Code_Aster
®
Version
4.0
Titrate:
Cyclic SDLS04 Under-structuring
Date:
01/12/98
Author (S):
G. ROUSSEAU, C. VARE
Key:
V2.03.004-B
Page:
1/8
Manual of Validation
V2.03 booklet: Linear dynamics of the hulls and the plates
HI-75/98/040 - Ind A
Organization (S):
EDF/EP/AMV
Manual of Validation
V2.03 booklet: Linear dynamics of the hulls and the plates
Document: V2.03.004
SDLS04 - Under-structuring cyclic:
Annular thin section embedded in its hub
Summary:
The applicability of this test relates to the dynamics of the structures, and more particularly calculation
modal by cyclic dynamic under-structuring.
It is a question of calculating the clean modes of an axisymmetric structure (annular thin section embedded in sound
hub) by regarding it as a structure with cyclic repetitivity.
The model consists of an angular sector of 20° of the ring, with a grid in triangles to which are affected
elements of the type plates: DKT. Two methods of calculation are tested:
·
cyclic dynamic Under-structuring of Craig-Bampton
·
cyclic dynamic Under-structuring of Mac Neal
The results of reference result from an analytical calculation. They validate the modal computational tools by
cyclic dynamic under-structuring implemented in
Code_Aster
.
Code_Aster
®
Version
4.0
Titrate:
Cyclic SDLS04 Under-structuring
Date:
01/12/98
Author (S):
G. ROUSSEAU, C. VARE
Key:
V2.03.004-B
Page:
2/8
Manual of Validation
V2.03 booklet: Linear dynamics of the hulls and the plates
HI-75/98/040 - Ind A
1
Problem of reference
1.1 Geometry
Interior radius:
R
I
= 0.1 m
External radius:
R
E
= 0.2 m
Thickness:
T = 0.001 m
1.2
Material properties
E = 2.10
11
AP
= 0.3
= 7.800kg/m
3
1.3
Boundary conditions and loadings
Embedding with the hub
For any point R = R
I
, U = v = W = 0. and
X =
y =
Z = 0.
1.4 Conditions
initial
Without object for the modal analysis.
Code_Aster
®
Version
4.0
Titrate:
Cyclic SDLS04 Under-structuring
Date:
01/12/98
Author (S):
G. ROUSSEAU, C. VARE
Key:
V2.03.004-B
Page:
3/8
Manual of Validation
V2.03 booklet: Linear dynamics of the hulls and the plates
HI-75/98/040 - Ind A
2
Reference solution
2.1
Method of calculation used for the reference solution
The reference solution is that given in card SDLS04/89 of the guide VPCS which presents
analytical solution in the following way:
The solution of the determinant of the frequencies established starting from the functions of Bessel leads to
formulate:
(
)
F
R
E T
ij
E
ij
=
-
1
2
12
1
2
2
2
2
With:
·
I = a number of nodal diameters
·
J = a number of nodal circles
and
ij
2
such as:
I
J
0
1
2
3
0
13.0
13.3
14.7
18.5
1
85.1
86.7
91.7
100.
Mode of bending to 2 nodal diameters and 1 nodal circle: F
2,1
= 559,09 H
Z
2.2
Results of reference
8 clean modes.
2.3
Uncertainty on the solution
Analytical solution.
2.4 References
bibliographical
[1]
A.W. LEISSA, Vibration off punts, Document NASA SP160, 1969, p. 19-30.
Code_Aster
®
Version
4.0
Titrate:
Cyclic SDLS04 Under-structuring
Date:
01/12/98
Author (S):
G. ROUSSEAU, C. VARE
Key:
V2.03.004-B
Page:
4/8
Manual of Validation
V2.03 booklet: Linear dynamics of the hulls and the plates
HI-75/98/040 - Ind A
3 Modeling
With
3.1
Characteristics of modeling
This structure with cyclic repetitivity is studied using the method of under-structuring
cyclic dynamics of CRAIG-BAMPTON.
A basic sector, consisted an angular sector of 20°, is with a grid in triangles to which are
affected elements of plate DKT.
The modal base used for the sector is made up of 20 clean modes and the constrained modes
associated the interfaces.
3.2
Characteristics of the mesh
A number of nodes: 66.
