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
Organization (S): EDF/EP/AMV
Handbook 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.
Handbook of Validation
V2.03 booklet: Linear dynamics of the hulls and the plates
HI-75/98/040 - Ind A

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
1
Problem of reference
1.1 Geometry
Interior radius:
IH = 0.1 m
External radius:
Re = 0.2 m
Thickness:

T = 0.001 m
1.2
Material properties
E = 2.1011 Pa
= 0.3
= 7.800kg/m3
1.3
Boundary conditions and loadings
Embedding with the hub
For any point R = IH, U = v = W = 0. and X = y = Z = 0.
1.4 Conditions
initial
Without object for the modal analysis.
Handbook of Validation
V2.03 booklet: Linear dynamics of the hulls and the plates
HI-75/98/040 - Ind A

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
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:
1
E T 2
F
=
2

ij
ij
2
R2
12 1 - 2


E
(
)
With:
· I = a number of nodal diameters
· J = a number of nodal circles
2
and such as:
ij
I
0
1
2
3
J
0
13.0
13.3
14.7
18.5
1
85.1
86.7
91.7
100.
Mode of inflection to 2 nodal diameters and 1 nodal circle: f2,1 = 559,09 Hz
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.
Handbook of Validation
V2.03 booklet: Linear dynamics of the hulls and the plates
HI-75/98/040 - Ind A

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
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 grid
A number of nodes: 66.
A number of meshs and types: 100 triangles with 3 nodes DKT
3.3 Functionalities
tested
Commands
Keys
DEFI_INTERF_DYNA
NUME_DDL
[U4.55.03]
INTERFACE
NOM
INTERFACE
TYPE
“CRAIGB”
INTERFACE
MASQUE
DEFI_BASE_MODALE
CLASSIQUE
INTERF_DYNA
[U4.55.04]
CLASSIQUE
MODE_MECA
CLASSIQUE
NMAX_MODE
MODE_ITER_CYCL
BASE_MODALE
[U4.52.03]
NB_MODE
NB_SECTEUR
LIAISON
DROITE
LIAISON
GAUCHE
CALCUL
NB_DIAM
CALCUL
NMAX_FREQ
REST_BASE_PHYS
RESU_GENE
[U4.64.01]
SECTEUR
Handbook of Validation
V2.03 booklet: Linear dynamics of the hulls and the plates
HI-75/98/040 - Ind A

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
4
Results of modeling A
4.1 Values
tested
Nb of
Nb of
Nume
diameters
circles
Reference
Aster
% difference
command
nodal
nodal
I
J
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
Obstruction memory:
8 megawords
Time CUP To use:
18.17 seconds
Handbook of Validation
V2.03 booklet: Linear dynamics of the hulls and the plates
HI-75/98/040 - Ind A

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
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 grid
A number of nodes: 66.
A number of meshs and types: 100 triangles with 3 nodes DKT
5.3 Functionalities
tested
Commands
Keys
DEFI_INTERF_DYNA
NUME_DDL
[U4.55.03]
INTERFACE
NOM
INTERFACE
TYPE
“MNEAL”
INTERFACE
DDL_ACTIF
DEFI_BASE_MODALE
CLASSIQUE
INTERF_DYNA
[U4.55.04]
CLASSIQUE
MODE_MECA
CLASSIQUE
NMAX_MODE
MODE_ITER_CYCL
BASE_MODALE
[U4.52.03]
NB_MODE
NB_SECTEUR
LIAISON
DROITE
LIAISON
GAUCHE
CALCUL
NB_DIAM
CALCUL
FREQ
CALCUL
OPTION
CALCUL
NMAX_FREQ
“BANDE”
REST_BASE_PHYS
RESU_GENE
[U4.64.01]
SECTEUR
Handbook of Validation
V2.03 booklet: Linear dynamics of the hulls and the plates
HI-75/98/040 - Ind A

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
6
Results of modeling B
6.1 Values
tested
Nb of
Nb of
Nume
diameter
circles
Reference
Aster
% difference
command
nodal
nodal
I
J
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
Obstruction memory:
8 megawords
Time CUP To use:
17.50 seconds
Handbook of Validation
V2.03 booklet: Linear dynamics of the hulls and the plates
HI-75/98/040 - Ind A

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
7
Summary of the results
The quality of the results seems to be able to be improved by the use of a grid of finer sector.
Handbook of Validation
V2.03 booklet: Linear dynamics of the hulls and the plates
HI-75/98/040 - Ind A