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
Manual of Validation
V2.02 booklet: Linear dynamics of the beams
HT-62/01/012/A
Organization (S):
EDF/RNE/AMV
Manual of Validation
V2.02 booklet: Linear dynamics of the beams
V2.02.104 document
SDLL104 - Structures primary education and secondary
subjected to a random excitation
Summary:
A main 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
main 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.
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:
2/6
Manual of Validation
V2.02 booklet: Linear dynamics of the beams
HT-62/01/012/A
1
Problem of reference
1.1 Geometry
dx
Observation of the result
AP
Dy
PB
Beam AP:
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 AP: 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 AP:
With
= 2000 kg/m
3
Density beam PB:
B
= 1000 kg/m
3
1.3
Boundary conditions and loadings
The movement is authorized in the plan (
DX
,
DY
).
Beam AP is embedded in the support.
The beam PB is connected to beam AP by three points. In each one, displacements in the direction
DX
and
DY
node of AP and PB node are identical. Rotations are not dependant.
The matrix interspectrale which transmits displacements of structure AP to the structure PB in
chained calculation is of dimension 6 (6 ddl of transmission).
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
Manual of Validation
V2.02 booklet: Linear dynamics of the beams
HT-62/01/012/A
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 AP 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 AP.
Calculated Eigen frequencies (Hz)
AP
PB
AP 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 “harmonic Response under random excitation in Code_Aster: principles
theoretical and examples of use " - Note HP-61/92.148
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:
4/6
Manual of Validation
V2.02 booklet: Linear dynamics of the beams
HT-62/01/012/A
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
(
BEAM
:
(
GROUP_MA
:
GRMAPRIM
......
SECTION:
“RIGHT-ANGLED”
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 mesh
A number of nodes:
AP: 31
PB: 21
A number of meshs and types:
AP: 30 SEG2
PB: 20 SEG2
3.3 Functionalities
tested
Controls
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
ANSWER
REST_SPEC_PHYS
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:
5/6
Manual of Validation
V2.02 booklet: Linear dynamics of the beams
HT-62/01/012/A
4
Results of modeling A
4.1 Values
tested
Values of the spectral concentration of acceleration at point PB25:
Frequency Direct Node
Channels
%
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
Overall dimension memory:
8 megawords
Time CPU To use:
11.11 seconds
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
Manual of Validation
V2.02 booklet: Linear dynamics of the beams
HT-62/01/012/A
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%).