Code_Aster ®
Version
5.0
Titrate:
SDLL104 Structures primary education and secondary


Date:
30/08/01
Author (S):
J. PIGAT Key
:
V2.02.104-B Page:
1/6

Organization (S): EDF/RNE/AMV

Handbook of Validation
V2.02 booklet: Linear dynamics of the beams
V2.02.104 document

SDLL104 - Primary and secondary Structures
subjected to a random excitation

Summary:

A principal beam of strong rigidity and important mass (primary structure), embedded at its base,
support in three points of transmission of efforts a light and flexible beam (secondary structure).

The primary structure is excited at its base by an acceleration given by its DSP.

The test compares a direct calculation of the whole of the two structures and a calculation chains where the answer of
principal beam at the points of connection is used like the excitation of the secondary beam.

The following functionalities are tested:

·
stamp interspectrale analytical preset by the function of KANAI-TAJIMI,
·
random dynamic response moving absolute, imposed acceleration,
·
modal answer interspectrale,
·
modal excitation interspectrale.

This approach is representative of what is required for the industrial studies: to determine them
answers of various secondary structures knowing the answer of the primary structure.
Handbook of Validation
V2.02 booklet: Linear dynamics of the beams
HT-62/01/012/A

Code_Aster ®
Version
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Titrate:
SDLL104 Structures primary education and secondary


Date:
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:
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1
Problem of reference

1.1 Geometry

Observation of the result
Dy
PB
dx
Pa


Beam Pa:

Section: 0.1 mm X 0.1 mm
Length: 3.0 m

Beam PB:

Section: 0.001 mm X 0.001 mm
Length: 2.0 m

Report/ratio of mass between PB and Pa: 0.33 E04

1.2
Material properties

Young modulus beams A and b:
E = 2.1 E+11 NR/M2
Poisson's ratio beams A and b:
= 0.3
Density beam Pa:
With = 2000 kg/m3
Density beam PB:
B = 1000 kg/m3

1.3
Boundary conditions and loadings

The movement is authorized in the plan (DX, DY).

Beam Pa is embedded in the support.

The beam PB is connected to beam Pa by three points. In each one, displacements in direction DX
and DY of the node of Pa and the PB node are identical. Rotations are not dependant.

The matrix interspectrale which transmits displacements of structure Pa to the structure PB in
chained calculation is of dimension 6 (6 ddl of transmission).
Handbook of Validation
V2.02 booklet: Linear dynamics of the beams
HT-62/01/012/A

Code_Aster ®
Version
5.0
Titrate:
SDLL104 Structures primary education and secondary


Date:
30/08/01
Author (S):
J. PIGAT Key
:
V2.02.104-B Page:
3/6

2
Reference solution

2.1
Method of calculation used for the reference solution

The reference solution is the direct calculation of the whole of the two structures.

It is supposed that the mass and the rigidity of secondary structure Pa do not disturb it
behavior of the primary structure. Thus chained calculation is supposed to be equivalent to direct calculation.
One can check on the table below that the structure PB modifies the Eigen frequencies little of
structure Pa.

Calculated Eigen frequencies (Hz)


Pa
PB
Pa and PB

1
6.5711
6.5711
0.
2
10.2655
10.2654
0.001
3 18.3759

18.3759 0.
4
26.2871
26.2871
0.
5
33.2716
33.2716
0.
6
59.1708
59.1708
0.
7
69.4570
69.4571
0.0001
8
105.3094 105.3091
0.0001
9 114.5567

114.5559 0.0007
10
118.9369
118.9376 0.0006

2.2
Results of reference

One observes the spectral concentration of acceleration on the node of the beam PB of X-coordinates 2.4 m (it
node PB25).

2.3 References
bibliographical

[1]
C. DUVAL “Réponse harmonic 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:
SDLL104 Structures primary education and secondary


Date:
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Author (S):
J. PIGAT Key
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3 Modeling
With

3.1
Characteristics of modeling

Discrete element in translation of the type DIS_T

PB11
PB15
PB21 PB25
PB31
PA1
PA11
PA21
PA31

Elements used: POU_D_T. The characteristics of beam are defined by:

CARELEM
=
AFFE_CARA_ELEM
(
POUTRE
:
(
GROUP_MA
:
GRMAPRIM
......
SECTION:
“RECTANGLE”
CARA:
(“HZ”
“HY”)
VALE:
(0.1
0.1)
)







…);

The method of calculation asks for the calculation of static modes corresponding to the DDL excitation.

The Eigen frequencies taking into account in calculations are all the frequencies in the tape
[0, 35 Hz].

3.2
Characteristics of the grid

A number of nodes:
Pa: 31
PB: 21
A number of meshs and types:
Pa: 30 SEG2
PB: 20 SEG2

3.3 Functionalities
tested

Commands


AFFE_CHAR_MECA DDL_IMPO


LIAISON_DDL
MODE_ITER_INV


MODE_STATIQUE DDL_IMPO
AVEC_CMP
DEFI_INTE_SPEC KANAI_TAJIMI


DYNA_ALEA_MODAL EXCIT


MODE_STAT
REPONSE
REST_SPEC_PHYS


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

Code_Aster ®
Version
5.0
Titrate:
SDLL104 Structures primary education and secondary


Date:
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Author (S):
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:
V2.02.104-B Page:
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4
Results of modeling A

4.1 Values
tested

Values of the spectral concentration of acceleration at point PB25:

Frequency Direct Node
Chains
%
difference
5. Hz
PB25
3.6913
3.7052
0.38%
10. Hz
PB25
75.439
75.797
0.47%
15. Hz
PB25
1.6777
1.6929
0.91%
20. Hz
PB25
1.1367
1.0987
3.34%
25. Hz
PB25
0.2927
0.2630
10.12%

4.2 Parameters
of execution

Version: STA 5.02
Machine: SGI-Origin 2000

System:
IRIX 64
Obstruction memory:
8 megawords
Time CPU To use:
11.11 seconds
Handbook of Validation
V2.02 booklet: Linear dynamics of the beams
HT-62/01/012/A

Code_Aster ®
Version
5.0
Titrate:
SDLL104 Structures primary education and secondary


Date:
30/08/01
Author (S):
J. PIGAT Key
:
V2.02.104-B Page:
6/6

5
Summary of the results

The results obtained confirm on the one hand the assumption of equivalence between direct calculation and calculation
chained, in addition the good coherence of the calculation algorithm of dynamic response random.

A variation is inevitable between calculations of the two methods: that obtained to 25 Hz is too high
(11%).

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

Outline document