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Titrate:
SDLX302 Poutre embedded 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:
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Organization (S): EDF/RNE/AMV, CS IF
Handbook of Validation
V2.05 booklet: Linear dynamics of the assembled structures
V2.05.302 document

SDLX302 - Embedded Poutre 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 inflection and that of
displacement within the framework of a stochastic approach.

Handbook of Validation
V2.05 booklet: Linear dynamics of the assembled structures
HT-62/01/012/A

Code_Aster ®
Version
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Titrate:
SDLX302 Poutre embedded and masses concentrated subjected to a force
Date:
30/08/01
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J. PIGAT, P. GUIHOT, T. FRIOU, E. LECLERE Key
:
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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 m2

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 Gaussien, centered, of white vibration 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 [H
1 Z,
H
101 Z]
2


S (F) = F = 104 N2 S
F
100
Handbook of Validation
V2.05 booklet: Linear dynamics of the assembled structures
HT-62/01/012/A

Code_Aster ®
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Titrate:
SDLX302 Poutre embedded and masses concentrated subjected to a force
Date:
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:
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S (F
F)
1
101
F (Hz)


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;
·
CASTOR:
10 elements of beam with shearing;
·
SYSTUS (2):
40 elements of beam with shearing;
·
PERMAS (2):
20 elements of beam with shearing;

Reduced damping is worth 1% 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 - Journée 2 .AS - Vol XVIII, n° 2. Damping in the structural analyzes. June 21
1994.
Handbook of Validation
V2.05 booklet: Linear dynamics of the assembled structures
HT-62/01/012/A

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SDLX302 Poutre embedded and masses concentrated subjected to a force
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3 Modeling
With

3.1
Characteristics of modeling

y
X


Along the beam, we have DY = DZ = DRX = DRY = 0.
At the base, all the ddls are blocked.

3.2
Characteristics of the grid

The grid consists of 21 nodes and 20 elements Timoshenko beam.

3.3
Functionalities tested

Commands



DEFI_FONCTION


DEFI_INTER_SPEC PAR_FONCTION


DYNA_ALEA_MODAL EXCIT
INTERSPECTRE


CHAM_NO

REPONSE


REST_SPEC_PHYS


POST_DYNA_ALEA GAUSS


Handbook of Validation
V2.05 booklet: Linear dynamics of the assembled structures
HT-62/01/012/A

Code_Aster ®
Version
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Titrate:
SDLX302 Poutre embedded and masses concentrated subjected to a force
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30/08/01
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:
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4
Results of modeling A

4.1 Values
tested

Eigen frequencies of inflection

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
CASTOR 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
PERMAS PERMAS SYSTUS
Value
Variation (%) Value
CASTEM DYNAM 2D
(1)
(2)
(1)
Average ABAQUS ASTER 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



Obstruction memory:
16 MW
Time CPU To use:
5.98 seconds
Handbook of Validation
V2.05 booklet: Linear dynamics of the assembled structures
HT-62/01/012/A

Code_Aster ®
Version
5.0
Titrate:
SDLX302 Poutre embedded 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

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.

Handbook of Validation
V2.05 booklet: Linear dynamics of the assembled structures
HT-62/01/012/A

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