Use of frequency data to predict buckling
The use of measured vibration frequencies to determine approximate values of buckling loads nondestructively has been discussed in a number of papers. For example, Singer (1982, 1983) and his colleagues carried out experiments on cylindrical shells and used measured frequencies at low load levels to predict buckling loads. In most cases, the predicted values were higher than the actual buckling loads. It would be advantageous if one could also determine a lower bound for the buckling load so that a safe range for loading could be established. The objective of this paper is to examine Singer's procedure and suggest how one can estimate lower and upper bounds on the buckling load, as well as predict its value. A simple example with an analytical solution is utilized to derive typical load-frequency curves for buckling at a limit point (case I) and a bifurcation point (case II). Buckling occurs when the fundamental (i.e., lowest) vibration frequency decreases to zero, and the prediction methods involve extrapolation from some measured frequencies to zero frequency.
Journal of Engineering Mechanics
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