Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

Online ISSN 1552-4485; Print ISSN 0033-569X



On the Timoshenko theory of transverse beam vibrations

Author: C. L. Dolph
Journal: Quart. Appl. Math. 12 (1954), 175-187
MSC: Primary 73.2X
DOI: https://doi.org/10.1090/qam/62620
MathSciNet review: 62620
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  • [1] Lord Rayleigh, The theory of sound, MacMillan Co., London, 1877, par. 186.
  • [2] S. P. Timoshenko, On the correction for shear of the differential equation for transverse vibration of prismatic bars, London Phil. Mag. (6) 41, 744 (1921).
  • [3] -, On the transverse vibrations of bars of uniform cross-section, London Phil. Mag. (6) 43, 125 (1921).
  • [4] R. D. Mindlin, Influence of rotary inertia and shear on flectural motions of isotropic, elastic plates, J. Appl. Mech. 18, 31 (1951).
  • [5] E. Goens, Über die Bestimmung der Elastizitätsmoduls von Stäben mit Hilfe von Biegungsschwingungen, Ann. Physik. (5) 11, 649 (1931).
  • [6] J. Ormondroyd, R. Hess and G. Hess, Theoretical research on the dynamics of a ship's structure, Univ. of Mich. Eng. Res. Inst., Third Progress Report, Office of Naval Research Contract n50-ri-116 (1949).
  • [7] R. Hess, Theoretical vibrations of beams, Ph. D. thesis, Dept. of Eng. Mechanics, Univ. of Mich., 1949.
  • [8] E. T. Kruszewski, Effect of transverse shear and rotary inertia on the natural frequency of a uniform beam, NACA, Tech. Note 1909 (1949).
  • [9] C. Howe, R. Howe, and L. Rauch, Application of the electronic differential analyzer to the oscillation of beams, including shear and rotary inertia, Ext. Memo. UMM-67, Univ. of Mich. Res. Inst., (1951).
  • [10] C. L. Dolph, Normal modes of oscillation of beams, Ext. Memo. UMM-79, Univ. of Mich. Res. Inst. (1950).
  • [11] R. D. Mindlin and L. E. Goodman, Beam vibrations with time-dependent boundary conditions, J. Appl. Mech. 17 (1950), 377–380. MR 0038830

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DOI: https://doi.org/10.1090/qam/62620
Article copyright: © Copyright 1954 American Mathematical Society

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