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FORMA11 - Practical works of the formation

“Analyzes dynamic”: modal analysis

Summary:

These tests correspond to practical works of the dynamic formation of Code_Aster. They are four geometries,
very made up of a linear elastic material for which one carries out a modal analysis: research of the Eigen
frequencies and the associated modes.

Modelings used are the following ones:

• Modeling a: Research of the multiple modes of a beam (POU_D_E)

• Modeling b: Research of the rigid modes of body of a sphere (3D)
• Modeling C: Use of the operator CALC_MODES for the analysis of a tower
cooling (DKT),

The statements of practical works of the dynamic formation are presented in this document:

• TP1: Research of the multiple modes of a beam,

• TP2: Research of the rigid modes of body,
• TP3: Use of the macro-order CALC_MODES.

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1 Modeling A
1.1 Description of the problem
1.1.1 Objective
The objective of this modeling is to determine the first 11 Eigen frequencies of the fixed beam, in the
presence of multiple modes, by using the four following methods:

• Method of SORENSEN,
• Method of LANCZOS,
• Method of BATHE and WILSON
• Method of opposite iteration

1.1.2 Geometry
x

L = 0,5 m R(x)
X j
A B z

i
a = 0,05 m 
y
a

1.1.3 Properties of materials

The material is elastic isotropic linear:

• the Young modulus E=210 000. 106 N /m 2 ,

• the Poisson's ratio  =0.3 ,
• density =7800 Kg / m3

1.1.4 Boundary conditions and loading

The beam is embedded at the point A.

1.2 Characteristics of modeling

1.2.1 Grid

The telegraphic grid could be built interactivement using Salomé. It is enough to define the points A ,
B then line AB . The size of the elements is identical. In the module of grid of Salomé, one will be
able to declare, while basing oneself on the geometry, like groups node the point A , then like meshs
the line groups AB . Then the grid will be saved with the format MED.

elements of right beam of Euler (POU_D_E) will be retained for modeling.

The grid consists of 10 SEG2 and 11 nodes.

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1.2.2 Command file Aster

Principal stages of calculation with Aster will be:

Reading of the grid to the format MED (LIRE_MAILLAGE (‘FORMAT=’ MED')).

Definition of the finite elements used (AFFE_MODELE). One will assign to the group of meshs composing
the beam modeling POU_D_E.
Definition and assignment of material (DEFI_MATERIAU and AFFE_MATERIAU). The mechanical
characteristics are identical on all the structure.
Assignment of the characteristics of the elements beams (AFFE_CARA_ELEM). The section of all the
elements of the beam is the same one.
Assignment of the boundary conditions (AFFE_CHAR_MECA).
Calculation of the elementary matrices rigidities (CALC_MATR_ELEM (OPTION=' RIGI_MECA')).
Calculation of the elementary matrices of masses (CALC_MATR_ELEM (OPTION=' MASS_MECA')).
Classification of the unknown factors of the system of linear equations (NUME_DDL)
Assembly of the elementary matrices of mass and rigidity (ASSE_MATRICE).

Notice : to go more quickly one can use the macro one ASSEMBLY to build the matrices!

N°1 question:

• To calculate the 11 smaller Eigen frequencies and the first associated modes (CALC_MODES
[U4.52.02]).
• To print the clean modes (IMPR_RESU) with the format MED for a visualization in Salomé.

N°2 question:

• To calculate the Eigen frequencies and the first associated modes present in the waveband
0 Hz and 6000 Hz , with the four methods SORENSEN, LANCZOS, BATHE, QZ
(CALC_MODES [U4.52.02], keyword factor SOLVEUR_MODAL=_F (METHODE=…)) then by
iterations opposite (simple keyword OPTION=' AJUSTE').
• To print the clean modes (IMPR_RESU) with the format MED for a visualization in Salomé.

1.3 Assistance for Postprocessing under Salomé

The various stages of visualization of the modal deformations with Salomé are the following ones:

To launch Salomé under linux

To click on Open file/ and to select the base Salomé (hdf) containing the geometry and the grid.
To launch the module of postprocessing Post-pro
To click on File/Import/MED slips by and to select file MED containing the modes suitable to
visualize
To deploy completely inObject Browser the tree structure of the line Post-pro in order to see in
details all the fields of displacements.
To click on one of the fields and with the right button mouse to click it on Deformed Shape. (the modal
deformation is displayed).
To deploy the line containing the visualized field, then to click on Def. Shape and then to click on the
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right button of the mouse and to select sweep to animate the deformation.

