6. D modeling#

6.1. 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.

_images/10000000000002A0000000DE179A8A60910DB795.png

Characteristics of the elements:

ORIENTATION:

in all the nodes

with an angle \(\alpha \mathrm{=}53.130102°\)

DISCRET:

with nodal masses all nodes

M_ TR_N

in absolute coordinate system

\(({I}_{\mathit{xx}}\mathrm{=}10.)\)

all-mesh stiffness matrices

K_ TR_L

in local coordinate system

\(({\mathit{KR}}_{x}\mathrm{=}1.{10}^{5})\)

at the knots endpoints

K_ TR_N

in local coordinate system

\(({\mathit{KR}}_{x}\mathrm{=}1.{10}^{5})\)

Boundary conditions:

DDL_IMPO: (TOUT: “OUI” DX: 0., DY: 0., DZ: 0., DRZ: 0.)

LIAISON_DDL: (such as \(\mathrm{3DRY}\mathrm{=}\mathrm{4DRY}\) in all nodes)

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

6.2. Characteristics of the mesh#

Number of knots: 8

Number of meshes and types: 7 SEG2

6.3. Tested sizes and results#

Identification Clean mode number

Reference

1

5.5274

2

10.8868

3

15.9155

4

20.4606

5

24.3840

6

27.5664

7

29.9113

8

31.3474

Standardized mode with 1 to the largest component

Nature of clean modes

Point

Reference

Rotation 1 (\(\mathit{DRY}\)) \({\Phi }_{1}\)

P1 P2 P3 P4 P5 P6 P7 P8

—0.3473 —0.6527 —0.8793 —1. —1. —0.8793 —0.6527 —0.3473

Rotation 8 (\(\mathit{DRY}\)) \({\Phi }_{8}\)

P1 P2 P3 P4 P5 P6 P7 P8

0.3473 —0.6527 0.8793 —1. 1. —0.8793 0.6527 —0.3473

Maximum error less than: 0.03%.

Mode standardized to the generalized unit mass

Nature of clean modes

Point

Reference

Rotation 1 (\(\mathit{DRY}\)) \({\Phi }_{1}\)

P1 P2 P3 P4 P5 P6 P7 P8

—4.0781E—2 —7.6654E—2 —1.0327E—1 —1.1743E—1 —1.1743E—1 —1.0327E—1 —7.6654E—2 —4.0781E—2

Rotation 8 (\(\mathit{DRY}\)) \({\Phi }_{8}\)

P1 P2 P3 P4 P5 P6 P7 P8

4.0781E—2 —7.6654E—2 1.0327E—1 —1.1743E—1 1.1743E—1 —1.0327E—1 7.6654E—2 —4.0781E—2

Maximum error less than: 0.03%.

Standardized mode with unitary generalized stiffness

Nature of clean modes

Point

Reference

Rotation 1 (\(\mathit{DRY}\)) \({\Phi }_{1}\)

P1 P2 P3 P4 P5 P6 P7 P8

—1.1742E—3 —2.2072E—3 —2.9735E—3 —3.3813E—3 —3.3813E—3 —2 9735E—3 —2.2072E—3 —1.1742E—3

Rotation 8 (\(\mathit{DRY}\)) \({\Phi }_{8}\)

P1 P2 P3 P4 P5 P6 P7 P8

2.0705E—4 —3.8918E—4 5.2432E—4 —5.9621E—4 5.9621E—4 —5.2432E—4 3.8918E—4 —2.0705E—4

Maximum error less than: 0.03%.

6.4. notes#

Calculations made by:

CALC_MODES

OPTION =' AJUSTE ',

CALC_FREQ =_F (FREQ =( 5., 10., 10., 15., 15., 15., 15., 20., 24., 27., 30., 32. )),

SOLVEUR_MODAL =_F (OPTION_INV =' DIRECT '),

Contents of the results file:

8 first natural frequencies, eigenvectors and modal parameters