3. Modeling A

3.1. Characteristics of modeling

Discrete translational stiffness element DIS_T

Characteristics of the elements

Boundary conditions:

DDL_IMPO:	( TOUT:’OUI’ DY: 0. , DZ: 0. )
At the end knots	( NŒUD: (A B) DX: 0. )

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

3.2. Characteristics of the mesh

Number of knots:	10
Number of meshes and types:	9 SEG2et 8 POI1

3.3. 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
Translation 1 (\(\mathit{Dy}\)) \({\mathrm{\Phi }}_{1}\)	P1 P2 P3 P4 P5 P6 P7 P8	4.07, —4.56 7.97, —8.28 10.9, —11.0 12.5, —12.5 12.5, —12.4 11.1, —10.9 8.24, —8.04 4.41, —4.25
Translation 8 (\(\mathit{Dy}\)) \({\mathrm{\Phi }}_{8}\)	P1 P2 P3 P4 P5 P6 P7 P8	2.23, —1.14 —3.71, 2.98 4.75, —4.41 —5.25, 5.27 5.14, —5.43 —4.44, 4.88 3.23, —3.69 —1.66, 2.01

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

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

3.4. Contents of the results file

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