**4. Finite element method, MEF**

An independent set of results for the natural frequencies, was also obtained by a finite element code. (Bambill et al., 2010). The finite element model employed in the analysis has 3000 beam elements of two nodes in the longitudinal direction (Rossi, 2007). See Table 2. This number of elements was proved to be enough with a convergence analysis.

The beam model also takes into account the shear deformation (Timoshenko beam's theory) and the increase in bending stiffness induced by the centrifugal force.

The term <sup>2</sup> () () *kk kk Ix x* of equation (13.b) was not included in the finite element formulation. Probably for this reason some small differences between both sets of numerical results (DQM and FEM) begin to appear when the rotational speed *η* increases.
