4. B modeling

4.1. Characteristics of modeling

Discrete translational stiffness element DIS_T

Characteristics of the elements:

ORIENTATION:

in all the nodes

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

DISCRET:
nodal masses all nodes	M_T_N	in absolute coordinate system	(\(m\mathrm{=}10.\))
all-mesh stiffness matrices	K_T_L	in local coordinate system	(\({K}_{x}\mathrm{=}1.{10}^{5}\))
at the end nodes	K_T_N	in local coordinate system	(\({K}_{x}\mathrm{=}1.{10}^{5}\))

Boundary conditions:

DDL_IMPO: (TOUT: “OUI” DZ: 0.)

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

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

4.2. Characteristics of the mesh

Number of knots: 8

Number of meshes and types: 7 SEG2

4.3. 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
Translation 1 (\(\mathit{Dy}\)) \({\Phi }_{1}\)	P1 P2 P3 P4 P5 P6 P7 P8	—0.3473 —0.6527 —0.8793 —1. —1. —0.8793 —0.6527 —0.3473
Translation 8 (\(\mathit{Dy}\)) \({\Phi }_{8}\)	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
Translation 1 (\(\mathit{Dy}\)) \({\Phi }_{1}\)	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
Translation 8 (\(\mathit{Dy}\)) \({\Phi }_{8}\)	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%.

Standard mode with unitary generalized stiffness

Nature of clean modes	Point	Reference
Translation 1 (\(\mathit{Dy}\)) \({\Phi }_{1}\)	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
Translation 8 (\(\mathit{Dy}\)) \({\Phi }_{8}\)	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%.

4.4. notes

Calculations made by:

CALC_MODES

OPTION =' PLUS_PETITE ',

CALC_FREQ =_F (NMAX_FREQ = 8),

Contents of the results file:

8 first natural frequencies, eigenvectors and modal parameters