A number of meshs and types: 100 triangles with 3 nodes DKT
3.3 Functionalities
tested
Controls
Keys
DEFI_INTERF_DYNA
NUME_DDL
[U4.55.03]
INTERFACE
NAME
INTERFACE
TYPE
“CRAIGB”
INTERFACE
MASK
DEFI_BASE_MODALE
CONVENTIONAL
INTERF_DYNA
[U4.55.04]
CONVENTIONAL
MODE_MECA
CONVENTIONAL
NMAX_MODE
MODE_ITER_CYCL
BASE_MODALE
[U4.52.03]
NB_MODE
NB_SECTEUR
CONNECTION
STRAIGHT LINE
CONNECTION
LEFT
CALCULATION
NB_DIAM
CALCULATION
NMAX_FREQ
REST_BASE_PHYS
RESU_GENE
[U4.64.01]
SECTOR
Code_Aster
®
Version
4.0
Titrate:
Cyclic SDLS04 Under-structuring
Date:
01/12/98
Author (S):
G. ROUSSEAU, C. VARE
Key:
V2.03.004-B
Page:
5/8
Manual of Validation
V2.03 booklet: Linear dynamics of the hulls and the plates
HI-75/98/040 - Ind A
4
Results of modeling A
4.1 Values
tested
Nb of
Nb of
Nume
command
diameters
nodal
I
circles
nodal
J
Reference
Aster
% difference
1
0
0
79.26
79.58
0.4
8
0
1
518.85
519.54
0.1
2.3
1
0
81.09
81.18
0.1
9.10
1
1
528.61
529.50
0.2
4.5
2
0
89.63
89.72
0.1
11.12
2
1
559.09
559.48
0.07
6.7
3
0
112.79
113.16
0.3
13.14
3
1
609.70
609.75
0.01
4.2 Remarks
The modes with more than 1 modal diameter are double modes.
4.3 Parameters
of execution
Version: 3.02.15
Machine: CRAY C90
System:
UNICOS 8.0
Overall dimension memory:
8 megawords
Time CUP To use:
18.17 seconds
Code_Aster
®
Version
4.0
Titrate:
Cyclic SDLS04 Under-structuring
Date:
01/12/98
Author (S):
G. ROUSSEAU, C. VARE
Key:
V2.03.004-B
Page:
6/8
Manual of Validation
V2.03 booklet: Linear dynamics of the hulls and the plates
HI-75/98/040 - Ind A
5 Modeling
B
5.1
Characteristics of modeling
This structure with cyclic repetitivity is studied using the method of under-structuring
cyclic dynamics of MAC-NEAL.
A basic sector, consisted an angular sector of 20°, is with a grid in triangles to which are
affected elements of plate DKT.
The modal base used for the sector is made up of 20 clean modes and the modes of fastener
associated the interfaces.
5.2
Characteristics of the mesh
A number of nodes: 66.
A number of meshs and types: 100 triangles with 3 nodes DKT
5.3 Functionalities
tested
Controls
Keys
DEFI_INTERF_DYNA
NUME_DDL
[U4.55.03]
INTERFACE
NAME
INTERFACE
TYPE
“MNEAL”
INTERFACE
DDL_ACTIF
DEFI_BASE_MODALE
CONVENTIONAL
INTERF_DYNA
[U4.55.04]
CONVENTIONAL
MODE_MECA
CONVENTIONAL
NMAX_MODE
MODE_ITER_CYCL
BASE_MODALE
[U4.52.03]
NB_MODE
NB_SECTEUR
CONNECTION
STRAIGHT LINE
CONNECTION
LEFT
CALCULATION
NB_DIAM
CALCULATION
FREQ
CALCULATION
OPTION
CALCULATION
NMAX_FREQ
“TAPE”
REST_BASE_PHYS
RESU_GENE
[U4.64.01]
SECTOR
Code_Aster
®
Version
4.0
Titrate:
Cyclic SDLS04 Under-structuring
Date:
01/12/98
Author (S):
G. ROUSSEAU, C. VARE
Key:
V2.03.004-B
Page:
7/8
Manual of Validation
V2.03 booklet: Linear dynamics of the hulls and the plates
HI-75/98/040 - Ind A
6
Results of modeling B
6.1 Values
tested
Nb of
Nb of
Nume
command
diameter
nodal
I
circles
nodal
J
Reference
Aster
% difference
1
0
0
79.26
79.58
0.4
8
0
1
518.85
519.53
0.1
2.3
1
0
81.09
81.18
0.1
9.10
1
1
528.61
529.50
0.2
4.5
2
0
89.63
89.72
0.1
11.12
2
1
559.09
559.48
0.07
6.7
3
0
112.79
113.16
0.3
13.14
3
1
609.70
609.76
0.01
6.2 Remarks
The modes with more than 1 modal diameter are double modes.
6.3 Parameters
of execution
Version: 3.02.15
Machine: CRAY C90
System:
UNICOS 8.0
Overall dimension memory:
8 megawords
Time CUP To use:
17.50 seconds
Code_Aster
®
Version
4.0
Titrate:
Cyclic SDLS04 Under-structuring
Date:
01/12/98
Author (S):
G. ROUSSEAU, C. VARE
Key:
V2.03.004-B
Page:
8/8
Manual of Validation
V2.03 booklet: Linear dynamics of the hulls and the plates
HI-75/98/040 - Ind A
7
Summary of the results
The quality of the results seems to be able to be improved by the use of a mesh of finer sector.