Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

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

   
 
 

 

Nonlinear dynamic buckling of a compressed elastic column


Authors: Edward L. Reiss and Bernard J. Matkowsky
Journal: Quart. Appl. Math. 29 (1971), 245-260
MSC: Primary 73.35
DOI: https://doi.org/10.1090/qam/286344
MathSciNet review: 286344
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  • [1] E. Mettler, Dynamic buckling, Handbook of engineering mechanics, McGraw-Hill, New York, 1962, chapter 62
  • [2] S. Woinowsky-Krieger, The effect of an axial force on the vibration of hinged bars, J. Appl. Mech. 17 35-36 (1950) MR 0034202
  • [3] N. J. Hoff, The dynamics of the buckling of elastic columns, J. Appl. Mech. 18, 68-74 (1951) MR 0047506
  • [4] N. J. Hoff, Dynamic stability of structures, Proceedings of an international conference on dynamic stability of structures, Pergamon Press, New York, 1967 MR 0202526
  • [5] J. D. Cole, Perturbation methods in applied mathematics, Blaisdell, Waltham, Mass., 1968 MR 0246537
  • [6] E. L. Reiss, On multi-variable asymptotic expansions, SIAM Rev. (to appear) MR 0289873
  • [7] B. J. Matkowsky, Asymptotic solution of a nonlinear stability problem, Studies in Appl. Math., no. 5; a collection of papers presented at the Conference on Qualitative Theory of Nonlinear Differential and Integral Equations (Madison, Wis., 1968), SIAM, Philadelphia, Pa., 1969. MR 0357924
  • [8] B. J. Matkowsky, Nonlinear dynamic stability: A formal theory, SIAM J. Appl. Math. 18, 872-883 (1970)
  • [9] B. J. Matkowsky, A simple nonlinear dynamic stability problem, Bull. Amer. Math. Soc. 17, 620-625 (1970) MR 0257544
  • [10] S. Lubkin and J. J. Stoker, Stability of columns and strings under periodically varying forces, Quart. Appl. Math. 1, 215-236 (1943) MR 0008982
  • [11] V. V. Bolotin, The dynamic stability of elastic systems, Holden-Day, San Francisco, Calif., 1964
  • [12] E. Sevin, On the elastic bending of columns due to dynamic axial forces including effects of axial inertia, J. Appl. Mech. 27, 125-131 (1960) MR 0111271
  • [13] R. W. Dickey, Free vibrations and dynamic buckling of the extensible beam, J. Math. Anal. Appl. 29, 443-454 (1970) MR 0253617
  • [14] E. L. Reiss, Column buckling--an elementary example of bifurcation, Bifurcation theory and nonlinear eigenvalue problems, Benjamin, New York, 1969, pp. 1-16
  • [15] J. J. Stoker, Nonlinear vibrations in mechanical and electrical systems, Interscience, New York, 1950 MR 0034932

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DOI: https://doi.org/10.1090/qam/286344
Article copyright: © Copyright 1971 American Mathematical Society

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