Code_Aster ®
Version
5.0
Titrate:
SDLL14 - Modes of vibration of a thin elbow of piping
Date:
19/08/02
Author (S):
P. MASSIN, F. LEBOUVIER Key
:
V2.02.014-A Page:
1/8
Organization (S): EDF/AMA, DeltaCAD
Handbook of Validation
V2.02 booklet: Linear dynamics of the beams
Document: V2.02.014
SDLL14 - Modes of vibration of an elbow
of thin piping
Summary:
This test consists in seeking the Eigen frequencies and the modes of vibration associated with a piping
bent. It makes it possible to validate modelings finite elements TUYAU (SEG3 and SEG4) and TUYAU_6M (SEG4).
The results obtained are compared with an analytical reference solution.
Handbook of Validation
V2.02 booklet: Linear dynamics of the beams
HT-66/02/001/A
Code_Aster ®
Version
5.0
Titrate:
SDLL14 - Modes of vibration of a thin elbow of piping
Date:
19/08/02
Author (S):
P. MASSIN, F. LEBOUVIER Key
:
V2.02.014-A Page:
2/8
1
Problem of reference
1.1 Geometry
y, v
Hollow circular cross-section
L
y
L =
2.0
m
With
R
= 1. m
C
D
= 0.020 m
E
D =
0.016
m
I
With
= 1.131 X 10-4 m ²
I = I = 4.637 X 10-9 m4
y
Z
R
I
= 9.274 X 10-9 m4
p
= 90°
O
B
X
X, U
Z
L
Z, W
D
1.2
Properties of material
The properties of material constituting the plate are:
E = 2.1 1011 Pa
Young modulus
= 0.3
Poisson's ratio
= 7800. Kg/m3 Masses
voluminal
1.3
Boundary conditions and loadings
· C.L. :
- sections out of C and D embedded
- Not a: displacements following y and Z null
- Not b: displacements according to X and Z null
1.4 Conditions
initial
Without object
Handbook of Validation
V2.02 booklet: Linear dynamics of the beams
HT-66/02/001/A
Code_Aster ®
Version
5.0
Titrate:
SDLL14 - Modes of vibration of a thin elbow of piping
Date:
19/08/02
Author (S):
P. MASSIN, F. LEBOUVIER Key
:
V2.02.014-A Page:
3/8
2
Reference solution
2.1
Method of calculation used for the reference solution
Method of Rayleigh applied to elements of hurled right beam and to an element of
thin curved beam makes it possible to determine parameters such as:
2
I.E.(internal excitation)
· inflection in the plan: F
I
Z
I =
i=1,2;
R
2
2
With
µ2
GI
·
I
p
transverse inflection: fi =
i=1,2;
R
2
2
With
Values 2
2
I and µi are drawn from an abacus.
This formulation is usable only for piping very slim:
L
· Twinge of the right parts higher than
20
of
I
· Thin elbow such as R
Z
100
with, angle in the center in radian. It is not
With
necessary to use here a coefficient of flexibility of the elbow.
2.2
Results of reference
· The first four Eigen frequencies,
· The first four clean modes (2 transverse modes, 2 modes in the plan).
- Frequency (transverse mode 1)
17.9 Hz
- Frequency (mode in plan 1)
24.8 Hz
- Frequency (transverse mode 2)
25.3 Hz
- Frequency (mode in plan 1)
27.0 Hz
2.3
Uncertainties on the solution
· ± 0.1% for the first transverse Eigen frequency,
· ± 3% for the other Eigen frequencies.
2.4 References
bibliographical
[1]
VPCS: Guide validation of the software packages of structural analysis: “test SDLL14”, SFM,
Technical AFNOR.
[2]
R.D. Blevins, formulated for natural frequency and shape mode, New York, Van Nostrand,
1979, P. 215.