1.4 Remarks
The good practice consists in using the option ‘BAND’ rather than ‘PLUS_PETITE’ or ‘CENTER’.

The number of frequencies is automatically given by the test of Sturm and thus all the multiplicities
are taken into account.

Method of ‘SORENSEN‘is fastest (in spite of its iterative character which allows D’ to obtain a better
precision)

One projects on a space moreover small (compared to ‘TRI_DIAG’ and with ‘JACOBI‘) and one does
not make qu’ a factorization (compared to the algorithms of the powers opposite implemented when
one uses ‘SEPARATE’ OPTION=' AJUSTE'//‘NEAR’).

In the presence of multiple modes, least modification of the parameter setting of the modal method (or
associated tripaille NUME_DDL…) product of the different clean vectors.

But they always generate same clean space,

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To be convinced some one can visualize the modal deformations or summon the effective modal
masses.

TRI_DIAG SORENSEN
MASS_EFFE_DY MASS_EFFE_DZ MASS_EFFE_DY MASS_EFFE_DZ
Mode 1 3.16920 2.80830 1.13915 4.83834
Mode 2 2.80672 3.17077 4.83834 1.13915
TOTAL 5.97592 5.97907 5.97749 5.97749

1.5 Sizes tested and results

Results got with the method of SORENSEN are presented in the table, and on the figures below

Frequency in Hz
Mode
(Method SORENSEN)
1 1.67638E+02
2 1.67638E+02
3 1.05060E+03
4 1.05060E+03
5 1.48054E+03
6 2.59704E+03
7 2.94237E+03
8 2.94237E+03
9 4.47822E+03
10 5.76991E+03
11 5.76991E+03

Modal deformation ( 167.638 Hz ) Modal deformation ( 167.638 Hz )

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Modal deformation ( 1050.60 Hz ) (Modal Deformation 1050.60 Hz )

Modal deformation ( 1480.54 Hz )

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2 Modeling B
2.1 Description of the problem
2.1.1 Objective
The objective of this modeling is to determine for a structure of type sphere into free free, (presence of
multiple modes of rigid body):
• Eigen frequencies located in a waveband with the method of SORENSEN,
• Eigen frequencies located in a waveband with the method of LANCZOS with or without rigid
mode (OPTION=MODE_RIGIDE),
• 16 smaller Eigen frequencies with the method of SORENSEN

2.1.2 Geometry
Y
R = 0.01

Z X

2.1.3 Properties of materials

The material is elastic isotropic linear:

• the Young modulus E=108 N /m2 ,

• the Poisson's ratio  =0.3 ,
• density =104 kg /m 3

2.1.4 Boundary conditions and loading

None

2.2 Characteristics of modeling

2.2.1 Characteristics of the grid

The grid comprises 160 meshs HEXA20, and 813 nodes.

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voluminal elements (3D) will be retained for modeling.

2.2.2 Orders Aster

Principal stages of calculation with Aster will be:

Reading of the grid (LIRE_MAILLAGE).

Definition of the finite elements used (AFFE_MODELE).
Definition and assignment of material (DEFI_MATERIAU and AFFE_MATERIAU).
The mechanical characteristics are identical on all the structure.
Calculation of the elementary matrices rigidities (CALC_MATR_ELEM (OPTION=' RIGI_MECA')).
Calculation of the elementary matrices of masses (CALC_MATR_ELEM (OPTION=' MASS_MECA')
Classification of the unknown factors of the system of linear equations (NUME_DDL)
Assembly of the elementary matrices of mass and rigidity (ASSE_MATRICE).

Notice : to go more quickly one can use the macro one ASSEMBLY to build the matrices!

N°1 question:

• To calculate with the method of SORENSEN (under the keyword factor SOLVEUR_MODAL),
frequencies located in the waveband 0. Hz , 2880 Hz  as well as the associated modes
(CALC_MODES).
• If calculation fails one will be able to extend the waveband on a slightly negative margin.

• To print the clean modes (IMPR_RESU) with the format MED for a visualization in Salomé.

N°2 question:

• To calculate with the method of LANCZOS with or without option MODE_RIGIDE frequencies
located in the waveband 0. Hz , 2880 Hz  as well as the associated modes
(CALC_MODES).

N°3 question:

• To calculate with the method of SORENSEN 16 smaller frequencies as well as the associated
modes (CALC_MODES). One will be able to use the parameter PREC_SHIFT (under the
keyword factor CALC_FREQ) to circumvent the problem of the worthless frequencies.

