Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

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



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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  • [1] R. Courant and D. Hilbert, Methods of mathematical physics. Vol. I, Interscience Publishers, Inc., New York, N.Y., 1953. MR 0065391
  • [2] R. D. Mindlin and L. E. Goodman, Beam vibrations with time-dependent boundary conditions, J. Appl. Mech. 17 (1950), 377–380. MR 0038830
  • [3] G. Herrmann, Forced motion of elastic rods, J. Appl. Mech. 21, 221-224, (1954)
  • [4] 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
  • [5] R. D. Mindlin, Influence of rotary inertia and shear on flexural motions of isotropic elastic plates, J. Appl. Mech. 18, 31-38 (1951)
  • [6] R. D. Mindlin and H. Deresiewicz, Timoshenko’s shear coefficient for flexural vibrations of beams, Proc. Second U.S. Nat. Congress of Applied Mechanics, University of Michigan, Ann Arbor, Michigan, June 14-18, 1954. MR 0095626
  • [7] 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)
  • [8] R. W. Leonard and B. Budianski, On traveling waves in beams, NACA TN 2874 (1953)

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DOI: https://doi.org/10.1090/qam/79436
Article copyright: © Copyright 1956 American Mathematical Society

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