Dynamic snap-through of a simple viscoelastic truss
Authors:
W. Nachbar and N. C. Huang
Journal:
Quart. Appl. Math. 25 (1967), 65-82
DOI:
https://doi.org/10.1090/qam/99908
MathSciNet review:
QAM99908
Full-text PDF Free Access
Abstract |
References |
Additional Information
Abstract: In order to understand the behavior of shallow structures in dynamic snap-through or buckling, a detailed study has been made for a plane, viscoelastic, three-hinged truss with a concentrated mass at the central hinge, and with a normal load of constant magnitude applied suddenly at this hinge. The dynamic buckling criterion is found to correspond to values of the parameters for which the solution goes into the saddle point of a two-dimensional autonomous system. It is shown that another dynamic buckling criterion, based upon the asymptotic behavior of solutions in time, can give incorrect results in certain cases. Two methods to compute buckling loads are investigated with the aid of a phase plane diagram and potential curves. Approximations to the buckling load, including an upper bound, are computed by means of an energy integral method. The exact buckling loads are computed by numerical integration of the governing differential equation.
R. Mises, Über die Stabilitätsprobleme der Elastizilätslheorie, Z. Angew. Math. Mech. 3, 406 (1923)
J. Hult, Oil canning problems in creep, Creep in Structures, (Ed. N. J. Hoff), Academic Press, New York, 1962, p. 161
N. C. Huang, Nonlinear creep buckling of some simple structures, IRPA Report 66-80 prepared for the U. S. Army Research Office-Durham under Contract DA-31-124-ARO-D-257 University of California at San Diego, La Jolla, California, May, 1966
- N. J. Hoff and Victor G. Bruce, Dynamic analysis of the buckling of laterally loaded flat arches, J. Math. Physics 32 (1954), 276–288. MR 0059763
- Earl A. Coddington and Norman Levinson, Theory of ordinary differential equations, McGraw-Hill Book Company, Inc., New York-Toronto-London, 1955. MR 0069338
- Witold Hurewicz, Lectures on ordinary differential equations, The Technology Press of the Massachusetts Institute of Technology, Cambridge, Mass.; John Wiley & Sons, Inc., New York, 1958. MR 0090703
- Solomon Lefschetz, Differential equations: Geometric theory, 2nd ed., Pure and Applied Mathematics, Vol. VI, Interscience Publishers, a division of John Wiley & Sons, New York-Lond on, 1963. MR 0153903
- Mathematical methods for digital computers, John Wiley & Sons, Inc., New York-London, 1960. MR 0117906
R. Mises, Über die Stabilitätsprobleme der Elastizilätslheorie, Z. Angew. Math. Mech. 3, 406 (1923)
J. Hult, Oil canning problems in creep, Creep in Structures, (Ed. N. J. Hoff), Academic Press, New York, 1962, p. 161
N. C. Huang, Nonlinear creep buckling of some simple structures, IRPA Report 66-80 prepared for the U. S. Army Research Office-Durham under Contract DA-31-124-ARO-D-257 University of California at San Diego, La Jolla, California, May, 1966
N. J. Hoff and V. G. Bruce, Dynamic analysis of the buckling of laterally loaded arches, J. Math. Phys. 32, 276 (1954)
E. A. Coddington and N. Levinson, Theory of ordinary differential equations, McGraw-Hill, New York, 1955; in particular, Chapters 15 and 16
W. Hurewicz, Lectures on ordinary differential equations, second printing, M.I.T., Technology Press, Wiley, New York; in particular, Chapters 4 and 5
S. Lefscetz, Differential equations-Geometric theory, Second Ed., Interscience, New York, 1963
A. Ralston and H. Wilf, Mathematical methods for digital computers, Wiley, New York, 1960, p. 110.
Additional Information
Article copyright:
© Copyright 1967
American Mathematical Society