2.3 Assistance for postprocessing under Salomé

The various stages of visualization of the modal deformations with Salomé are the following ones:

To launch Salomé under linux

To launch the module of grid Mesh/New
To click on File/Import/MED slips by and to select the file med containing the grid
To launch the module of postprocessing Post-pro
To click on File/Import/MED slips by and to select the file med containing the modes suitable to
visualize
To deploy completely inObject Browser the tree structure of the line Post-pro in order to see in

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details all the fields of displacements.

To click on one of the fields and with the right button mouse to click it on Deformed Shape. ( modal
deformation is displayed).
To deploy the line containing the visualized field, then to click on Def. Shape and then to click on the
right button of the mouse and to select sweep to animate the deformation.

2.4 Remarks
The factorization of the shiftées matrices  K − −1= LDL T control by the parameter setting:
NMAX_ITER_SHIFT, SOLVEUR/NPREC[U4.50.01] and PREC_SHIFT, can be carried out only if those
are regular.

That often poses problem when magnitude of the terms of K is large in front of that of the terms of
M and that  is one good approximate eigenvalue. The policy of the operator is to emit one ALARM
when it is about a test of Sturm and one ERREUR_FATALE when it is the matrix of work of the
operator. In the event of problem, one can always change option or of shift.

The detection of modes of rigid body is often problematic for the classical modal solveurs! The good
practice consists in using the method of SORENSEN by using a waveband whose lower limit is
worthless, even slightly negative. The solvor normally the capture without any problem (they are just

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a little particular multiple modes). Failing this, with TRI_DIAG, the option MODE_RIGIDE is
recommended.

2.5 Sizes tested and results

Results got with the method of SORENSEN and method of LANCZOS with and without the option
OPTION= MODE_RIGIDE are presented in the table below.

CALC_MODES

Method Sorensen Method of Lanczos Method of Lanczos

(METHOD = ' SORENSEN') (with the option MODE_RIGIDE) (without the option MODE_RIGIDE)
Mode Frequency Mode Frequency Mode Frequency
5 -3.88562E-05 6 0.00000E+00 4 1.22874E-04
4 -3.88562E-05 5 0.00000E+00 5 2.70602E-04
3 -6.73009E-05 4 0.00000E+00 3 -5.03634E-04
2 1.09902E-04 3 0.00000E+00 2 -5.69081E-04
6 1.25908E-04 2 0.00000E+00 6 4.46762E-03
1 1.73770E-04 1 0.00000E+00 7 2.46964E+03
7 2.46964E+03 7 2.46964E+03 8 2.46964E+03
8 2.46964E+03 8 2.46964E+03 9 2.47084E+03
9 2.47084E+03 9 2.47084E+03 10 2.47084E+03
10 2.47084E+03 10 2.47084E+03 11 2.47084E+03
11 2.47084E+03 11 2.47084E+03 12 2.61345E+03
12 2.61345E+03 12 2.61345E+03 13 2.61345E+03
13 2.61345E+03 13 2.61345E+03 14 2.61345E+03
14 2.61345E+03 14 2.61345E+03 15 2.61364E+03
15 2.61364E+03 15 2.61364E+03 16 2.61364E+03
16 2.61364E+03 16 2.61364E+03 17 3.48770E+03

Modal deformation ( 2469.64 Hz ) Modal deformation ( 2469.64 Hz )

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Modal deformation ( 2470.84 Hz )

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3 Modeling C
3.1 Description of the problem
The objective of this modeling is the use of the macro-order CALC_MODES [U4.52.02] with the option
‘BAND’ cut out in several sub-bands. This order allows to launch a succession of calculations of real
clean modes.

The following actions are carried out:

• Obtaining the modes by simultaneous iterations, in specified wavebands,

• Application of a standard, filtering according to a criterion of value of modal parameter higher
than a certain threshold and finally concatenation of the structures of data calculated in only
one.

The modes are calculated by the order CALC_MODES [U4.52.02] with the option ‘BAND’ and
normalized by the order NORM_MODE [U4.52.11]. The calculated modes are filtered and concaténés by
means of the order EXTR_MODE [U4.52.12].

3.1.1 Objective
The objective of this modeling is:

• “To weigh” the model finite elements and to evaluate the number of modes,
• To use the macro-order CALC_MODES with the option ‘BAND’ cut out in several sub-bands to
calculate the Eigen frequencies.

