Use of Frequency Data to Predict Buckling
Publication: Journal of Engineering Mechanics
Volume 116, Issue 10
Abstract
Vibration frequency measurements are sometimes used to nondestructively predict buckling loads. Various powers of the fundamental frequency may be plotted as a function of the load. A curve-fitting procedure may be applied to obtain estimates of the buckling load, which occurs when the fundamental frequency decreases to zero. Often such predictions lead to a value that is higher than the actual buckling load. It would be useful if both lower and upper bounds on the buckling load could be obtained from the vibration data. In this technical note, the convexity properties of the curves of load versus a power of the frequency are utilized to predict such bounds. These ideas are demonstrated on typical curves associated with buckling at a limit point and a bifurcation point. The curves are derived from an example of a shallow elastic arch with pinned ends and a sinusoidal initial shape, which is subjected to a sinusoidal distributed load.
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References
1.
Huseyin, K. (1978). Vibrations and stability of multiple parameter systems. Noordhoff Int. Publishing, Alphen aan den Rijn, The Netherlands.
2.
Jubb, J. E. M., Phillips, I. G., and Becker, H. (1975). “Interrelation of structural stability, stiffness, residual stress and natural frequency.” J. Sound Vib., 39(1), 121–134.
3.
Plaut, R. H., and Johnson, E. R. (1981). “The effects of initial thrust and elastic foundation on the vibration frequencies of a shallow arch.” J. Sound Vib., 78(4), 565–571.
4.
Singer, J. (1982). “Vibration correlation techniques for improved buckling predictions of imperfect stiffened shells.” Buckling of shells in off‐shore structures, J. E. Harding, P. J. Dowling, and N. Agelidis, eds., Granada Publishing, London, England, 285–329.
5.
Singer, J. (1983). “Vibrations and buckling of imperfect stiffened shells—Recent developments.” Collapse: The buckling of structures in theory and practice, J. M. T. Thompson and G. W. Hunt, eds., Cambridge Univ. Press, Cambridge, England, 443–479.
6.
Souza, M. A., Fok, W. C., and Walker, A. C. (1983). “Review of experimental techniques for thin‐walled structures liable to buckling, Part 1: Neutral and unstable buckling.” Exptl. Techs., 7(9), 21–25.
7.
Virgin, L. N. (1986). “Parametric studies on the dynamic evolution through a fold.” J. Sound Vib., 110(1), 99–109.
8.
Virgin, L. N. (1987). “Free vibrations of imperfect cantilever bars under self‐weight loading.” Proc. Instn. Mech. Engrs., 201(C5), 345–347.
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Copyright © 1990 ASCE.
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Published online: Oct 1, 1990
Published in print: Oct 1990
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