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Eigenvalue formulas for the uniform Timoshenko beam: the free-free problem


Authors: Bruce Geist and Joyce R. McLaughlin
Journal: Electron. Res. Announc. Amer. Math. Soc. 4 (1998), 12-17
MSC (1991): Primary 34Lxx; Secondary 73Dxx
DOI: https://doi.org/10.1090/S1079-6762-98-00041-9
Published electronically: March 20, 1998
MathSciNet review: 1611829
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Abstract | References | Similar Articles | Additional Information

Abstract: This announcement presents asymptotic formulas for the eigenvalues of a free-free uniform Timoshenko beam.


References [Enhancements On Off] (What's this?)

  • 1. Bruce Geist, The asymptotic expansion of the eigenvalues of the Timoshenko beam, Ph.D. Dissertation, Rensselaer Polytechnic Institute, Troy, NY, 1994.
  • 2. Bruce Geist and J. R. McLaughlin, Double eigenvalues for the uniform Timoshenko beam, Applied Mathematics Letters, 10 (1997), 129-134. CMP 97:15
  • 3. T. C. Huang, The effect of rotatory inertia and of shear deformation on the frequency and normal mode equations of uniform beams with simple end conditions, Journal of Applied Mechanics 28 (1961), 579-584. MR 24:B579
  • 4. Edwin T. Kruszewski, Effect of transverse shear and rotary inertia on the natural frequency of a uniform beam, National Advisory Committee for Aeronautics, Technical Note no. 1909, July 1949.
  • 5. Stephen Timoshenko, On the correction for shear of the differential equation for transverse vibrations of prismatic bars, Philisophical Magazine 41 (1921), 744-746.
  • 6. -, On the transverse vibrations of bars of uniform cross-section, Philisophical Magazine 43 (1922), 125-131.
  • 7. R. W. Trail-Nash and A. R. Collar, The effects of shear flexibility and rotatory inertia on the bending vibrations of beams, Quart. J. Mech. Appl. Math. 6 (1953), 186-222. MR 16:541f

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Additional Information

Bruce Geist
Affiliation: Unisys Corporation, 41100 Plymouth Road, Plymouth, MI 48170
Email: Bruce.Geist@unisys.com

Joyce R. McLaughlin
Affiliation: Department of Mathematical Sciences, Rensselaer Polytechnic Institute, Troy, NY 12180
Email: mclauj@rpi.edu

DOI: https://doi.org/10.1090/S1079-6762-98-00041-9
Keywords: Timoshenko beam, asymptotic distribution of eigenvalues, boundary value problems
Received by editor(s): January 5, 1998
Published electronically: March 20, 1998
Additional Notes: The work of both authors was completed at Rensselaer Polytechnic Institute, and was partially supported by funding from the Office of Naval Research, grant number N00014-91J-1166. The work of the first author was also partially supported by the Department of Education fellowship grant number 6-28069. The work of the second author was also partially supported by the National Science Foundation, grant number DMS-9410700.
Communicated by: Michael Taylor
Article copyright: © Copyright 1998 American Mathematical Society

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