Bayón A., Nieves F., Gascón F.

A study of the axisymmetric vibration modes of a short cylinder is presented. The Ritz method is applied to calculate the non-dimensional frequency and its dependence on both the slenderness L/D and Poisson's ratio. The plot of the non-dimensional frequency versus L/D is analysed to determine the frequency crossings and the mode shapes. In the case of Poisson's ratio equal to zero, it is verified that there are multiple frequencies for the antisymmetric modes and that the mode shapes below and above the first crossing are interchanged. The natural frequencies and the mode shapes are accurately calculated for stainless-steel cylinders with a Poisson's ratio of 0.298. It is found that although actually no frequency crossing occurs, the mode shapes below and above the false crossing are interchanged. The theoretical results are experimentally verified by using a laser speckle interferometer as detector of vibration of two stainless-steel cylinders with L/D=1.2 and 1.5, respectively. Free vibration is induced by an impact and the out-of-plane component of the displacements is detected. An analysis of the spectrum provides the natural frequencies. Forced vibration is then excited by adhering two piezoelectric transducers to the cylinder's ends. The out-of-plane and in-plane displacement components are detected along one generatrix on the lateral surface. An excellent concordance between the theoretical and the experimental results is found.