6. Summary of results

The results obtained with the beam elements POU_D_E and POU_D_TG are in very good agreement with the analytical solution and are lower than :math:`0.46`% and :math:`0.61`% respectively. The results obtained by mixing two types of elements (beam and volume) and then by connecting the degrees of freedom using option LIAISON_ELEM are less accurate (but the difference remains less than :math:`3.61`%).

It should be noted that the calculated natural frequencies are identical regardless of the method used in the modal solver (SORENSEN or JACOBI).