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

Electronic Research Announcements of the American Mathematical Society

Volumn 4, Issue 3, 1998, Pages 12-17

  Geist, Bruce ^a   McLaughlin, Joyce R ^b  

^a Unisys   (United States)

^b RENSSELAER POLYTECHNIC INSTITUTE   (United States)

Author keywords

Asymptotic distribution of eigenvalues; Boundary value problems; Timoshenko beam

Indexed keywords

EID: 85009742752     PISSN: None     EISSN: 10796762     Source Type: Journal    
DOI: 10.1090/S1079-6762-98-00041-9     Document Type: Article

References (7)

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. Stephen Timoshenko, 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