Experimental study of the Timoshenko beam theory predictions

Abstract

The theory of flexural vibrations proposed by Timoshenko almost 90 years ago has been the subject of several recent papers. In the Timoshenko beam theory a critical frequency fc is expected and for frequencies f larger than fc, some authors argue that a second spectrum exists. This is still the matter of much debate. In order to settle this question we have performed experimental measurements of flexural normal-mode frequencies and amplitudes which are much more precise than what has been obtained up to now. For some purposes cylindrical rods are more convenient, whereas in other cases rectangular beams are easier to deal with, so we analyze rods and beams of different shapes and sizes. We show that, below fc, all observed resonant peaks can be associated with one of the compressional, torsional or Timoshenko resonances and that no resonant peaks are left undetected. The validity of Timoshenko beam theory below fc and that only one spectrum appears in this regime is therefore proved. The comparison between theory and experiment for rectangular beams also shows that our experimental setup is appropriate, so we can use it confidently for f>fc. The measurements we report here in this regime show the existence of a second spectrum, at least for free–free boundary conditions.