Dynamic buckling of a damped imperfect column on a nonlinear foundation
Author:
Deborah F. Lockhart
Journal:
Quart. Appl. Math. 36 (1978), 49-55
MSC:
Primary 73.41
DOI:
https://doi.org/10.1090/qam/478937
MathSciNet review:
478937
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Abstract: The dynamic buckling of a finite damped imperfect column which rests on a nonlinear foundation and which is subjected to axial step-loading is studied using a perturbation method. The imperfection is considered to be small. A simple asymptotic expression for the dynamic buckling load is obtained in terms of the Fourier component of the imperfection in the shape of the classical buckling mode. This leads to simple relations, independent of the imperfection, between the dynamic and static buckling loads for the damped and undamped column.
W. T. Koiter, On the stability of elastic equilibrium (in Dutch), Thesis, Delft, Amsterdam (1945); English translation issued as NASA TT F-10, 1967
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B. Budiansky and J. W. Hutchinson, Dynamic buckling of imperfection-sensitive structures, in Proceedings of the Eleventh International Congress of Applied Mechanics, ed. H. Gortler, Springer-Verlag, 1966, 636–651
J. W. Hutchinson and B. Budiansky, Dynamic buckling estimates, A.I.A.A. J. 4, 525–530 (1966)
B. Budiansky, Dynamic buckling of elastic structures: criteria and estimates, in Dynamic stability of structures, ed. G. Herrmann, Pergamon, New York, 1966
J. C. Amazigo and D. Frank, Dynamic buckling of an imperfect column on nonlinear foundation. Quart. Appl. Math. 31, 1–9 (1973)
W. B. Fraser and B. Budiansky, The buckling of a column with random initial deflections, J. Appl. Mech. 36, 233–240 (1969)
J. C. Amazigo. B. Budiansky and G. F. Carrier, Asymptotic analyses of the buckling of imperfect columns on nonlinear elastic foundations, Int. J. Solids. Struct. 6, 1341–1356 (1970)
J. C. Amazigo, Buckling of stochastically imperfect columns on nonlinear elastic foundations, Quart. Appl. Math. 29, 403–409 (1971)
- Edward L. Reiss and Bernard J. Matkowsky, Nonlinear dynamic buckling of a compressed elastic column, Quart. Appl. Math. 29 (1971), 245–260. MR 286344, DOI https://doi.org/10.1090/S0033-569X-1971-0286344-8
- J. J. Stoker, Nonlinear Vibrations in Mechanical and Electrical Systems, Interscience Publishers, Inc., New York, N.Y., 1950. MR 0034932
W. T. Koiter, On the stability of elastic equilibrium (in Dutch), Thesis, Delft, Amsterdam (1945); English translation issued as NASA TT F-10, 1967
W. T. Koiter, Elastic stability and post-buckling behavior, in Nonlinear problems, ed. R. E. Langer, University of Wisconsin Press, Madison, 1963
B. Budiansky and J. W. Hutchinson, Dynamic buckling of imperfection-sensitive structures, in Proceedings of the Eleventh International Congress of Applied Mechanics, ed. H. Gortler, Springer-Verlag, 1966, 636–651
J. W. Hutchinson and B. Budiansky, Dynamic buckling estimates, A.I.A.A. J. 4, 525–530 (1966)
B. Budiansky, Dynamic buckling of elastic structures: criteria and estimates, in Dynamic stability of structures, ed. G. Herrmann, Pergamon, New York, 1966
J. C. Amazigo and D. Frank, Dynamic buckling of an imperfect column on nonlinear foundation. Quart. Appl. Math. 31, 1–9 (1973)
W. B. Fraser and B. Budiansky, The buckling of a column with random initial deflections, J. Appl. Mech. 36, 233–240 (1969)
J. C. Amazigo. B. Budiansky and G. F. Carrier, Asymptotic analyses of the buckling of imperfect columns on nonlinear elastic foundations, Int. J. Solids. Struct. 6, 1341–1356 (1970)
J. C. Amazigo, Buckling of stochastically imperfect columns on nonlinear elastic foundations, Quart. Appl. Math. 29, 403–409 (1971)
E. L. Reiss and B. J. Matkowsky, Nonlinear dynamic buckling of a compressed elastic column, Quart. Appl. Math. 29, 245–260 (1971)
J. J. Stoker, Nonlinear vibrations in mechanical and electrical systems, Interscience, New York, 1950, 75–80
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Article copyright:
© Copyright 1978
American Mathematical Society
