On the vibration of elastic bodies having time-dependent boundary conditions
Authors:
J. G. Berry and P. M. Naghdi
Journal:
Quart. Appl. Math. 14 (1956), 43-50
MSC:
Primary 73.2X
DOI:
https://doi.org/10.1090/qam/79436
MathSciNet review:
79436
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Additional Information
- R. Courant and D. Hilbert, Methods of mathematical physics. Vol. I, Interscience Publishers, Inc., New York, N.Y., 1953. MR 0065391
- R. D. Mindlin and L. E. Goodman, Beam vibrations with time-dependent boundary conditions, J. Appl. Mech. 17 (1950), 377–380. MR 0038830
G. Herrmann, Forced motion of elastic rods, J. Appl. Mech. 21, 221-224, (1954)
A. Clebsch, Théorie de l’élasticité des corps solides, translated from the German by B. de Saint-Venant and Flamant, Paris 1883, p. 129. Also see A. E. H. Love, Mathematical theory of elasticity, Dover, 1944, p. 180
R. D. Mindlin, Influence of rotary inertia and shear on flexural motions of isotropic elastic plates, J. Appl. Mech. 18, 31-38 (1951)
- R. D. Mindlin and H. Deresiewicz, Timoshenko’s shear coefficient for flexural vibrations of beams, University of Michigan, Ann Arbor, Michigan, June 14-18, 1954. Proc. Second U.S. Nat. Congress of Applied Mechanics. MR 0095626
S. P. Timoshenko, On the correction for shear in the differential equations for transverse vibrations of prismatic bars, Phil. Mag. ser. 6, 41, 744-746 (1921)
R. W. Leonard and B. Budianski, On traveling waves in beams, NACA TN 2874 (1953)
R. Courant and D. Hilbert, Methods of mathematical physics, Vol. I, Interscience, 1953
R. D. Mindlin and L. E. Goodman, Beam vibrations with time-dependent boundary conditions, J. Appl. Mech. 17, 377-380 (1950)
G. Herrmann, Forced motion of elastic rods, J. Appl. Mech. 21, 221-224, (1954)
A. Clebsch, Théorie de l’élasticité des corps solides, translated from the German by B. de Saint-Venant and Flamant, Paris 1883, p. 129. Also see A. E. H. Love, Mathematical theory of elasticity, Dover, 1944, p. 180
R. D. Mindlin, Influence of rotary inertia and shear on flexural motions of isotropic elastic plates, J. Appl. Mech. 18, 31-38 (1951)
R. D. Mindlin and H. Deresiewicz, Timoshenko’s shear coefficient for flexural vibrations of beams, Proc. Second U.S. Natl. Congr. Appl. Mech. 175-178 (1955)
S. P. Timoshenko, On the correction for shear in the differential equations for transverse vibrations of prismatic bars, Phil. Mag. ser. 6, 41, 744-746 (1921)
R. W. Leonard and B. Budianski, On traveling waves in beams, NACA TN 2874 (1953)
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Article copyright:
© Copyright 1956
American Mathematical Society
