Abstract
A dynamic method for predicting the buckling load of an elastic column is formulated. The method is based on the integral-equation representation of a column with varying cross section and elastic springs at the boundaries. The experimental inputs are the dynamic properties of the unloaded column (trequencies, mode shapes and masses). The buckling loads predicted for three tested configurations agreed well with loads defined by other static and dynamic methods.
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Abbreviations
- G(x;ζ):
-
influence function
- ℓ:
-
length of the column
- m(x) :
-
distributed mass
- \(\bar M\) :
-
generalized mass
- P cr :
-
buckling load
- x :
-
length coordinate
- y :
-
deflection, lateral
- ϕ:
-
mode shape
- ω:
-
resonance frequency
References
Klein, B., “Determination of Effective End Fixity of Columns with Unequal Rotational End Restraints by Means of Vibration Test Data,”J. of the Royal Aeron. Soc.,61,131–132 (Feb.1957).
Jacobson, M.J. andWenner, M.L., “Predicting Buckling Loads from Vibrational Data,”Experimental Mechanics,8 (10),35N-38N (Oct.1968).
Segall, A., “Nondestructive Dynamic Methods for the Determination of the Critical Loads of Elastic Columns,” MSc Thesis in Aeronautical Engineering, Technion, Haifa, Israel, in Hebrew (June 1973).
Massonnet, Ch., “Les Relations Entre les Modes Normaux de Vibration et la Stabilité des Systèmes Elastiques.” Goemaere, Bruxelles, (1940).
Lurie, H. “Lateral Vibrations as Related to Structural Stability,”J. of Appl. Mech.,19 (2),195–203 (June1952).
Baruch, M., “Integral Equations for Nondestructive Determination of Buckling Loads for Elastic Plates and Bars,”Israel J. of Tech.,11 (1–2),1–8 (1973).
Bolotin, V.V., “The Dynamic Stability of Elastic Systems,” Holden-Day (1964).
Beatrix, C., “Les Procédés Experimentaux de L'Essai Global de Vibration d'une Structure,” La Recherche Aerospatiale, No. 109 (Nov. 1965).
Baruch, M., “On Undestructive Determination of the Buckling Load of an Elastic Bar,”AIAA J.,8 (12),2274–2276 (1970).
Baruch, M., “Determination of the Stiffness of an Elastic Bar,”AIAA J,9 (8),1637–1639 (1971).
Goldhammer, B.F. andJohnson, E.E., “The Determination of the Critical Load of a Column or Stiffened Panel in Compression by the Vibration Method,”Proc. of SESA XI (1),221–232 (1953).
Horton, W.H., Cundari, F.L. andJohnson, R.W., “The Analysis of Experimental Data Obtained from Stability Studies on Elastic Column and Plate Structures,”Israel J. of Tech.,5 (1–2),104–113 (1967).
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Segall, A., Baruch, M. A nondestructive dynamic method for the determination of the critical load of elastic columns. Experimental Mechanics 20, 285–288 (1980). https://doi.org/10.1007/BF02328413
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DOI: https://doi.org/10.1007/BF02328413