Code_Aster
®
Version
6.4
Titrate:
SDLS106 - Modal calculation of plate in under-structuring
Date:
01/03/04
Author (S):
E. BOYERE
Key
:
V2.03.106-A
Page:
1/4
Manual of Validation
V2.03 booklet: Dynamics linear of the hulls and the plates
HT-66/04/005/A
Organization (S):
EDF-R & D/AMA
Manual of Validation
V2.03 booklet: Linear dynamics of the hulls and the plates
Document: V2.03.106
SDLS106 - Modal calculation of plate in
under-structuring with base of Ritz
Summary:
This test of the field of the modal analysis implements the calculation of Eigen frequencies of bending in
under-structuring of a plate pressed on its edges. The interface is of type CRAIG-BAMPTON.
The reference solution is analytical.
Code_Aster
®
Version
6.4
Titrate:
SDLS106 - Modal calculation of plate in under-structuring
Date:
01/03/04
Author (S):
E. BOYERE
Key
:
V2.03.106-A
Page:
2/4
Manual of Validation
V2.03 booklet: Dynamics linear of the hulls and the plates
HT-66/04/005/A
1
Problem of reference
1.1 Geometry
interface
simple support
I
plate
L
SS2
SS1
substructure 1
L = 2 m
L = 1,5 m
1.2
Properties of the structure
S
= 7800 kg/m
3
E
= 2.10
11
AP
= 0.3
thickness 1 Misters.
1.3
Boundary conditions and loadings
The plate is in simple support on its four edges. The interface of each substructure is
embedded.
Code_Aster
®
Version
6.4
Titrate:
SDLS106 - Modal calculation of plate in under-structuring
Date:
01/03/04
Author (S):
E. BOYERE
Key
:
V2.03.106-A
Page:
3/4
Manual of Validation
V2.03 booklet: Dynamics linear of the hulls and the plates
HT-66/04/005/A
2
Reference solution
2.1
Reference solution of each substructure
Each substructure is a plate length 1,5 m and width 1 m, supported on three dimensioned and
embedded on the fourth, vibrating in bending.
It is shown [bib1] that the Eigen frequencies are worth:
F
L
Eh
ij
ij
=
-
2
2
2
2
1
2
2
12 1
(
)
with
,
00
,
121
30
,
116
00
,
69
53
,
42
2
12
2
31
2
21
2
11
=
=
=
=
what gives for the first frequencies
.
47
,
134
,
24
,
129
,
57
,
76
,
26
,
47
12
31
21
11
Hz
F
Hz
F
Hz
F
Hz
F
=
=
=
=
2.2
Reference solution of the assembled problem
According to
[bib1], one has for the Eigen frequencies of vibration of a supported plate
ij
I
L
L
J
2
2
2
2 2
=
+
That is to say
.
48
,
68
,
42
,
66
,
99
,
49
,
61
,
35
,
12
,
17
22
31
12
21
11
Hz
F
Hz
F
Hz
F
Hz
F
Hz
F
=
=
=
=
=
2.3 Reference
bibliographical
[1]
BLEVINS R.D: Formulated for natural frequency and shape mode. ED. Krieger 1984.
Code_Aster
®
Version
6.4
Titrate:
SDLS106 - Modal calculation of plate in under-structuring
Date:
01/03/04
Author (S):
E. BOYERE
Key
:
V2.03.106-A
Page:
4/4
Manual of Validation
V2.03 booklet: Dynamics linear of the hulls and the plates
HT-66/04/005/A
3 Modeling
With
3.1
Characteristics of modeling
For each substructure: 600 meshs QUAD4.
3.2 Functionalities
tested
Controls
DEFI_BASE_MODALE OPTION
RITZ
MODE_STATIQUE
FREQ
MODE_ITER_SIMULT
“REAL”
4
Results of modeling A
4.1
Values tested on the complete structure
Identification Reference
Aster %
difference
N°11 mode
frequency
17.12 Hz
17.12 Hz
0.00
N°21 mode
frequency
35.61 Hz
35.59 Hz
0.05
N°12 mode
frequency
49.99 Hz
50.03 Hz
0.08
N°31 mode
frequency 66.42
Hz
66.57 Hz
0.2
N°22 mode
frequency 68.48
Hz
68.36 Hz
0.01
5
Summary of the results
Calculation in under-structuring with modal base of type “Ritz” was validated on the modes of bending
of a plate pressed on its four edges.