Code_Aster
®
Version
4.0
Titrate:
SDLX01 Bending of a symmetrical gantry
Date:
09/01/98
Author (S):
B. QUINNEZ
Key:
V2.05.001-C
Page:
1/6
Manual of Validation
V2.05 booklet: Linear dynamics of the assembled structures
HI-75/96/004 - Ind A
Organization (S):
EDF/IMA/MN
Manual of Validation
V2.05 booklet: Linear dynamics of the assembled structures
V2.05.001 document
SDLX01 - Bending 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%.
Code_Aster
®
Version
4.0
Titrate:
SDLX01 Bending of a symmetrical gantry
Date:
09/01/98
Author (S):
B. QUINNEZ
Key:
V2.05.001-C
Page:
2/6
Manual of Validation
V2.05 booklet: Linear dynamics of the assembled structures
HI-75/96/004 - Ind A
1
Problem of reference
1.1 Geometry
E
F
C
D
With
B
y, v
X, U
y'
z'
B
H
section:
y'
z'
B
H
cross-pieces
posts
Rectangular cross-sections:
thickness
H = 0.0048 m
width
B = 0.029 m
surface
To = 1.392 10
- 4
m
2
inertia
lz = 2.673 10
- 10
m
4
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 10
11
AP
= 0.3
= 7.800. kg/m
3
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.
Code_Aster
®
Version
4.0
Titrate:
SDLX01 Bending of a symmetrical gantry
Date:
09/01/98
Author (S):
B. QUINNEZ
Key:
V2.05.001-C
Page:
3/6
Manual of Validation
V2.05 booklet: Linear dynamics of the assembled structures
HI-75/96/004 - Ind A
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 (Theory 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 Directed Work of vibrations of the structures. Mechanical option. School
Higher main road of Mechanics and Micromechanics. Laboratory of Mechanics
Applied. Besancon (France) (1983).
Code_Aster
®
Version
4.0
Titrate:
SDLX01 Bending of a symmetrical gantry
Date:
09/01/98
Author (S):
B. QUINNEZ
Key:
V2.05.001-C
Page:
4/6
Manual of Validation
V2.05 booklet: Linear dynamics of the assembled structures
HI-75/96/004 - Ind A
3 Modeling
With
3.1
Characteristics of modeling
POU_D_T
E
F
C
D
With
B
y
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:
(ALL:“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 mesh
A number of nodes:
50
A number of meshs and types:
50 SEG2
3.3 Functionalities
tested
Controls
Keys
AFFE_CARA_ELEM
BEAM
“RIGHT-ANGLED”
ALL
[U4.24.01]
AFFE_CHAR_MECA
DDL_IMPO
ALL
[U4.25.01]
GROUP_NO
AFFE_MATERIAU
ALL
[U4.23.02]
AFFE_MODELE
“MECHANICAL”
“POU_D_T'
ALL
[U4.22.01]
DEFI_MATERIAU
ELAS
[U4.23.01]
MODE_ITER_INV
CALC_FREQ
OPTION
“ADJUSTS”
[U4.52.01]
FREQ
NMAX_FREQ
Code_Aster
®
Version
4.0
Titrate:
SDLX01 Bending of a symmetrical gantry
Date:
09/01/98
Author (S):
B. QUINNEZ
Key:
V2.05.001-C
Page:
5/6
Manual of Validation
V2.05 booklet: Linear dynamics of the assembled structures
HI-75/96/004 - Ind A
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
Overall dimension memory:
8 megawords
Time CPU To use:
8.7 seconds
Code_Aster
®
Version
4.0
Titrate:
SDLX01 Bending of a symmetrical gantry
Date:
09/01/98
Author (S):
B. QUINNEZ
Key:
V2.05.001-C
Page:
6/6
Manual of Validation
V2.05 booklet: Linear dynamics of the assembled structures
HI-75/96/004 - Ind A
5
Summary of the results
Precision < 0.2% on all the Eigen frequencies until the 13
ème
mode.