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Eigenvalue formulas for the uniform Timoshenko beam: the free-free problem
Author(s):
Bruce
Geist;
Joyce
R.
McLaughlin
Journal:
Electron. Res. Announc. Amer. Math. Soc.
4
(1998),
12-17.
MSC (1991):
Primary 34Lxx;
Secondary 73Dxx
Posted:
March 20, 1998
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Abstract:
This announcement presents asymptotic formulas for the eigenvalues of a free-free uniform Timoshenko beam.
References:
- 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:
10.1090/S1079-6762-98-00041-9
PII:
S 1079-6762(98)00041-9
Keywords:
Timoshenko beam,
asymptotic distribution of eigenvalues,
boundary value problems
Received by editor(s):
January 5, 1998
Posted:
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
Copyright of article:
Copyright
1998,
American Mathematical Society
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