7. E modeling

7.1. Characteristics of modeling

Transposition of the reference test to the case of degrees of freedom of rotation (torsion+inertia spring) using the discrete element of translation/rotation stiffness: DIS_TR

Characteristics of the elements

Boundary conditions:

DDL_IMPO:	( TOUT:’OUI’ DX: 0., DY: 0., DZ: 0., DRZ: 0. )
LIAISON_DDL:	(telle que :math:`\mathrm{3DRy}\mathrm{=}\mathrm{4DRx}`en tous les nœuds)

Node names: \({P}_{\mathrm{1,}}{P}_{\mathrm{2,}}\mathrm{....},{P}_{8}\)

7.2. Characteristics of the mesh

Number of knots:	8
Number of meshes and types:	7 SEG2

Nodes \({P}_{1}\) and \({P}_{8}\) are connected to a fixed fictional node by nodal springs (K_ TR_N, A_ TR_N).

7.3. Tested sizes and results

Frequency	Reference
Clean mode order 1	5.53
Clean mode order 2	10.90
Clean mode order 3	15.93
Clean mode order 4	20.45
Clean mode order 5	24.34
Clean mode order 6	27.49
Clean mode order 7	29.84
Clean mode order 8	31.29

Depreciation	Reference
Clean mode order 1	1.521e—2
Clean mode order 2	2.877e—2
Clean mode order 3	3.960e—2
Clean mode order 4	4.709e—2
Clean mode order 5	5.098e—2
Clean mode order 6	5.183e—2
Clean mode order 7	5.115e—2
Clean mode order 8	5.036e—2

Nature of clean mode	Point	Clean mode Reference in 10 —3 Real part Imaginary part
Rotation 1 (\(\mathit{DRx}\)) \({\Phi }_{1}\)	P1 P2 P3 P4 P5 P6 P7 P8	—2.442, 2.736 —4.782, 4.968 —6.54, 6.6 —7.5, 7.5 —7.5, 7.4 —6.66, 6.54 —4.944, 4.824 —2.646, 2.55
Rotation 8 (\(\mathit{DRx}\)) \({\Phi }_{8}\)	P1 P2 P3 P4 P5 P6 P7 P8	—1.338, 0.684 —2.226, 1.788 —2.85, 2.646 —3.15, 3.162 —3.084, 3.258 —2.664, 2.928 —1.938, 2.214 —0.996, 1.206

Eigenmode standardized to the unit modal mass: \({\phi }_{i}^{t}C{\phi }_{i}+2{\lambda }_{i}{\phi }_{i}^{t}M{\phi }_{i}\mathrm{=}1\)

\(\lambda\): is the eigenvalue associated with damping and natural frequency.

7.4. Contents of the results file

The 8 damping and natural frequencies, as well as the associated natural vectors.