Code_Aster ®
Version
7.4
Titrate:
Operator CALC_AMOR_MODAL


Date:
08/02/05
Author (S):
G. DEVESA, Y. PONS Key
:
U4.52.13-F Page
: 1/6

Organization (S): EDF-R & D/AMA

Handbook of Utilization
U4.5- booklet: Methods of resolution
Document: U4.52.13

Operator CALC_AMOR_MODAL

1 Goal

To create a list of modal depreciation calculated according to the rule of the RCC-G. Calculation is carried out in
postprocessing of the modal calculation of a structure of the building type whose foundation raft rests on a ground
modelled by springs.

The principle of calculation is based on weighting by the rates of potential energy (compared to
the total energy) of the reduced depreciation affected by groups of meshs constitutive of the structure
(in fact of the parameters of input of the table of potential energy created by POST_ELEM) and of
depreciation radiated in the ground, by, function degree of freedom of the frequency [bib1] [bib2].

The list created is usable thereafter in command DYNA_TRAN_MODAL [U4.53.21] behind
key word LIST_AMOR.

Product a concept of the listr8 type.
Handbook of Utilization
U4.5- booklet: Methods of resolution
HT-66/05/004/A

Code_Aster ®
Version
7.4
Titrate:
Operator CALC_AMOR_MODAL


Date:
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Author (S):
G. DEVESA, Y. PONS Key
:
U4.52.13-F Page
: 2/6

2 Syntax


listr8 [listr8] = CALC_AMOR_MODAL (

ENER_SOL =_F (MODE_MECA
=
MOD, [mode_meca]






METHOD =/“DEPL”, [DEFECT]
/
“RIGI_PARASOL”,






KX = kx,






[R]






KY = ky,






[R]






KZ = kz,






[R]







KRX = krx
,




[R]







KRY = kry
,




[R]







KRZ = krz
,




[R]






/GROUP_NO_RADIER
=
l_grno,
[l_group_no]







/
GROUP_MA_RADIER
=
l_grma,
[l_group_ma]






/FONC_GROUP =
l_fonc,
[l_fonction]







/
COEF_GROUP =
l_coef,
[l_R]






/GROUP_NO_CENTER
=
grno, [group_noeud]







/
NOEUD_CENTER
=
node,
[node]







/
COOR_CENTER
= (X, y, Z),
[l_R]





)
AMOR_INTERN
=_F
(







ENER_POT
=
epot, [tabl_ener_pot]







GROUP_MA
=
l_grma,
[l_group_ma]







AMOR_REDUIT
=
l_amor,
[l_R]






)
AMOR_SOL =_F
(







AMOR_REDUIT =
/
0.,
[DEFAUT]
/
amor, [R]






FONC_AMOR_GEO
=
l_f_amor,
[l_fonction]







HOMOGENE =
/
“OUI”,
[DEFAUT]
/
“NON”,







SEUIL =
/
0.3,
[DEFAUT]
/
threshold,
[R]





)











)
Handbook of Utilization
U4.5- booklet: Methods of resolution
HT-66/05/004/A

Code_Aster ®
Version
7.4
Titrate:
Operator CALC_AMOR_MODAL


Date:
08/02/05
Author (S):
G. DEVESA, Y. PONS Key
:
U4.52.13-F Page
: 3/6

3 Operands

3.1 Word
key
ENER_SOL

This key word factor used only once is used to introduce the data necessary to calculation of
potential energy in the ground per degree of freedom for all the frequencies of a concept of the type
mode_meca.

3.1.1 Operand
METHODE

This operand makes it possible to define the method of calculation of energy in the ground by frequency.

With value “DEPL”, one calculates energy starting from the displacements realized on the nodes of
1
to erase for each mode: E =
K U 2 (Fr
I
I
), where K represent 6 components KX, KY,
I
2
I
i=1,6
KZ, KRX, KRY and KRZ of the total rigidity within the competences of ground (cf [§3.1.3]).

With value “RIGI_PARASOL”, one calculates energy starting from the efforts realized on the nodes of
1
F 2
to erase for each mode: E
I
=

(Fr).
2
K
I
i=1,6
I

The efforts with the nodes with this method are given starting from the values of rigidity distributed
with the nodes under the foundation raft as by option RIGI_PARASOL of AFFE_CARA_ELEM [U4.42.01].

