Code_Aster
®
Version
5.0
Titrate:
SDLL400 - Beam 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
Manual of Validation
V2.02 booklet: Linear dynamics of the beams
HT-66/02/001/A
Organization (S):
EDF/AMA, IAT St CYR, CNAM
Manual of Validation
V2.02 booklet: Linear dynamics of the beams
Document
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SDLL400 - Beam 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).
Code_Aster
®
Version
5.0
Titrate:
SDLL400 - Beam 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
Manual of Validation
V2.02 booklet: Linear dynamics of the beams
HT-66/02/001/A
1
Problem of reference
1.1 Geometry
B
With
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].
C
G
B
H
E
y
Z
G: center of gravity
C: center torsion
E
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 10
5
m
4
ZGC = 221,5 mm
One calculates starting from the geometry of the section:
S =
6,117
10
3
m
2
J
X
= 1,28
10
7
m
4
With
y
= 3,65
1.2
Properties of materials
Young modulus:
E = 2.07 10
11
AP
Poisson's ratio:
= 0,3
Density:
= 7850 kg/m
3
1.3
Boundary conditions
Boundary condition:
Plane problem: Locked DZ and DRY.
Supported nodes A and B: Locked DX and DY
The taking into account of the eccentricity is done using the operand
LIAISON_DDL
control
AFFE_CHAR_MECA
.
The ddl are always in G, and one takes account of the eccentricity by:
DY G DY C
GC
X
()
()
=
+
Code_Aster
®
Version
5.0
Titrate:
SDLL400 - Beam 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
Manual of Validation
V2.02 booklet: Linear dynamics of the beams
HT-66/02/001/A
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 roll are neglected, which brings back modeling to one
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: Results 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 torsion J
X
and
of shearing K
y
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 (STONE [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 STONE version 4 of October 30, 1996, IAT
[3]
Report/ratio n° 2314/A of the Institute Aerotechnics “Proposal and realization for new cases
tests missing with the validation beams ASTER “
Code_Aster
®
Version
5.0
Titrate:
SDLL400 - Beam 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
Manual of Validation
V2.02 booklet: Linear dynamics of the beams
HT-66/02/001/A
3 Modeling
With
3.1
Characteristics of modeling
The model is composed of 15 elements right beam of Euler.
3.2
Characteristics of the mesh
15 elements POU_D_E
3.3 Functionalities
tested
Controls
MODE_ITER_SIMULT METHOD
JACOBI
4
Results of modeling A
4.1 Results
Results mode
STONE
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: Comparison ASTER/STONE 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: Comparison ASTER/Reference [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 the code STONE 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.