Code_Aster ®
Version
5.0
Titrate:
SDLL400 - Poutre in vibration with center of excentré torsion
Date:
12/04/02
Author (S):
J.M. PROIX, m.t. BOURDEIX, P. HEMON, O. WILK Key
:
V2.02.400-A Page:
1/4

Organization (S): EDF/AMA, IAT St CYR, CNAM
Handbook of Validation
V2.02 booklet: Linear dynamics of the beams
V2.02.400 document

SDLL400 - Poutre in vibration with center
of excentré torsion

Summary:

This test results from the validation independent of version 4 of the models of beam.

It makes it possible to test the taking into account of an eccentricity of the center of torsion on the calculation of frequencies
clean of a right beam (a modeling with elements POU_D_E, right beam of Euler).
Handbook of Validation
V2.02 booklet: Linear dynamics of the beams
HT-66/02/001/A

Code_Aster ®
Version
5.0
Titrate:
SDLL400 - Poutre in vibration with center of excentré torsion
Date:
12/04/02
Author (S):
J.M. PROIX, m.t. BOURDEIX, P. HEMON, O. WILK Key
:
V2.02.400-A Page:
2/4

1
Problem of reference

1.1 Geometry
With
B
L = 7,5 m

Appear 1.1-A
Right beam length 7,5 Mr.

Characteristics of the section:

It is about the U-shaped beam presented [Figure 1.1-b].
B
G: center of gravity
E
C: center torsion
Z
C
G
H
E
y

Appear 1.1-b: Section of the U-shaped beam
H = 200 mm
B = 273 mm
E = 8,2 mm

One has by [bib1] the following data:

Iy = Iz = 5,022 10­5 m4
ZGC = 221,5 mm

One calculates starting from the geometry of the section:

S =
6,117
10­3 m2
Jx = 1,28
10­7 m4
Ay = 3,65

1.2
Properties of materials

Young modulus:
E = 2.07 1011 Pa

Poisson's ratio: = 0,3
Density:
= 7850 kg/m3

1.3
Boundary conditions

Boundary condition:

Plane problem: Blocked DZ and DRY.
Supported nodes A and B: Blocked DX and DY

The taking into account of the eccentricity is done using operand LIAISON_DDL of the command
AFFE_CHAR_MECA.

The ddl are always in G, and one takes account of the eccentricity by: DY (G) =DY (C) + GC X

Handbook of Validation
V2.02 booklet: Linear dynamics of the beams
HT-66/02/001/A

Code_Aster ®
Version
5.0
Titrate:
SDLL400 - Poutre in vibration with center of excentré torsion
Date:
12/04/02
Author (S):
J.M. PROIX, m.t. BOURDEIX, P. HEMON, O. WILK Key
:
V2.02.400-A Page:
3/4

2
Reference solutions

2.1
Method of calculation used for the reference solutions

They are the Eigen frequencies solutions of the homogeneous problem without damping.

It is partially given in [bib1]. The method of resolution, of finite elements type, concerns
a model POU_D_TG. However, a series of results is provided if the effects of
torsion of warping are neglected, which brings back modeling to a POU_D_T.

N° mode
1
2
3
4
5
Frequency (Hz)
3,797
7,788
11,74
15,68
19,62

Table 2.1-a: Résultats of reference according to [bib1]

One can grant a certain confidence to these results published in a newspaper at reading panel.
However uncertainties exist if one wants to reproduce these calculations: constants of Jx torsion and
of shearing ky are not provided in the article. They should have been recomputed starting from the geometry of
the section.

2.2
Results of reference

Eigen frequencies of the beam without damping

2.3
Uncertainty on the solution

Comparison between codes (CAILLOU [bib2] and ASTER), and analytical solution.

2.4 References
bibliographical

[1]
WU J.S. & CHEN K.Z. : Dynamic Analysis off has Chanel beam had to has moving load. J. off
Sound and Vibration, vol. 188, n° 3, p 337-345, 1995.
[2]
Code CAILLOU version 4 of October 30, 1996, IAT
[3]
Report/ratio n° 2314/A of Institut Aérotechnique “Proposition and realization of new cases
tests missing with the validation beams ASTER “
Handbook of Validation
V2.02 booklet: Linear dynamics of the beams
HT-66/02/001/A

Code_Aster ®
Version
5.0
Titrate:
SDLL400 - Poutre in vibration with center of excentré torsion
Date:
12/04/02
Author (S):
J.M. PROIX, m.t. BOURDEIX, P. HEMON, O. WILK Key
:
V2.02.400-A Page:
4/4

3 Modeling
With

3.1
Characteristics of modeling

The model is composed of 15 elements right beam of Euler.

3.2
Characteristics of the grid

15 elements POU_D_E

3.3 Functionalities
tested

Commands


MODE_ITER_SIMULT METHOD
JACOBI


4
Results of modeling A

4.1 Results
Results mode
CAILLOU
Results
Aster Variation
(%)
1 3,79432
3.7966
0.063
2 7,43340
7.4513
0.242
3 11,4450
11.5108
0.575
4 15,3439
15.5027
1.036
5 19,4766
19.8060
1.692

Table 4.1-a: Comparaison ASTER/CAILLOU in POU_D_E with eccentricity

Mode
Reference results
Aster results
Variation (%)
1 3.79700
3.7966
­ 0.008
2 7.78800
7.4513
­ 4.322
3 11.7400
11.5108
­ 1.952
4 15.6800
15.5027
­ 1.130
5 19.6200
19.8060
0.948

Table 4.1-b: Comparaison ASTER/Référence [bib1] in POU_D_E with eccentricity

5
Summary of the results

The results are rather close to the reference solution (numerical). (variation < 5%), for which
certain data missed and thus had to be estimated. They correspond on the other hand very well
with the results of code CAILLOU of the IAT (given identical to those of Code_Aster).

This makes it possible to validate the taking into account of the offsetting of the center of torsion in the matrices of
mass and of rigidity.
Handbook of Validation
V2.02 booklet: Linear dynamics of the beams
HT-66/02/001/A

Outline document