Abstract
Singular perturbation techniques are employed to estimate the natural frequencies and mode shapes of a highly flexible spinning Bernoulli-Euler beam. The normalized beam stiffness ε = El/mΩ 2R 4 is introduced and treated as a small parameter. Then, perturbation-based approximations of the natural frequencies and mode shapes are first derived for a general hub radius. The special cases of a zero hub radius and a normalized hub radius approaching 1.0 are investigated. The frequency predictions obtained for a zero hub radius matched the exact values within 3% for the first two vibration modes. Mode shape predictions are better for lower modes with an accuracy decreasing at higher modes. Excellent accuracy on both frequencies and mode shapes is obtained for the case of normalized hub radius approaching 1.0.
| Original language | English (US) |
|---|---|
| Title of host publication | Collection of Technical Papers - AIAA/ASME Structures, Structural Dynamics and Materials Conference |
| Publisher | Publ by AIAA |
| Pages | 2130-2137 |
| Number of pages | 8 |
| Edition | pt 4 |
| State | Published - 1993 |
| Event | 34th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference - La Jolla, CA, USA Duration: Apr 19 1993 → Apr 22 1993 |
Other
| Other | 34th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference |
|---|---|
| City | La Jolla, CA, USA |
| Period | 4/19/93 → 4/22/93 |
Fingerprint
ASJC Scopus subject areas
- Engineering(all)
Cite this
Natural frequencies and mode shapes of flexible spinning beams. / Eick, Chris D.; Mignolet, Marc.
Collection of Technical Papers - AIAA/ASME Structures, Structural Dynamics and Materials Conference. pt 4. ed. Publ by AIAA, 1993. p. 2130-2137.Research output: Chapter in Book/Report/Conference proceeding › Conference contribution
}
TY - GEN
T1 - Natural frequencies and mode shapes of flexible spinning beams
AU - Eick, Chris D.
AU - Mignolet, Marc
PY - 1993
Y1 - 1993
N2 - Singular perturbation techniques are employed to estimate the natural frequencies and mode shapes of a highly flexible spinning Bernoulli-Euler beam. The normalized beam stiffness ε = El/mΩ 2R 4 is introduced and treated as a small parameter. Then, perturbation-based approximations of the natural frequencies and mode shapes are first derived for a general hub radius. The special cases of a zero hub radius and a normalized hub radius approaching 1.0 are investigated. The frequency predictions obtained for a zero hub radius matched the exact values within 3% for the first two vibration modes. Mode shape predictions are better for lower modes with an accuracy decreasing at higher modes. Excellent accuracy on both frequencies and mode shapes is obtained for the case of normalized hub radius approaching 1.0.
AB - Singular perturbation techniques are employed to estimate the natural frequencies and mode shapes of a highly flexible spinning Bernoulli-Euler beam. The normalized beam stiffness ε = El/mΩ 2R 4 is introduced and treated as a small parameter. Then, perturbation-based approximations of the natural frequencies and mode shapes are first derived for a general hub radius. The special cases of a zero hub radius and a normalized hub radius approaching 1.0 are investigated. The frequency predictions obtained for a zero hub radius matched the exact values within 3% for the first two vibration modes. Mode shape predictions are better for lower modes with an accuracy decreasing at higher modes. Excellent accuracy on both frequencies and mode shapes is obtained for the case of normalized hub radius approaching 1.0.
UR - http://www.scopus.com/inward/record.url?scp=0027206085&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=0027206085&partnerID=8YFLogxK
M3 - Conference contribution
AN - SCOPUS:0027206085
SP - 2130
EP - 2137
BT - Collection of Technical Papers - AIAA/ASME Structures, Structural Dynamics and Materials Conference
PB - Publ by AIAA
ER -