3.1.2 Operand
MODE_MECA

Allows to introduce the concept of the mode_meca type containing the frequencies of calculation of energy
potential.

3.1.3 Operands
KX/KY/KZ/KRX/KRY/KRZ

The values of the components of the total rigidity within the competences of ground represent.

Intervene in the calculation of the terms K .U2, I
I
I
= 1, NCmp.

NCmp is the component count (3 or 6) determined by the presence or the absence of the operands
KRX, KRY, KRZ used (if they are it) obligatorily together. NCmp and the number of ddls increased by
the nodes of the foundation raft can be different.

3.1.4 Operand
GROUP_NO_RADIER

This operand is related to value “DEPL” of operand METHODE.

List groups of nodes constituting the foundation raft of the structure posed on the ground. One calculates thereafter
the displacement realized in these nodes U of Ui components for each mode calculated of
frequency Fr in order to be able to determine energy in the ground by ddl and frequency:
1
2
K .U (Fr
I
I
).
2
Handbook of Utilization
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Code_Aster ®
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Titrate:
Operator CALC_AMOR_MODAL


Date:
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:
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3.1.5 Operand
GROUP_MA_RADIER

This operand is related to value “RIGI_PARASOL” of operand METHODE.

List groups of meshs constituting the foundation raft of the structure posed on the ground. Allows to calculate
effort realized with the nodes of these meshs F of Fi components for each mode calculated of
1
2
F
frequency Fr in order to determine energy in the ground by ddl and frequency:
I (Fr).
2 ki

3.1.6 Operand
FONC_GROUP/COEF_GROUP/GROUP_NO_CENTER/NOEUD_CENTER/
COOR_CENTER

These operands are also related to value “RIGI_PARASOL” of operand METHODE.

These are the same ones as in option RIGI_PARASOL of AFFE_CARA_ELEM [U4.42.01]. They allow
also to obtain the values of rigidity distributed with the nodes under the foundation raft being used to determine them
nodal efforts by mode then their average F of Fi component.

An operand chosen among FONC_GROUP/COEF_GROUP makes it possible to determine weightings,
real functions of the X-coordinate or, each group of meshs constitutive of the foundation raft.
formulas remain with the choice of the user. By defect, one considers that the function of distribution is
constant and unit, i.e. that each surface is affected same weight [bib2].

One thus needs as many terms in the corresponding list than in the list of the groups of meshs
data by operand GROUP_MA_RADIER.

An operand chosen among GROUP_NO_CENTER/NOEUD_CENTER/COOR_CENTER makes it possible to provide
that is to say the central node of the foundation raft by a group of nodes of only one name or by a single name of node,
that is to say directly its co-ordinates.

3.2 Word
key
AMOR_INTERN

Used only once.

The contribution to the reduced damping of each mode is established starting from the distribution of
potential energy in the structure for the mode considered. This distribution is obtained using
command POST_ELEM [U4.81.22] starting from the concept of the mode_meca type (cf [§3.1.1]) which produces
a table.

The parameters of input of this table are names of groups of meshs, defined by the user
according to the distributions of material damping in the structure.

3.2.1 Operand
ENER_POT

Name of the table of potential energy produced by command POST_ELEM [U4.81.22].

3.2.2 Operand
GROUP_MA

The list of names of groups of meshs from which one will point in the table defined by
ENER_POT (cf [§3.2.1]).

3.2.3 Operand
AMOR_REDUIT

The list of the actual values of material damping corresponding, term for term, with the list of
names of groups of meshs defined by GROUP_MA (cf [§3.2.2]).
Handbook of Utilization
U4.5- booklet: Methods of resolution
HT-66/05/004/A

Code_Aster ®
Version
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Titrate:
Operator CALC_AMOR_MODAL


Date:
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Author (S):
G. DEVESA, Y. PONS Key
:
U4.52.13-F Page
: 5/6

3.3 Word
key
AMOR_SOL

Used only once.

