E=1 GPa, A=1 m2 , L=1 m, ρ=1 kg/m3 , l=1 m4 , and λ=Ω.l2.m/E.I=12. (a) N1; (b) N2; (c) N3; (d) N4; –×, ω1, 1st natural frequency;  −Δ, ω2, 2nd natural frequency; –⋆, ω3, 3rd natural frequency; −⋄, ω4, 4th natural frequency.  
Grahic Jump Location
The change of the fourth dynamic shape function, N4, at the third natural frequency, ω3, vs spinning speed for the same beam as in Fig. 9. –×, Ω=4 rad/s; –Δ, Ω=8 rad/s, –⋆, Ω=12 rad/s.

Tables

Errata

Discussions

Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In