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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Additional Information
E. Mettler, Dynamic buckling, Handbook of engineering mechanics, McGraw-Hill, New York, 1962, chapter 62
- S. Woinowsky-Krieger, The effect of an axial force on the vibration of hinged bars, J. Appl. Mech. 17 (1950), 35–36. MR 0034202
- N. J. Hoff, The dynamics of the buckling of elastic columns, J. Appl. Mech. 18 (1951), 68–74. MR 0047506
- George Herrmann (ed.), Dynamic stability of structures, Pergamon Press, Oxford-New York-Toronto, Ont., 1967. MR 0202526
- Julian D. Cole, Perturbation methods in applied mathematics, Blaisdell Publishing Co. Ginn and Co., Waltham, Mass.-Toronto, Ont.-London, 1968. MR 0246537
- Edward L. Reiss, On multivariable asymptotic expansions, SIAM Rev. 13 (1971), 189–196. MR 289873, DOI https://doi.org/10.1137/1013036
- John A. Nohel (ed.), Advances in differential and integral equations, Society for Industrial and Applied Mathematics, Philadelphia, Pa., 1969. A collection of papers presented at the Conference on Qualitative Theory of Nonlinear Differential and Integral Equations held at the University of Wisconsin, Madison, Wis., August 12–23, 1968; In memoriam: Rudolph E. Langer (March 8, 1894 to March 11, 1968). MR 0357924
B. J. Matkowsky, Nonlinear dynamic stability: A formal theory, SIAM J. Appl. Math. 18, 872–883 (1970)
- B. J. Matkowsky, A simple nonlinear dynamic stability problem, Bull. Amer. Math. Soc. 76 (1970), 620–625. MR 257544, DOI https://doi.org/10.1090/S0002-9904-1970-12461-2
- S. Lubkin and J. J. Stoker, Stability of columns and strings under periodically varying forces, Quart. Appl. Math. 1 (1943), 215–236. MR 8982, DOI https://doi.org/10.1090/S0033-569X-1943-08982-X
V. V. Bolotin, The dynamic stability of elastic systems, Holden-Day, San Francisco, Calif., 1964
- Eugene Sevin, On the elastic bending of columns due to dynamic axial forces including effects of axial inertia, J. Appl. Mech. 7 (1960), 125–131. MR 0111271
- R. W. Dickey, Free vibrations and dynamic buckling of the extensible beam, J. Math. Anal. Appl. 29 (1970), 443–454. MR 253617, DOI https://doi.org/10.1016/0022-247X%2870%2990094-6
E. L. Reiss, Column buckling—an elementary example of bifurcation, Bifurcation theory and nonlinear eigenvalue problems, Benjamin, New York, 1969, pp. 1–16
- J. J. Stoker, Nonlinear Vibrations in Mechanical and Electrical Systems, Interscience Publishers, Inc., New York, N.Y., 1950. MR 0034932
E. Mettler, Dynamic buckling, Handbook of engineering mechanics, McGraw-Hill, New York, 1962, chapter 62
S. Woinowsky-Krieger, The effect of an axial force on the vibration of hinged bars, J. Appl. Mech. 17 35–36 (1950)
N. J. Hoff, The dynamics of the buckling of elastic columns, J. Appl. Mech. 18, 68–74 (1951)
N. J. Hoff, Dynamic stability of structures, Proceedings of an international conference on dynamic stability of structures, Pergamon Press, New York, 1967
J. D. Cole, Perturbation methods in applied mathematics, Blaisdell, Waltham, Mass., 1968
E. L. Reiss, On multi-variable asymptotic expansions, SIAM Rev. (to appear)
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.
B. J. Matkowsky, Nonlinear dynamic stability: A formal theory, SIAM J. Appl. Math. 18, 872–883 (1970)
B. J. Matkowsky, A simple nonlinear dynamic stability problem, Bull. Amer. Math. Soc. 17, 620–625 (1970)
S. Lubkin and J. J. Stoker, Stability of columns and strings under periodically varying forces, Quart. Appl. Math. 1, 215–236 (1943)
V. V. Bolotin, The dynamic stability of elastic systems, Holden-Day, San Francisco, Calif., 1964
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)
R. W. Dickey, Free vibrations and dynamic buckling of the extensible beam, J. Math. Anal. Appl. 29, 443–454 (1970)
E. L. Reiss, Column buckling—an elementary example of bifurcation, Bifurcation theory and nonlinear eigenvalue problems, Benjamin, New York, 1969, pp. 1–16
J. J. Stoker, Nonlinear vibrations in mechanical and electrical systems, Interscience, New York, 1950
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© Copyright 1971
American Mathematical Society