It makes it possible to determine the contribution of geometrical damping due to the reflection of the waves
rubber bands. These directional values of damping are obtained while interpolating for each
(
Im K ())
calculated Eigen frequency geometrical functions of damping
(cf § [3.3.1]) where
2 Re (K ())
K ()
is the complex impedance of the ground determined using one of software MISS 3D, CLASSI or
PARASOL:

(
Im K ()
I)
amor () =
I
, I


2 Re (K ()
I)

3.3.1 Operand
FONC_AMOR_GEO

Defines the list of functions of the frequency of geometrical depreciation, one by ddl (3 or 6).

3.3.2 Operand
AMOR_REDUIT

Correction in the calculation of geometrical damping due to the reduced material damping of the ground.

Note:

The value of reduced damping is necessary only if the impedance of the ground is
produced by PARASOL. If the impedance of the ground is produced by MISS 3D, this value is not
necessary that if the ground is homogeneous (see operand HOMOGENE [§3.3.3]).

3.3.3 Operand
HOMOGENE

If the ground is homogeneous (“OUI”), one balances the calculation of damping in the ground (material more
geometrical) by factor 0.5. Then if the impedance of the ground is produced by MISS 3D, one
must introduce for operand AMOR_REDUIT (cf [§3.3.2]) the half-value of material damping
tiny room of the ground.

3.3.4 Operand
SEUIL

Value defined in the RCC-G [bib1] (0.3 per defect) for the threshold beyond which one truncates
possibly modal damping. This threshold operates after the possible preceding corrections.

4 Bibliography

[1]
RCC-G: Rules of design and construction of nuclear small islands REP. EDF - Direction
of Equipement Edition Juillet 1988
[2]
Fe. Seismic WAECKEL Réponse by transitory analysis [R4.05.01]
Handbook of Utilization
U4.5- booklet: Methods of resolution
HT-66/05/004/A

Code_Aster ®
Version
7.4
Titrate:
Operator CALC_AMOR_MODAL


Date:
08/02/05
Author (S):
G. DEVESA, Y. PONS Key
:
U4.52.13-F Page
: 6/6

5 Example
of use

The use of CALC_AMOR_MODAL requires the calculation of the clean modes of the structure on
springs of ground in the form of a concept of the mode_meca type and a concept of the type
tabl_ener_pot of these modes calculated by means of command POST_ELEM [U4.61.04].

The following example is extracted from test SDLL109B.


# CALCULATION OF THE MODAL QUANTITIES -----------------------------------------

MODE0=MODE_ITER_SIMULT (MATR_A=RIGIDITE,
MATR_B=MASSE,
CALC_FREQ=_F (OPTION = “PLUS_PETITE”,
DIM_SOUS_ESPACE = 125,
NMAX_FREQ = 33))

MODE0=NORM_MODE (reuse=MODE0, MODE=MODE0, NORME=' TRAN_ROTA',
MASS_INER=MASSESTR)

EPOT=POST_ELEM (MODELE=STICKMOD,
RESULTAT=MODE0,
CHAM_MATER=CHAMPMAT, CARA_ELEM=CARA_ELE,
ENER_POT=_F (ALL = “YES”,
GROUP_MA = (“POU_D_T', “MASSES”, “LIAI_NOE”, “LIAI_SOL”,))
)

#
FT=DEFI_FONCTION (NOM_PARA=' FREQ',
VALE= (0., 0.0, 10., 0.3, 30., 1.5, 100., 1.5,))

#
FR=DEFI_FONCTION (NOM_PARA=' FREQ',
VALE= (0., 0.0, 10., 0.05, 30., 0.75, 100., 0.75,))

L_AMOR=CALC_AMOR_MODAL (
ENER_SOL=_F (MODE_MECA = MODE0,
GROUP_NO_RADIER = “P1”,
KX = 6.295E11, KY = 6.295E11, KZ = 6.864E11,
KRX = 3.188E14, KRY = 3.188E14, KRZ = 3.2E14),
AMOR_INTERN=_F (
ENER_POT = EPOT,
GROUP_MA = (“POU_D_T', “MASSES”, “LIAI_NOE”,),
AMOR_REDUIT = (0.07, 0.07, 0.02,)),
AMOR_SOL=_F (
FONC_AMOR_GEO = (FT, FT, FT, FR, FR, FR,),
HOMOGENEOUS = “NOT”)
)

Handbook of Utilization
U4.5- booklet: Methods of resolution
HT-66/05/004/A

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