Natural frequencies and mode shapes of flexible spinning beams

Chris D. Eick; Marc Mignolet

Natural frequencies and mode shapes of flexible spinning beams

IAFSE-SEMTE: Mechanical and Aerospace Engineering

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

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

ASJC Scopus subject areas

Engineering(all)

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@inproceedings{9894dcb831ed48da9edab4021656b566,

title = "Natural frequencies and mode shapes of flexible spinning beams",

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. ",

author = "Eick, {Chris D.} and Marc Mignolet",

year = "1993",

language = "English (US)",

pages = "2130--2137",

booktitle = "Collection of Technical Papers - AIAA/ASME Structures, Structural Dynamics and Materials Conference",

publisher = "Publ by AIAA",

edition = "pt 4",

note = "34th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference ; Conference date: 19-04-1993 Through 22-04-1993",

}

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.

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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

T2 - 34th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference

Y2 - 19 April 1993 through 22 April 1993

ER -

Natural frequencies and mode shapes of flexible spinning beams

Abstract

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ASJC Scopus subject areas

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