Code_Aster
®
Version
5.0
Titrate:
SDLX302
Fixed beam and masses concentrated subjected to a force
Date:
30/08/01
Author (S):
J. PIGAT, P. GUIHOT, T. FRIOU, E. LECLERE
Key
:
V2.05.302-A
Page:
1/6
Manual of Validation
V2.05 booklet: Linear dynamics of the assembled structures
HT-62/01/012/A
Organization (S):
EDF/RNE/AMV, CS IF
Manual of Validation
V2.05 booklet: Linear dynamics of the assembled structures
Document
V
V
2
2
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5
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3
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2
SDLX302 - Fixed beam and masses concentrated
subjected to a transverse random force
Summary:
A beam fixed with a concentrated mass is subjected to a random effort in the direction
transverse.
This test validates, using a comparison between codes, the calculation of the clean modes of bending and that of
displacement within the framework of a stochastic approach.
Code_Aster
®
Version
5.0
Titrate:
SDLX302
Fixed beam and masses concentrated subjected to a force
Date:
30/08/01
Author (S):
J. PIGAT, P. GUIHOT, T. FRIOU, E. LECLERE
Key
:
V2.05.302-A
Page:
2/6
Manual of Validation
V2.05 booklet: Linear dynamics of the assembled structures
HT-62/01/012/A
1
Problem of reference
1.1 Geometry
F (T)
L
Length of the beam
L = 20.0 m
Internal diameter
D = 0.388 m
External diameter
D = 0.400 m
Mass concentrated at the top
M = 300. kg
Mass moment of inertia
J = 200. kg m
2
1.2
Properties of materials
Density of the tube
= 7850 kg.m
- 3
Young modulus
E = 210. E+9 N.m
- 2
Poisson's ratio
= 0.
1.3
Boundary conditions and loading
The tube is embedded at the base. The mass is free. The movement is authorized in a vertical plane
(DX, DRZ).
A random effort F (T), applied to the concentrated mass is compared to a random process
stationary Gaussian, centered, of white Gaussian noise type to tape limited of 1.Hz to 101.Hz. It is characterized
by a standard deviation
F
= 1 kN, and a unilateral spectral concentration in frequency
()
S
F
F
such as:
[
]
()
=
=
F
Hz
Hz
S
F
NR S
F
F
1
101
100
10
2
4
2
,
Code_Aster
®
Version
5.0
Titrate:
SDLX302
Fixed beam and masses concentrated subjected to a force
Date:
30/08/01
Author (S):
J. PIGAT, P. GUIHOT, T. FRIOU, E. LECLERE
Key
:
V2.05.302-A
Page:
3/6
Manual of Validation
V2.05 booklet: Linear dynamics of the assembled structures
HT-62/01/012/A
1
101
F (Hz)
()
S F
F
2
Reference solution
2.1
Method of calculation used for the reference solution
Calculations are carried out with 8 computer codes, for 10 modelings. The different ones
modelings are presented below.
·
Castem:
20 elements of beam without shearing;
·
Dynam 2D:
20 elements of beam without shearing;
·
PERMAS (1): 20 elements of beam without shearing;
·
Nastran:
20 elements of beam without shearing;
·
SYSTUS (1):
20 elements of beam without shearing;
·
ABAQUS:
20 elements of beam with shearing;
·
MECHANICA: 5 elements of beam with shearing, convergence with degree 7;
·
BEAVER:
10 elements of beam with shearing;
·
SYSTUS (2):
40 elements of beam with shearing;
·
PERMAS (2):
20 elements of beam with shearing;
Reduced damping
1% are worth on all the modes.
2.2
Results of reference
Frequencies.
Value RMS, for displacement at the loose lead of the beam.
2.3
Uncertainty on the solution
Comparison between codes.
2.4 References
bibliographical
[1]
IPSI - Day
2
.AS - Flight XVIII, n° 2. Damping in the structural analyzes. June 21
1994.
