Code_Aster ®
Version
4.0
Titrate:
SDLX01 Flection of a symmetrical gantry
Date:
09/01/98
Author (S):
B. QUINNEZ
Key:
V2.05.001-C Page:
1/6
Organization (S): EDF/IMA/MN
Handbook of Validation
V2.05 booklet: Linear dynamics of the assembled structures
V2.05.001 document
SDLX01 - Flection of a symmetrical gantry
Summary:
This plane problem consists in seeking the frequencies of vibration of a mechanical structure made up of one
assembly of beams with rectangular section (symmetrical gantry). This test of mechanics of the structures
corresponds to a dynamic analysis of an assembled structure having a linear behavior. It includes/understands
only one modeling.
Via this problem, one tests the element of beam of Timoshenko as well as the calculation of
frequencies of vibration by the method of the iterations opposite.
The results obtained are in very good agreement with those of guide VPCS. The error on the thirteen first
frequencies of vibration is lower than 0,2%.
Handbook of Validation
V2.05 booklet: Linear dynamics of the assembled structures
HI-75/96/004 - Ind A

Code_Aster ®
Version
4.0
Titrate:
SDLX01 Flection of a symmetrical gantry
Date:
09/01/98
Author (S):
B. QUINNEZ
Key:
V2.05.001-C Page:
2/6
1
Problem of reference
1.1 Geometry
E
F
Rectangular cross-sections:
thickness
H = 0.0048 m
y, v
C
D
width
B = 0.029 m
surface

To = 1.392 10-4 m2

inertia
lz = 2.673 10-10 m4
With
B
X, U
y'
z'
section:
z'
H
B
y'
B
posts
cross-pieces
H
Co-ordinates of the points (in meters):
With
B
C
D
E
F
X
­ 0.30
0.30
­ 0.30
0.30
­ 0.30
0.30
y
0.
0.
0.36
0.36
0.81
0.81
1.2
Material properties
E = 2.1 1011 Pa
= 0.3
= 7.800. kg/m3
1.3
Boundary conditions and loadings
Embedded points A and b: (U = v = 0, = 0).
1.4 Conditions
initial
Without object for the modal analysis.
Handbook of Validation
V2.05 booklet: Linear dynamics of the assembled structures
HI-75/96/004 - Ind A

Code_Aster ®
Version
4.0
Titrate:
SDLX01 Flection of a symmetrical gantry
Date:
09/01/98
Author (S):
B. QUINNEZ
Key:
V2.05.001-C Page:
3/6
2
Reference solution
2.1
Method of calculation used for the reference solution
The reference solution is that given in card SDLX01/89 of the guide VPCS which presents
method of calculation in the following way:
Method of the dynamic stiffness (Théorie of the slim beams)
2.2
Results of reference
the first 13 Eigen frequencies.
2.3
Uncertainty on the solution
(F/F) < 0.5%.
2.4 References
bibliographical
[1]
J. PIRANDA. Run and Travaux Dirigés of vibrations of the structures. Mechanical option. School
Main road Supérieure de Mécanique and Micromécanique. Laboratory of Mécanique
Applied. Besancon (France) (1983).
Handbook of Validation
V2.05 booklet: Linear dynamics of the assembled structures
HI-75/96/004 - Ind A

Code_Aster ®
Version
4.0
Titrate:
SDLX01 Flection of a symmetrical gantry
Date:
09/01/98
Author (S):
B. QUINNEZ
Key:
V2.05.001-C Page:
4/6
3 Modeling
With
3.1
Characteristics of modeling
POU_D_T
y
E
F
C
D
With
B
X
Cutting:
AC and data base
6 meshs SEG2
EC and DF
9 meshs SEG2
CD and EFF
10 meshs SEG2
Limiting conditions:
plane problem
DDL_IMPO:
(TOUT:“YES” DZ:0., DRX:0., DRY:0. )
embedded nodes A and B
(GROUP_NO:AB DX:0., DY:0., DRZ:0. )
Name of the nodes:
Not A = N100
Not B = N600
Not C = N200
Not D = N500
Not E = N300
Not F = N400
3.2
Characteristics of the grid
A number of nodes:
50
A number of meshs and types:
50 SEG2
3.3 Functionalities
tested
Commands
Keys
AFFE_CARA_ELEM
POUTRE
“RECTANGLE”
TOUT
[U4.24.01]
AFFE_CHAR_MECA
DDL_IMPO
TOUT
[U4.25.01]
GROUP_NO
AFFE_MATERIAU
TOUT
[U4.23.02]
AFFE_MODELE
“MECANIQUE”
“POU_D_T'
TOUT
[U4.22.01]
DEFI_MATERIAU
ELAS
[U4.23.01]
MODE_ITER_INV
CALC_FREQ
OPTION
“AJUSTE”
[U4.52.01]
FREQ
NMAX_FREQ
Handbook of Validation
V2.05 booklet: Linear dynamics of the assembled structures
HI-75/96/004 - Ind A

Code_Aster ®
Version
4.0
Titrate:
SDLX01 Flection of a symmetrical gantry
Date:
09/01/98
Author (S):
B. QUINNEZ
Key:
V2.05.001-C Page:
5/6
4
Results of modeling A
4.1 Values
tested
Identification
Reference
Aster
% difference
1 anti
8.8
8.7802
­ 0.23
2 anti
29.4
29.4341
0.12
3 sym
43.8
43.8385
0.09
4 sym
56.3
56.2826
­ 0.03
5 anti
96.2
96.1506
­ 0.05
6 sym
102.6
102.6408
0.04
7 anti
147.1
147.0437
­ 0.04
8 sym
174.8
174.8118
0.01
9 anti
178.8
178.7979
­ 0.00
10 anti
206.0
206.0614
0.03
11 sym
266.4
266.4698
0.03
12 anti
320.0
320.1142
0.03
13 sym
335.0
335.2300
0.07
4.2 Remarks
Calculations carried out by:
MODE_ITER_INV
OPTION:LIST_FREQ “ADJUSTS”:(5., 350.) NMAX_FREQ: 13
4.3
Contents of the file results
the first 13 Eigen frequencies (clean vectors and modal parameters).
4.4 Parameters
of execution
Version: 3.4.10
Machine: CRAY C90
System:
UNICOS 8.0
Obstruction memory:
8 megawords
Time CPU To use:
8.7 seconds
Handbook of Validation
V2.05 booklet: Linear dynamics of the assembled structures
HI-75/96/004 - Ind A

Code_Aster ®
Version
4.0
Titrate:
SDLX01 Flection of a symmetrical gantry
Date:
09/01/98
Author (S):
B. QUINNEZ
Key:
V2.05.001-C Page:
6/6
5
Summary of the results
Precision < 0.2% on all the Eigen frequencies until the 13th mode.
Handbook of Validation
V2.05 booklet: Linear dynamics of the assembled structures
HI-75/96/004 - Ind A