Code_Aster
Version
6.4
Titrate:
SDLS106 - Modal Calcul of plate in under-structuring

Date:
01/03/04
Author (S):
E. BOYERE Key
:
V2.03.106-A Page:
1/4

Organization (S): EDF-R & D/AMA
Handbook of Validation
V2.03 booklet: Linear dynamics of the hulls and the plates
Document: V2.03.106

SDLS106 - Modal Calcul 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 inflection in
under-structuring of a plate pressed on its edges. The interface is of type CRAIG-BAMPTON.

The reference solution is analytical.
Handbook of Validation
V2.03 booklet: Dynamics linear of the hulls and the plates
HT-66/04/005/A

Code_Aster
Version
6.4
Titrate:
SDLS106 - Modal Calcul of plate in under-structuring

Date:
01/03/04
Author (S):
E. BOYERE Key
:
V2.03.106-A Page:
2/4

1
Problem of reference

1.1 Geometry

plate
L
SS1
substructure 1
SS2
I
interface
simple support


L = 2 m

L = 1,5 m

1.2
Properties of the structure

= 7800 kg/m3
E = 2.1011 Pa
= 0.3
thickness 1 Misters.
S

1.3
Boundary conditions and loadings

The plate is in simple support on its four edges. The interface of each substructure is
embedded.

Handbook of Validation
V2.03 booklet: Dynamics linear of the hulls and the plates
HT-66/04/005/A

Code_Aster
Version
6.4
Titrate:
SDLS106 - Modal Calcul of plate in under-structuring

Date:
01/03/04
Author (S):
E. BOYERE Key
:
V2.03.106-A Page:
3/4

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 inflection.

It is shown [bib1] that the Eigen frequencies are worth:

1
2
2
ij

Eh
2
fij =



2 L2 12 1
(- 2)

with 2
=
53
,
42
2


=
00
,
69
2


=
30
,
116
2


=
00
,
121
,
11
21
31
12


what gives for the first frequencies

F =
,
47 26Hz,
11
F
=
57
,
76
Hz,
21

F
=
,
129 24Hz,
31
F
=
,
134 47
.
12
Hz

2.2
Reference solution of the assembled problem

According to [bib1], one has for the Eigen frequencies of vibration of a supported plate

2


2

=
L
2
2
2
ij
I
+
J




L




That is to say

F =
12
,
17
Hz,
11
F
=
61
,
35
Hz,
21
F
=
99
,
49
Hz,
12

F
=
,
66 42Hz,
31
F
=,
68 48
.
22
Hz

2.3 Reference
bibliographical

[1]
BLEVINS R.D: Formulated for natural frequency and shape mode. ED. Krieger 1984.

Handbook of Validation
V2.03 booklet: Dynamics linear of the hulls and the plates
HT-66/04/005/A

Code_Aster
Version
6.4
Titrate:
SDLS106 - Modal Calcul of plate in under-structuring

Date:
01/03/04
Author (S):
E. BOYERE Key
:
V2.03.106-A Page:
4/4

3 Modeling
With

3.1
Characteristics of modeling

For each substructure: 600 meshs QUAD4.

3.2 Functionalities
tested

Commands
DEFI_BASE_MODALE OPTION
RITZ


MODE_STATIQUE
FREQ


MODE_ITER_SIMULT
“REEL”


4
Results of modeling A

4.1
Values tested on the complete structure

Identification Reference
Aster %
difference
N11 mode



frequency
17.12 Hz
17.12 Hz
0.00
N21 mode



frequency
35.61 Hz
35.59 Hz
0.05
N12 mode



frequency
49.99 Hz
50.03 Hz
0.08
N31 mode



frequency 66.42
Hz
66.57 Hz
0.2

N22 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 inflection
of a plate pressed on its four edges.

Handbook of Validation
V2.03 booklet: Dynamics linear of the hulls and the plates
HT-66/04/005/A

Outline document