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Rotating Beams and Nonrotating Beams With Shared Eigenpair.

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Title: Rotating Beams and Nonrotating Beams With Shared Eigenpair.
Authors: Kumar, Ananth1 ae05b004@iitm.ac.in, Gangu, Ranja2 ganguli@aero.iisc.ernet.in
Source: Journal of Applied Mechanics. Sep2009, Vol. 76 Issue 5, p051006:1-051006:14. 14p. 9 Charts, 22 Graphs.
Subjects: Girders, Finite element method, Cantilevers, Stiffness (Mechanics), Military strategy
Abstract: In this paper we look for rotating beams whose eigenpair (frequency and mode-shape) is the same as that of uniform nonrotating beams for a particular mode. It is found that, for any given mode, there exist flexural stiffness functions (FSFs) for which the jth mode eigenpair of a rotating beam, with uniform mass distribution, is identical to that of a corresponding nonrotating uniform beam with the same length and mass distribution. By putting the derived FSF in the finite element analysis of a rotating cantilever beam, the frequencies and mode-shapes of a nonrotaring cantilever beam are obtained. For the first mode, a physically feasible equivalent rotating beam exists, but for higher modes, the flexural stiffness has internal singularities. Strategies for addressing the singularities in the FSFforfinite element analysis are provided. The proposed functions can be used as test-functions for rotating beam codes and for targeted destiffening of rotating beams. [ABSTRACT FROM AUTHOR]
Copyright of Journal of Applied Mechanics is the property of American Society of Mechanical Engineers and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
Database: Engineering Source
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DbLabel: Engineering Source
An: 44125936
AccessLevel: 6
PubType: Academic Journal
PubTypeId: academicJournal
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  Data: Rotating Beams and Nonrotating Beams With Shared Eigenpair.
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  Data: <searchLink fieldCode="AR" term="%22Kumar%2C+Ananth%22">Kumar, Ananth</searchLink><relatesTo>1</relatesTo><i> ae05b004@iitm.ac.in</i><br /><searchLink fieldCode="AR" term="%22Gangu%2C+Ranja%22">Gangu, Ranja</searchLink><relatesTo>2</relatesTo><i> ganguli@aero.iisc.ernet.in</i>
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  Data: <searchLink fieldCode="JN" term="%22Journal+of+Applied+Mechanics%22">Journal of Applied Mechanics</searchLink>. Sep2009, Vol. 76 Issue 5, p051006:1-051006:14. 14p. 9 Charts, 22 Graphs.
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  Data: <searchLink fieldCode="DE" term="%22Girders%22">Girders</searchLink><br /><searchLink fieldCode="DE" term="%22Finite+element+method%22">Finite element method</searchLink><br /><searchLink fieldCode="DE" term="%22Cantilevers%22">Cantilevers</searchLink><br /><searchLink fieldCode="DE" term="%22Stiffness+%28Mechanics%29%22">Stiffness (Mechanics)</searchLink><br /><searchLink fieldCode="DE" term="%22Military+strategy%22">Military strategy</searchLink>
– Name: Abstract
  Label: Abstract
  Group: Ab
  Data: In this paper we look for rotating beams whose eigenpair (frequency and mode-shape) is the same as that of uniform nonrotating beams for a particular mode. It is found that, for any given mode, there exist flexural stiffness functions (FSFs) for which the jth mode eigenpair of a rotating beam, with uniform mass distribution, is identical to that of a corresponding nonrotating uniform beam with the same length and mass distribution. By putting the derived FSF in the finite element analysis of a rotating cantilever beam, the frequencies and mode-shapes of a nonrotaring cantilever beam are obtained. For the first mode, a physically feasible equivalent rotating beam exists, but for higher modes, the flexural stiffness has internal singularities. Strategies for addressing the singularities in the FSFforfinite element analysis are provided. The proposed functions can be used as test-functions for rotating beam codes and for targeted destiffening of rotating beams. [ABSTRACT FROM AUTHOR]
– Name: AbstractSuppliedCopyright
  Label:
  Group: Ab
  Data: <i>Copyright of Journal of Applied Mechanics is the property of American Society of Mechanical Engineers and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
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RecordInfo BibRecord:
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        Value: 10.1115/1.3112741
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      – Code: eng
        Text: English
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      Pagination:
        PageCount: 14
        StartPage: 051006:1
    Subjects:
      – SubjectFull: Girders
        Type: general
      – SubjectFull: Finite element method
        Type: general
      – SubjectFull: Cantilevers
        Type: general
      – SubjectFull: Stiffness (Mechanics)
        Type: general
      – SubjectFull: Military strategy
        Type: general
    Titles:
      – TitleFull: Rotating Beams and Nonrotating Beams With Shared Eigenpair.
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            NameFull: Kumar, Ananth
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            NameFull: Gangu, Ranja
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            – D: 01
              M: 09
              Text: Sep2009
              Type: published
              Y: 2009
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              Value: 76
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              Value: 5
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            – TitleFull: Journal of Applied Mechanics
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