0
Research Papers

Rotating Beams and Nonrotating Beams With Shared Eigenpair

[+] Author and Article Information
Ananth Kumar

Department of Aerospace Engineering, Indian Institute of Technology Madras, Chennai 600036, Indiaae05b004@iitm.ac.in

Ranjan Ganguli1

Department of Aerospace Engineering, Indian Institute of Science, Bangalore 560012, Indiaganguli@aero.iisc.ernet.in

1

Corresponding author.

J. Appl. Mech 76(5), 051006 (Jun 18, 2009) (14 pages) doi:10.1115/1.3112741 History: Received July 11, 2008; Revised February 05, 2009; Published June 18, 2009

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 nonrotating 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 FSF for finite element analysis are provided. The proposed functions can be used as test-functions for rotating beam codes and for targeted destiffening of rotating beams.

Copyright © 2009 by American Society of Mechanical Engineers
Your Session has timed out. Please sign back in to continue.

References

Figures

Grahic Jump Location
Figure 1

Schematic of a rotating beam

Grahic Jump Location
Figure 2

EI1(x) variation for first four modes for a beam with properties given in Table 1

Grahic Jump Location
Figure 3

Beam element used for p-version FEM

Grahic Jump Location
Figure 4

Gauss-quadrature points of order 30 for the domain (0,0.6) and the singularity points of the flexural stiffness functions

Grahic Jump Location
Figure 5

Convergence of the p-version finite element code for first four modes using derived flexural stiffness functions

Grahic Jump Location
Figure 6

Residue of mode-shapes obtained from p-version FEM

Grahic Jump Location
Figure 7

Convergence characteristics and residue of nodal displacements for first mode with h-version finite element code

Grahic Jump Location
Figure 8

Fundamental mesh for the second mode h-version FEM, and the first two refinements

Grahic Jump Location
Figure 9

Convergence characteristics and residue of nodal displacements for second mode with h-version finite element code

Grahic Jump Location
Figure 10

Fundamental mesh for the third mode h-version FEM, and the first two refinements

Grahic Jump Location
Figure 11

Convergence characteristics and residue of nodal displacements for third mode with h-version finite element code

Grahic Jump Location
Figure 12

Fundamental mesh for the fourth mode h-version FEM, and the first two refinements

Grahic Jump Location
Figure 13

Convergence characteristics and residue of nodal displacements for fourth mode with h-version finite element code

Grahic Jump Location
Figure 14

Variation in height and breadth of a rotating beam equivalent to a uniform nonrotating beam for the first mode

Grahic Jump Location
Figure 15

Top and side views of a rotating beam equivalent to a uniform rotating beam for the first mode

Grahic Jump Location
Figure 16

Realistic beams: approximations to the exact function for the second mode

Grahic Jump Location
Figure 17

Variation in height and breadth of a rotating beam equivalent to a uniform nonrotating beam for the second mode

Grahic Jump Location
Figure 18

Realistic beams: approximations to the exact function for the third mode

Grahic Jump Location
Figure 19

Variation in height and breadth of a rotating beam equivalent to a uniform nonrotating beam for the third mode

Grahic Jump Location
Figure 20

Realistic beams: approximations to the exact function for the fourth mode

Grahic Jump Location
Figure 21

Variation in height and breadth of a rotating beam equivalent to a uniform nonrotating beam for the fourth mode

Grahic Jump Location
Figure 22

Destiffening effects of flexural stiffness variations for various modes compared with uniform rotating beam (EI1(r))

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.

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