Code_Aster
®
Version
5.0
Titrate:
SDLX302
Fixed beam and masses concentrated subjected to a force
Date:
30/08/01
Author (S):
J. PIGAT, P. GUIHOT, T. FRIOU, E. LECLERE
Key
:
V2.05.302-A
Page:
4/6
Manual of Validation
V2.05 booklet: Linear dynamics of the assembled structures
HT-62/01/012/A
3 Modeling
With
3.1
Characteristics of modeling
X
y
Along the beam, we have DY = DZ = DRX = DRY = 0.
At the base, all the ddls are locked.
3.2
Characteristics of the mesh
The mesh consists of 21 nodes and 20 elements Timoshenko beam.
3.3
Functionalities tested
Controls
DEFI_FONCTION
DEFI_INTER_SPEC PAR_FONCTION
DYNA_ALEA_MODAL EXCIT
INTERSPECTRE
CHAM_NO
ANSWER
REST_SPEC_PHYS
POST_DYNA_ALEA GAUSS
Code_Aster
®
Version
5.0
Titrate:
SDLX302
Fixed beam and masses concentrated subjected to a force
Date:
30/08/01
Author (S):
J. PIGAT, P. GUIHOT, T. FRIOU, E. LECLERE
Key
:
V2.05.302-A
Page:
5/6
Manual of Validation
V2.05 booklet: Linear dynamics of the assembled structures
HT-62/01/012/A
4
Results of modeling A
4.1 Values
tested
Eigen frequencies of bending
Number
mode 1 2 3 4 5 6 7 8 9 10
Castem 0.70
5.04
14.69
28.78
46.19 66.82 92.74 125.15 163.91 208.81
DYNAM 2D/DRAM 0.70 5.04 14.67
28.75 46.18 66.86 92.77 125.05 163.38 208.81
PERMAS (1)
0.70
5.04
14.69
28.78
46.19 66.82 92.74 125.15 163.91 208.81
Nastran 0.70
5.04
14.67
28.75
46.18 66.86 92.78 125.05 163.48 207.70
SYSTUS (1)
0.72
5.13
14.91
29.19
46.83 67.65 93.64 125.95 164.39 208.61
ABAQUS 0.70
5.02
14.57
28.42
45.40 65.17 89.26 118.50 152.33
MECHANICA 0.70
5.03
14.62
28.54
45.63 65.60 90.21 120.43 155.88 196.01
BEAVER 0.70
5.03
14.59
28.46
45.48 65.35 89.88 120.24 154.40 194.06
SYSTUS
(2)
0.70
5.03
14.59
28.42
45.35
PERMAS (2)
0.70
5.03
14.60
28.48 45.50 65.29 89.59 119.41 138.42
Average values
0.70
5.04
14.66
28.66 45.89 66.27 91.51 122.77 157.79 204.69
ASTER 0.70
5.03
14.59
28.43
45.38 65.07 89.17 118.67 153.24 192.40
Variation Aster
0.00 0.26 0.48 0.79 1.12 1.81 2.56 3.34 2.88 6.00
Average values
in %
Displacement (m): with Fx = 1000
CASTEM DYNAM 2D PERMAS
(1)
PERMAS
(2)
SYSTUS
(1)
ABAQUS
Value
average
ASTER
Variation (%) Value
average/ASTER
0.039 0.038 0.041 0.038 0.035 0.039 0.038 0.0344
9.4
4.2 Remarks
Problems of definition between effort intern and forced do not allow to compare them
results of ASTER with the other codes (bending moment and sharp effort).
4.3 Parameters
of execution
Version: 5.02
Machine: SGI ORIGIN 2000
Overall dimension memory:
16 MW
Time CPU To use:
5.98 seconds
Code_Aster
®
Version
5.0
Titrate:
SDLX302
Fixed beam and masses concentrated subjected to a force
Date:
30/08/01
Author (S):
J. PIGAT, P. GUIHOT, T. FRIOU, E. LECLERE
Key
:
V2.05.302-A
Page:
6/6
Manual of Validation
V2.05 booklet: Linear dynamics of the assembled structures
HT-62/01/012/A
5
Summary of the results
The results of the modal base are good since the maximum change is to the maximum of 6% on
last frequency.
For the results in displacement we obtain a variation of 9.4.