Code_Aster ®
Version
5.0
Titrate:
SDLL106 Poutre subjected to a random excitation distributed
Date:
29/08/00
Author (S):
J. PIGAT Key
:
V2.02.106-B Page:
1/6

Organization (S): EDF/RNE/AMV

Handbook of Validation
V2.02 booklet: Linear dynamics of the beams
V2.02.106 document

SDLL106 - Poutre subjected to an excitation
random distributed

Summary:

An Bi-embedded beam is subjected over all its length to an effort distributed. Profile of distribution of the force
is identical to all the frequencies.

The random movement of this beam is evaluated by a stochastic approach: the density is determined
spectral of power of displacement in various points of the beam.

The two possibilities are tested:

·
space function of the efforts applied with interspectre unit (method 1),
·
interspectre builds directly for the excited ddl (method 2).

This test is an illustration of the response of a structure subjected to a Eolienne excitation.

Handbook of Validation
V2.02 booklet: Linear dynamics of the beams
HT-62/01/012/A

Code_Aster ®
Version
5.0
Titrate:
SDLL106 Poutre subjected to a random excitation distributed
Date:
29/08/00
Author (S):
J. PIGAT Key
:
V2.02.106-B Page:
2/6

1
Problem of reference

1.1 Geometry

obstacle
flexible
excitation
DY
DX


Beam:

Square section: 0.001 m X 0.001 m
Length: 0.8 m

One does not take account of the field of gravity.

1.2
Material properties

Young modulus:
E = 2.1 E+11 NR
Coefficient of compressibility:
= 0.3
Density:
= 7000 kg/m3

1.3
Boundary conditions and loadings

The beam is embedded at the two ends.

Ddl DZ is blocked in any point.

The effort applied is distributed with the following space distribution:

1
/
2
01
P1
P2
P3
P4
P5
P6
P7
P8
P9
0
L/4
L/2
3l/4
L
Handbook of Validation
V2.02 booklet: Linear dynamics of the beams
HT-62/01/012/A

Code_Aster ®
Version
5.0
Titrate:
SDLL106 Poutre subjected to a random excitation distributed
Date:
29/08/00
Author (S):
J. PIGAT Key
:
V2.02.106-B Page:
3/6

2
Reference solution

2.1
Method of calculation used for the reference solution

Direct calculation defines an assembled vector of space distribution of the effort and applies the density
spectral of effort G
()
FF on this distribution (method 1).

Broken up calculation defines the excitation as a matrix interspectrale of dimension 3 (equalizes with
a many excited nodes) and apply, in effort imposed on the nodes, the following matrix interspectrale
(method 2):





1 1 1


4 2 4




1
1 .G
()

1
FF
2
2




1 1 1


4 2 4

The two results must be identical without any approximation.

2.2
Results of reference

Spectral concentration of power of displacement of the P3 node at the frequencies: 4., 6., 8., 10. and 12 Hz.

2.3 References
bibliographical

[1]
C. DUVAL “Réponse dynamic under random excitation in Code_Aster: principles
theoretical and examples of use " - Note HP-61/92.148
Handbook of Validation
V2.02 booklet: Linear dynamics of the beams
HT-62/01/012/A

Code_Aster ®
Version
5.0
Titrate:
SDLL106 Poutre subjected to a random excitation distributed
Date:
29/08/00
Author (S):
J. PIGAT Key
:
V2.02.106-B Page:
4/6

3 Modeling
With

3.1
Characteristics of modeling

Discrete element in translation of the type DIS_T

Observation of the DSP of displacement
P1
P2
P3
P4
P5
P6
P7
P8
P9
Load application


Elements of beam: POU_D_T

The exiting spectral concentration is a white vibration of level 1.

The first 2 clean modes were taken into account in calculation.

Damping is introduced in the form of modal damping into the operator of answer
random dynamics. For all the calculation cases, it is taken equal to 5%

3.2
Characteristics of the grid

A number of nodes: 9

A number of meshs and types: 8 SEG2

3.3 Functionalities
tested

Commands
AFFE_CHAR_MECA FORCE_NODALE


MODE_ITER_INV


CONSTANT DEFI_INTE_SPEC


DYNA_ALEA_MODAL EXCIT
GRANDEUR:
“EFFO”

CHAM_NO
REPONSE


REST_SPEC_PHYS



3.4 Remarks

The spectral concentrations are expressed in their physical unit. For a force it will be out of N2/Hz.
Handbook of Validation
V2.02 booklet: Linear dynamics of the beams
HT-62/01/012/A

Code_Aster ®
Version
5.0
Titrate:
SDLL106 Poutre subjected to a random excitation distributed
Date:
29/08/00
Author (S):
J. PIGAT Key
:
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4
Results of modeling A

4.1 Values
tested

Spectral concentration of displacement at point AM10:

Frequency
Method 1
Method 2
% difference
4 Hz
4.0298E02
4.0298E02
0%
6 Hz
9.2971E02
9.2971E02
0%
8 Hz
9.5164E01
9.5164E01
0%
10 Hz
1.7617E01
1.7617E01
0%
12 Hz
2.6695E02
2.6695E02
0%

4.2 Parameters
of execution

Version: STA 5.02
Machine: SGI-Origin 2000

System:
IRIX 64
Obstruction memory:
8 megawords
Time CPU To use:
2.39 seconds

Handbook of Validation
V2.02 booklet: Linear dynamics of the beams
HT-62/01/012/A

Code_Aster ®
Version
5.0
Titrate:
SDLL106 Poutre subjected to a random excitation distributed
Date:
29/08/00
Author (S):
J. PIGAT Key
:
V2.02.106-B Page:
6/6

5
Summary of the results

Method 1 (space distribution of the efforts) and indirect method (by decomposition on the three
excited nodes) provide the same result.

This checking ensures a good coherence of the two methods and the quality of their
programming.

Handbook of Validation
V2.02 booklet: Linear dynamics of the beams
HT-62/01/012/A

Outline document