10. Summary of results

Given the nature of the numerical solution (finite volume elements), the results obtained are satisfactory for:

• modeling A and B (DST) the maximum difference is less than \(\text{4\%}\) for the first 5 modes,

• E and F modeling (COQUE_3D), the maximum difference is around \(\text{5\%}\) for the first 5 modes,

• G modeling (3D), the maximum difference is around \(\text{5\%}\) for the first 5 modes,

• the off-plane reference modes 5 and 6 have symmetries different from those encountered in the E, F and G models, but they are equivalent because they are modal recombinations.

The C and D models (DKT) are less satisfactory with relative differences reaching \(\text{10\%}\) on mode 7 out of plane, this is due to the fact that transverse shear is not taken into account for this relatively thick plate.

In addition, we observe the appearance of flexure and membrane modes for all these models, including 3D volume modeling. When the meshes are sufficiently refined, this trend is confirmed and the relative differences regress. The 3D calculation also showed that below a \(6\times 6\) mesh in the plane (\(\mathrm{XY}\)), the flexure and membrane modes were not detected.