3. Modeling A

3.1. Characteristics of modeling

DKT cases

Discretized geometry is shown above. Elements DKT are 3-node planar facets. The number of knots on the meridian and on the equator is: 34.

The boundary conditions applied on the three borders correspond to the symmetry conditions (movements and rotations blocked).

3.2. Characteristics of the mesh

Number of knots: 1128

Number of meshes and types: 2125 TRIA3

3.3. Tested sizes and results

(Frequencies in hertz)

Value of the parameter i of the reference solution	Reference	Aster	% difference
	237.25	237.24 237.24	—0.005 —0.003
2
3	282.85	not obtained []
4	305.24	304.97 304.99 305.08	—0.089 —0.080 —0.054
5	324.17	not obtained []
6	346.76	346.11 346.12 346.12 346.12 346.30 346.38	—0.186 —0.185 —0.185 —0.133 —0.108
7	376.68	not obtained []
8	416.00	414.89 414.92 414.92 415.16 415.16 415.24 415.33	—0.266 —0.259 —0.259 —0.201 —0.201 —0.183 —0.161
9	465.75	not obtained []
10	526.20	524.34 524.43 524.43 524.43 524.43 524.71 524.71 524.94 524.97 525.12	—0.353 —0.337 —0.337 —0.283 —0.283 —0.283 —0.240 —0.234 —0.205

3.4. notes

The reference solution does not give the multiplicity of modes. With the calculations, orders of multiplicity are observed which increase with the value of the frequency.

Modes 3, 5, 7, 9 are not obtained because of the boundary conditions chosen for this model, with the three planes of symmetry.