Experimental testing of Timoshenko predictions of supercritical natural frequencies and mode shapes for free-free beams

In this experimental work a scanning laser Doppler vibrometer is used to measure mode shapes and natural frequencies of beam bending vibrations above the critical frequency predicted by Timoshenko theory. Above the critical frequency the mode shapes are intricate, so to quantitative compare theoretical and experimental mode shapes, the modal assurance criterion (MAC) is applied.

This reveals that the order of the modes is not as theory predicts, and that other plane modes can easily be misinterpreted as bending modes. This can lead to an incorrect comparison of natural frequencies. With the MAC tool it is found that the correlation between theoretical mode shapes and measured mode shapes is very high; It can be concluded that supercritical Timoshenko-predicted mode shapes agrees well with the experimentally observed modes, and the supercritical natural frequencies deviate from Timoshenko theory within five percent.

Comparisons are made to other studies, and against a numerical 3D model.