Handbook of Validation
V2.02 booklet: Linear dynamics of the beams
HT-66/02/001/A
Code_Aster ®
Version
5.0
Titrate:
SDLL14 - Modes of vibration of a thin elbow of piping
Date:
19/08/02
Author (S):
P. MASSIN, F. LEBOUVIER Key
:
V2.02.014-A Page:
4/8
3 Modeling
With
3.1
Characteristics of modeling
y, v
Modeling PIPE (SEG3)
Boundary conditions:
C
10
With
Points C and D:
8
- DDL of Poutre: DX = DY = DZ = DRX = DRY = DRZ = 0
- DDL of Coque: UIm = VIm = Wim = 0 (m=2,3)
X, U UOm = VOm = WOm = 0 (m=2,3)
WI1 = WO1 = WO = 0
B
Not a:
- DDL of Poutre: DY = DZ = 0
Not b:
10
Z, W
- DDL of Poutre: DX = DZ = 0
D
3.2
Characteristics of the grid
A number of nodes: 57
A number of meshs and types: 28 SEG3
3.3 Functionalities
tested
Commands Key word
factor
Key word
AFFE_MODELE
AFFE
MODELISATION=' TUYAU'
AFFE_CARA_ELEM
POUTRE:(SECTION:“CERCLE”)
ORIENTATION:(CARA:“GENE_TUYAU”
VALE: (X Y Z)
MACRO_MATR_ASSE
MATR_ASSE
OPTION=' RIGI_MECA'
OPTION=' MASS_MECA'
MODE_ITER_SIMULT
CALC_FREQ
OPTION=' PLUS_PETITE'
4
Results of modeling A
4.1 Values
tested
Identification Moments
Reference Aster %
difference
Frequency (Hz) Transverse 1
17.9
17.84
0.308
Frequency (Hz) in plan 1
24.8
24.82
0.083
Frequency (Hz) Transverse 2
25.3
25.82
2.039
Frequency (Hz) in plan 2
27.0
27.65
2.406
4.2 Parameters
of execution
Version: NEW 5.04.20
Machine: SGI-Origin2000 R12000
Obstruction memory: 16 megabytes
Time CPU To use: 13.36 seconds
Handbook of Validation
V2.02 booklet: Linear dynamics of the beams
HT-66/02/001/A
Code_Aster ®
Version
5.0
Titrate:
SDLL14 - Modes of vibration of a thin elbow of piping
Date:
19/08/02
Author (S):
P. MASSIN, F. LEBOUVIER Key
:
V2.02.014-A Page:
5/8
5 Modeling
B
5.1
Characteristics of modeling
y, v
Modeling TUYAU_6M (SEG3)
Boundary conditions:
C
10
With
Points C and D:
8
- DDL of Poutre: DX = DY = DZ = DRX = DRY = DRZ = 0
- DDL of Coque: UIm = VIm = Wim = 0 (m=2,6)
X, U UOm = VOm = WOm = 0 (m=2,6)
WI1 = WO1 = WO = 0
B
Not a:
- DDL of Poutre: DY = DZ = 0
Not b:
10
Z, W
- DDL of Poutre: DX = DZ = 0
D
5.2
Characteristics of the grid
A number of nodes: 57
A number of meshs and types: 28 SEG3
5.3 Functionalities
tested
Commands Key word
factor
Key word
AFFE_MODELE
AFFE
MODELISATION=' TUYAU_6M'
AFFE_CARA_ELEM
POUTRE:(SECTION:“CERCLE”)
ORIENTATION:(CARA:“GENE_TUYAU”
VALE: (X Y Z)
MACRO_MATR_ASSE
MATR_ASSE
OPTION=' RIGI_MECA'
OPTION=' MASS_MECA'
MODE_ITER_SIMULT
CALC_FREQ
OPTION=' PLUS_PETITE'
6
Results of modeling B
6.1 Values
tested
Identification Moments
Reference Aster %
difference
Frequency (Hz) Transverse 1
17.9
17.74
0.914
Frequency (Hz) in plan 1
24.8
24.67
0.525
Frequency (Hz) Transverse 2
25.3
25.66
1.439
Frequency (Hz) in plan 2
