SDLL14 - Modes of vibration dun thin elbow of piping

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

Manual of Validation

V2.02 booklet: Linear dynamics of the beams

HT-66/02/001/A

Organization (S):

EDF/AMA, DeltaCAD

Manual 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 PIPE (SEG3 and SEG4) and TUYAU_6M (SEG4).

The results obtained are compared with an analytical reference solution.

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

Manual of Validation

V2.02 booklet: Linear dynamics of the beams

HT-66/02/001/A

Problem of reference

1.1 Geometry

With

y, v

X, U

Z, W

Hollow circular cross-section

L =

2.0

= 1. m

= 0.020 m

0.016

With

= 1.131 X 10

- 4

m ²

= I

= 4.637 X 10

- 9

= 9.274 X 10

- 9

= 90°

1.2

Properties of material

The properties of material constituting the plate are:

= 2.1 10

Young modulus

= 0.3

Poisson's ratio

= 7800. Kg/m

Mass

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

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

Manual of Validation

V2.02 booklet: Linear dynamics of the beams

HT-66/02/001/A

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:

bending in the plan:

I.E.(internal excitation)

With

i=1,2;

transverse bending:

With

i=1,2;

Values

and

are drawn from an abacus.

This formulation is usable only for piping very slim:

Twinge of the right parts higher than

Thin elbow such as

With

100

with

, angle in the center in radian. It is not

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.

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

Manual of Validation

V2.02 booklet: Linear dynamics of the beams

HT-66/02/001/A

3 Modeling

With

3.1

Characteristics of modeling

With

Modeling PIPE (SEG3)

y, v

X, U

Z, W

Boundary conditions:

Points C and D:
- DDL of Beam: DX = DY = DZ = DRX = DRY = DRZ

= 0

- DDL of Hull: UIm = VIm = Wim = 0 (m=2,3)
UOm = VOm = WOm = 0 (m=2,3)
WI1 = WO1 = WO = 0
Not a:
- DDL of Beam: DY = DZ = 0
Not b:
- DDL of Beam: DX = DZ = 0

3.2

Characteristics of the mesh

A number of nodes: 57
A number of meshs and types: 28 SEG3

3.3 Functionalities

tested

Controls Key word

factor

Key word

AFFE_MODELE

AFFE

MODELISATION=' TUYAU'

AFFE_CARA_ELEM

BEAM:(SECTION:“CIRCLE”)
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'

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

Overall dimension memory: 16 megabytes

Time CPU To use: 13.36 seconds

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

Manual of Validation

V2.02 booklet: Linear dynamics of the beams

HT-66/02/001/A

5 Modeling

5.1

Characteristics of modeling

With

Modeling TUYAU_6M (SEG3)

y, v

X, U

Z, W

Boundary conditions:

Points C and D:
- DDL of Beam: DX = DY = DZ = DRX = DRY = DRZ

= 0

- DDL of Hull: UIm = VIm = Wim = 0 (m=2,6)
UOm = VOm = WOm = 0 (m=2,6)
WI1 = WO1 = WO = 0
Not a:
- DDL of Beam: DY = DZ = 0
Not b:
- DDL of Beam: DX = DZ = 0

5.2

Characteristics of the mesh

A number of nodes: 57
A number of meshs and types: 28 SEG3

5.3 Functionalities

tested

Controls Key word

factor

Key word

AFFE_MODELE

AFFE

MODELISATION=' TUYAU_6M'

AFFE_CARA_ELEM

BEAM:(SECTION:“CIRCLE”)
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'

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

Overall dimension memory: 16 megabytes

Time CPU To use: 42.82 seconds

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

Manual of Validation

V2.02 booklet: Linear dynamics of the beams

HT-66/02/001/A

7 Modeling

7.1

Characteristics of modeling

With

Modeling PIPE (SEG4)

y, v

X, U

Z, W

Boundary conditions:

Points C and D:
- DDL of Beam: DX = DY = DZ = DRX = DRY = DRZ

= 0

- DDL of Hull: UIm = VIm = Wim = 0 (m=2,3)
UOm = VOm = WOm = 0 (m=2,3)
WI1 = WO1 = WO = 0
Not a:
- DDL of Beam: DY = DZ = 0
Not b:
- DDL of Beam: DX = DZ = 0

7.2

Characteristics of the mesh

A number of nodes: 85
A number of meshs and types: 28 SEG4

7.3 Functionalities

tested

Controls Key word

factor

Key word

CREA_MAILLAGE

MODI_MAILLE

OPTION:“SEG3_4”

AFFE_MODELE

AFFE

MODELISATION=' TUYAU'

AFFE_CARA_ELEM

BEAM:(SECTION:“CIRCLE”)
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'

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 mesh in SEG4 is obtained starting from a mesh SEG3 with the control

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

Overall dimension memory: 16 megabytes

Time CPU To use: 28.44 seconds

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

Manual of Validation

V2.02 booklet: Linear dynamics of the beams

HT-66/02/001/A

Summary of the results

The results obtained with modeling PIPE (SEG3 and SEG4) and TUYAU_6M (SEG4) are
satisfactory. The maximum change observed is lower than 2.1%.