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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Additional Information
Lord Rayleigh, The theory of sound, MacMillan Co., London, 1877, par. 186.
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).
---, On the transverse vibrations of bars of uniform cross-section, London Phil. Mag. (6) 43, 125 (1921).
R. D. Mindlin, Influence of rotary inertia and shear on flectural motions of isotropic, elastic plates, J. Appl. Mech. 18, 31 (1951).
E. Goens, Über die Bestimmung der Elastizitätsmoduls von Stäben mit Hilfe von Biegungsschwingungen, Ann. Physik. (5) 11, 649 (1931).
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).
R. Hess, Theoretical vibrations of beams, Ph. D. thesis, Dept. of Eng. Mechanics, Univ. of Mich., 1949.
E. T. Kruszewski, Effect of transverse shear and rotary inertia on the natural frequency of a uniform beam, NACA, Tech. Note 1909 (1949).
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).
C. L. Dolph, Normal modes of oscillation of beams, Ext. Memo. UMM-79, Univ. of Mich. Res. Inst. (1950).
- R. D. Mindlin and L. E. Goodman, Beam vibrations with time-dependent boundary conditions, J. Appl. Mech. 17 (1950), 377–380. MR 0038830
Lord Rayleigh, The theory of sound, MacMillan Co., London, 1877, par. 186.
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).
---, On the transverse vibrations of bars of uniform cross-section, London Phil. Mag. (6) 43, 125 (1921).
R. D. Mindlin, Influence of rotary inertia and shear on flectural motions of isotropic, elastic plates, J. Appl. Mech. 18, 31 (1951).
E. Goens, Über die Bestimmung der Elastizitätsmoduls von Stäben mit Hilfe von Biegungsschwingungen, Ann. Physik. (5) 11, 649 (1931).
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).
R. Hess, Theoretical vibrations of beams, Ph. D. thesis, Dept. of Eng. Mechanics, Univ. of Mich., 1949.
E. T. Kruszewski, Effect of transverse shear and rotary inertia on the natural frequency of a uniform beam, NACA, Tech. Note 1909 (1949).
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).
C. L. Dolph, Normal modes of oscillation of beams, Ext. Memo. UMM-79, Univ. of Mich. Res. Inst. (1950).
R. Mindlin and L. E. Goodman, Beam vibrations with time dependent boundary conditions, J. App. Mech. 17, 377 (1950).
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Article copyright:
© Copyright 1954
American Mathematical Society