27.0
27.49
1.800
6.2 Parameters
of execution
Version: NEW 5.04.20
Machine: SGI-Origin2000 R12000
Obstruction memory: 16 megabytes
Time CPU To use: 42.82 seconds
Handbook of Validation
V2.02 booklet: Linear dynamics of the beams
HT-66/02/001/A
Code_Aster ®
Version
5.0
Titrate:
SDLL14 - Modes of vibration of a thin elbow of piping
Date:
19/08/02
Author (S):
P. MASSIN, F. LEBOUVIER Key
:
V2.02.014-A Page:
6/8
7 Modeling
C
7.1
Characteristics of modeling
Modeling PIPE (SEG4)
y, v
Boundary conditions:
C
10
With
Points C and D:
8
- DDL of Poutre: DX = DY = DZ = DRX = DRY = DRZ = 0
- DDL of Coque: UIm = VIm = Wim = 0 (m=2,3)
X, U UOm = VOm = WOm = 0 (m=2,3)
WI1 = WO1 = WO = 0
B
Not a:
- DDL of Poutre: DY = DZ = 0
Not b:
10
Z, W
- DDL of Poutre: DX = DZ = 0
D
7.2
Characteristics of the grid
A number of nodes: 85
A number of meshs and types: 28 SEG4
7.3 Functionalities
tested
Commands Key word
factor
Key word
CREA_MAILLAGE
MODI_MAILLE
OPTION:“SEG3_4”
AFFE_MODELE
AFFE
MODELISATION=' TUYAU'
AFFE_CARA_ELEM
POUTRE:(SECTION:“CERCLE”)
ORIENTATION:(CARA:“GENE_TUYAU”
VALE: (X Y Z)
MACRO_MATR_ASSE
MATR_ASSE
OPTION=' RIGI_MECA'
OPTION=' MASS_MECA'
MODE_ITER_SIMULT
CALC_FREQ
OPTION=' PLUS_PETITE'
8
Results of modeling C
8.1 Values
tested
Identification Moments
Reference Aster %
difference
Frequency (Hz) Transverse 1
17.9
17.66
- 1.332
Frequency (Hz) in plan 1
24.8
24.45
- 1.400
Frequency (Hz) Transverse 2
25.3
24.97
- 1.322
Frequency (Hz) in plan 2
27.0
26.75
- 0.914
8.2 Remarks
The grid in SEG4 is obtained starting from a grid SEG3 with command CREA_MAILLAGE,
MODI_MAILLE with option “SEG3_4”. It is important that the node medium of the SEG3 is well with
medium, Code_Aster checks this condition with a tolerance.
8.3 Parameters
of execution
Version: NEW 5.04.20
Machine: SGI-Origin2000 R12000
Obstruction memory: 16 megabytes
Time CPU To use: 28.44 seconds
Handbook of Validation
V2.02 booklet: Linear dynamics of the beams
HT-66/02/001/A
Code_Aster ®
Version
5.0
Titrate:
SDLL14 - Modes of vibration of a thin elbow of piping
Date:
19/08/02
Author (S):
P. MASSIN, F. LEBOUVIER Key
:
V2.02.014-A Page:
7/8
9
Summary of the results
The results obtained with modeling TUYAU (SEG3 and SEG4) and TUYAU_6M (SEG4) are
satisfactory. The maximum change observed is lower than 2.1%.
Handbook of Validation
V2.02 booklet: Linear dynamics of the beams
HT-66/02/001/A
Code_Aster ®
Version
5.0
Titrate:
SDLL14 - Modes of vibration of a thin elbow of piping
Date:
19/08/02
Author (S):
P. MASSIN, F. LEBOUVIER Key
:
V2.02.014-A Page:
8/8
Intentionally white left page.
Handbook of Validation
V2.02 booklet: Linear dynamics of the beams
HT-66/02/001/A
Outline document