3.1.2 Geometry
One will be able to recover the grid in the repertoire of the cases tests.
The thickness of the hull is of e=0,3045 m

3.1.3 Properties Materials

The material is elastic isotropic linear:

• the Young modulus E =2,76. 10 10 N /m2 ,

• the Poisson's ratio ν=0,166 ,

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• density =2244 Kg /m3

3.1.4 Boundary conditions and loading

The tower is embedded at its base.

3.2 Characteristics of modeling

3.2.1 Characteristics of the grid
The grid is composed of 1860 QUAD4 and 1860 nodes

The tower is modelled with elements of hull DKT

3.2.2 Orders Aster

Principal stages of calculation with Aster will be:

Reading of the grid (LIRE_MAILLAGE).

Definition of the finite elements used (AFFE_MODELE). Modeling will be affected DKT with the whole of
the elements of the tower.
Definition and assignment of material (DEFI_MATERIAU and AFFE_MATERIAU).
The mechanical characteristics are identical on all the structure.
Assignment of the characteristics of the elements of hull (AFFE_CARA_ELEM).
The thickness of all the elements is the same one.
Assignment of the boundary conditions (AFFE_CHAR_MECA).
Calculation of the elementary matrices rigidities (CALC_MATR_ELEM (OPTION=' RIGI_MECA‘)).
Calculation of the elementary matrices of masses (CALC_MATR_ELEM (OPTION=' MASS_MECA').
Classification of the unknown factors of a system of linear equations (NUME_DDL)
Assembly of the elementary matrices of mass and rigidity (ASSE_MATRICE).

Notice : to go more quickly one can use the macro one ASSEMBLY to build the matrices!

N°1 question:

• To weigh the model (POST_ELEM) and to evaluate the number of mode whose frequency is
lower than 4 Hz (INFO_MODE).

N°2 question:

• To calculate the Eigen frequencies and the first associated modes present in the waveband
0. Hz with 4 Hz (CALC_MODES)
• To standardize with the infinite standard, on all the components of the physical nodes while
requiring the calculation of the unit effective masses (NORM_MODE, EXTR_MODE).
• To print the clean modes (IMPR_RESU) with the format MED for a visualization in Salomé.

N°3 question:

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• To calculate the Eigen frequencies by gathering the three operations CALC_MODES,

NORM_MODE and EXTR_MODE in one (while crossing in 2 intervals) with CALC_MODES and the
option ‘BAND’ cut out in several sub-bands.

N°4 question:

• To calculate the Eigen frequencies by gathering the three operations CALC_MODES,

NORM_MODE and EXTR_MODE in one (while crossing in 4 intervals) with CALC_MODES and the
option ‘BAND’ cut out in several sub-bands.

N°5 question:

• One carries out the same thing as that requested in question 4 but with the method of
LANCZOS.

3.3 Assistance for postprocessing under Salomé

The various stages of visualization of the modal deformations with Salomé are the following ones:

To launch Salomé under linux

To launch the module of grid Mesh/New
To click on File/Import/MED slips by and to select the file med containing the grid
To launch the module of postprocessing Post-pro
To click on File/Import/MED slips by and to select the file med containing the modes suitable to
visualize
To deploy completely inObject Browser the tree structure of the line Post-pro in order to see in
details all the fields of displacements.
To click on one of the fields and with the right button mouse to click it on Deformed Shape. (the modal
deformation is displayed).
To deploy the line containing the visualized field, then to click on Def. Shape and then to click on the
right button of the mouse and to select sweep to animate the deformation.

Warning : The translation process used on this website is a "Machine Translation". It may be imprecise and inaccurate in whole or in part and is
provided as a convenience.
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3.4 Remarks
Good practices: it is necessary as a preliminary:

To weigh its model with POST_ELEM,

To evaluate the spectrum with
INFO_MODE.

The order CALC_MODES, with the option ‘BAND’ cut out in several sub-bands, is more economic to
search a large spectrum.

On condition that not too much picnicking it,

It is necessary to check the agreement of the identified ends of spectrum,
Time-saver can be very important: 500% ,
One can easily and to associate other operations automatically there: standardisation, filtering,
concatenation of structures of data.

3.5 Sizes tested and results

Mode Frequency in Hz
1 2.80065 Hz
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2 2.80065 Hz

Modal deformation ( 2.80065 Hz ) Modal deformation ( 2.80065 Hz )

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