3. Modeling A

3.1. Characteristics of modeling

POU_D_E beam element and DIS_TR discrete element

Cutting: beam \(\mathrm{AB}\): 20 meshes SEG2.

Boundary conditions:

At the \(A\) end node

DDL_IMPO: (NOEUD: A DX: 0., DY: 0., DY: 0., DZ: 0., DRX: 0., DRY: 0., DRZ: 0.)

Nodal mass in \(B\) with an eccentricity	\(\mathit{ey}\mathrm{=}0.\)	Case 1
	\(\mathrm{ey}=1.\)	Case 2

Node names:

Points

\(A\mathrm{=}\mathit{N100}\)

\(B=\mathrm{N200}\)

3.2. Characteristics of the mesh

Number of knots:	21
Number of meshes and types:	20 SEG2

3.3. Tested sizes and results

Case	Nature of the clean mode	Frequency Reference	\(\mathrm{Hz}\) Aster	% difference
	flexure 1.2	1.65	1.65	1.6554	0.33
	flex 3.4	16.07	16.07	16.0712
CAS 1	flexure 5.6	50.02	50.0240
	traction 1	76.47	76.4727	76.4727
\(\mathrm{yc}=0.\)	twist 1	80.47	80.47	80.4688
	flexure 7.8	103.20	103.20444
	\({f}_{z}+{t}_{o}\) 1	1.636	1.636	1.6363
	\({f}_{y}+{t}_{r}\) 2	1.642	1.642	1.6416
CAS 2	\({f}_{y}+{t}_{r}\) 3	13.46	13.46	13.4551
	\({f}_{z}+{t}_{o}\) 4	13.59	13.59	13.5919
\(\mathrm{yc}=1.\)	\({f}_{z}+{t}_{o}\) 5	28.90	28.90	28.8972
	\({f}_{y}+{t}_{r}\) 6	31.96	31.96	31.9594
	\({f}_{z}+{t}_{o}\) 7	61.61	61.61	61.6091
	\({f}_{y}+{t}_{r}\) 8	63.93	63.93	63.9289
Fashion	\({\theta }_{\mathit{xB}}\)	0.03	3.039 10—2	1.321
1	\({w}_{C}\mathrm{/}{w}_{B}\)	1.030	1.030	1.030
2	\({u}_{C}\mathrm{/}{v}_{B}\)	—0.148	—0.148
3	\({u}_{C}/{v}_{B}\)	—2.882	—2.880	0.07
4	\({w}_{C}\mathrm{/}{w}_{B}\)	—0.922	—0.923	0.108
5	\({\theta }_{\mathit{xB}}\)	—1.922	—1.92268	0.036

with:

\({f}_{z}+{t}_{o}\mathrm{=}\mathit{flexion}x,z+\mathit{torsion}\)

\({f}_{y}+{t}_{r}\mathrm{=}\mathit{flexion}x,y+\mathit{traction}\)

3.4. notes

Calculations made by:

OPTION = “PLUS_PETITE” CALC_FREQ =_F (NMAX_FREQ = n) Case 1: n=10, Case 2: n=8 SOLVEUR_MODAL =_F (METHODE = “TRI_DIAG”)

In the test, you cannot check the values of the \(\frac{{u}_{C}}{{v}_{B}}\) ratios for modes 2 and 3 (except manually). As for the values of \(\frac{{w}_{C}}{{w}_{B}}\), the technique is as follows: if we impose \({w}_{B}\mathrm{=}1\) (command NORM_MODE), we then have \(\frac{{w}_{C}}{{w}_{B}}\mathrm{=}1+{\theta }_{\mathit{xB}}\) and we can check the values of \({\theta }_{\mathit{xB}}\).

Contents of the results file:

Case 1:11 first natural frequencies, eigenvectors and modal parameters.

Case 2:9 first natural frequencies, eigenvectors and modal parameters.