Use of Frequency Data to Predict Buckling

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.