Experimental study of the Timoshenko beam theory predictions: Further results

In a previous paper (2012) we presented experimental results proving that the critical frequency fCfC predicted by Timoshenko beam theory indeed exists. We also showed that for frequencies f   smaller than fCfC the spectrum is formed by almost equally spaced levels whereas for f>fCf>fC the spectrum consists of pairs of eigenvalues very close to each other as predicted by numerical solutions of Timoshenko׳s equation: we shall refer to them as Timoshenko doublets. In this work we measure for the first time experimental dispersion relations. For this purpose it was necessary to obtain normal-mode amplitudes with a high precision, which was done with a new experimental setup developed by us. We found that experimental dispersion relations coincide very well with theoretical predictions. Furthermore, we provide an explanation of Timoshenko doublets.