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Titrate:
Operator
DYNA_ALEA_MODAL
Date:
08/02/05
Author (S):
S. CAMBIER, J. PIGAT
Key:
U4.53.22-G
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Instruction manual
U4.5- booklet: Methods of resolution
HT-66/05/004/A
Organization (S):
EDF-R & D/AMA














Instruction manual
U4.5- booklet: Methods of resolution
Document: U4.53.22





Operator
DYNA_ALEA_MODAL





1 Goal
To calculate the spectral response of a linear structure under an excitation known by its DSP.
The operator provides the modal response in the form of interspectre of power.
The produced concept is of tabl_intsp type.
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Titrate:
Operator
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Key:
U4.53.22-G
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2 Syntax
int
[tabl_intsp] = DYNA_ALEA_MODAL
(
BASE_MODALE =_F
(
MODE_MECA
=
modemec [mode_meca]
/
NUME_ORDRE =
command
[l_I]
AMOR_REDUIT
=
lamor
[l_R]
/
BANDAGE
=
(f1, f2) [l_R]
AMOR_UNIF
=
amor [R]
)

MODE_STAT
=
mosta
[mode_stat]

EXCIT
=_F
(
# Command of derivation of the excitation
DERIVATION
=
/
0
[DEFECT]
/1
/2
SIZE =
/
“DEPL_R”
[DEFECT]
/
“EFFO”
/
“SOUR_DEBI_VOLU”
/
“SOUR_DEBI_MASS”
/
“SOUR_PRESS”
/
“SOUR_FORCE”
#
interspectre
excitation
INTE_SPEC
=
interexc
[tabl_intsp]
NUME_VITE_FLUI
=
list_ind
[l_I]
OPTION
=
/
“ALL”
[DEFECT]
/“DIAG”
#
place
of application
of
the excitation
/
NUME_ORDRE_I
=
noi
[l_I]
NUME_ORDRE_J
=
noj
[l_I]
/
NODE
=
list_noe [l_noeud]
NOM_CMP =
list_comp [l_cmp]
MODAL
=
“NOT” [DEFECT]
/
CHAM_NO =
list_vass [l_cham_no_ *]
MODAL
=
“NOT” [DEFECT]
/
MODAL
= “YES”
/
NOEUD_I
=
noeudi
[l_noeud]
NOEUD_J
=
noeudj
[l_noeud]
NOM_CMP_I
=
cmpi
[l_cmp]
NOM_CMP_J
=
cmpj
[l_cmp]
NODE =
list_noe [l_noeud]
NOM_CMP
=
list_comp
[l_cmp]
MODAL =
“NOT” [DEFECT]
)
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Titrate:
Operator
DYNA_ALEA_MODAL
Date:
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Key:
U4.53.22-G
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ANSWER =_F
(
# command of derivation of the answer
DERIVATION =
/
0
[DEFECT]
/1
/2
# possible limitation of calculation to the diagonal
OPTION
=
/
“ALL”
[DEFECT]
/
“DIAG”

# frequential dicretisation for the answer

FREQ_MIN
= fmin [R]
FREQ_MAX
= fmax [R]
NOT
=
not
[R]
FREQ_EXCIT =
/
“WITH”
[DEFECT]
/
“WITHOUT”
NB_POIN_MODE
=
/
50 [DEFECT]
/N
[I]

)

TITRATE
=
titrate
[l_Kn]

INFORMATION =
/
1
[DEFECT]
/2
);
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Code_Aster
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Version
7.4
Titrate:
Operator
DYNA_ALEA_MODAL
Date:
08/02/05
Author (S):
S. CAMBIER, J. PIGAT
Key:
U4.53.22-G
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:
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U4.5- booklet: Methods of resolution
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3 Functionalities
The operator
DYNA_ALEA_MODAL
allows to calculate the response in the frequential field, on basis
modal, of a structure subjected to an excitation represented by a matrix interspectrale
(cf.
DEFI_INTE_SPEC
[U4.36.02]).
The size excitation can be of imposed ddl type or effort associated with a ddl. It also can
to correspond to sources of fluid excitation [R4.05.02].
The excitation can be given in form derived of a nature equal to 0, 1 or 2 (displacement, speed or
acceleration).
L `operator
REST_SPEC_PHYS
[U4.63.22] allows to restore the response in displacement or effort
with the ddl “of observation” (couple node, component).
The matrix interspectrale modal answer thus calculated can be reintroduced in a new calculation.


4 Operands
4.1 Word
key
BASE_MODALE
BASE_MODALE = _F (
Key word factor for the definition of the parameters of selection of the modal base of calculation.
4.1.1 Operand
MODE_MECA
MODE_MECA
= modemec
modemec
is the concept of the type
mode_meca
containing the dynamic modes.
4.1.2 Operands
NUME_ORDRE
/
AMOR_REDUIT
/NUME_ORDRE = lordre
lordre
is the list of the sequence numbers of the modes of the concept
modemec
actually taken
in account in calculation. Example:
(2 3 4)
.
AMOR_REDUIT = lamor
lamor
is the list of reduced modal depreciation corresponding to the modes selected.
a many elements of the list are equal to the number of elements of
lordre
. Example:
(0.05
0.05 0.02
)
.
This key word is usable only with
NUME_ORDRE
.
4.1.3 Operands
BANDAGE
/
AMOR_UNIF
/
BANDAGE = (f1 f2)
The dynamic modes taken into account will be those of
modemec
whose frequency is in
the tape
(f1 f2)
AMOR_UNIF = amor
For each mode selected, damping is equal to
amor
. This key word is not usable
that with
BANDAGE
.
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Titrate:
Operator
DYNA_ALEA_MODAL
Date:
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Key:
U4.53.22-G
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4.2 Operand
MODE_STAT
MODE_STAT = mosta
Concept of the type
mode_stat
containing the static modes necessary to calculation.
This key word is necessary only in the case of a seismic calculation multi-supports where the excitation
fact on ddl (I. E. when the key word
SIZE
under the key word factor
EXCIT
is worth '
DEPL_R'
).
4.3 Word
key
EXCIT
EXCIT = _F (
Key word factor defining all the parameters relating to the excitation.
Key words
DERIVATION
,
SIZE
and
MODAL
define the type of excitation.
Key words
INTE_SPEC, NUME_VITE_FLUI, NUME_ORDRE_I, NUME_ORDRE_J,
NOEUD_I, NOEUD_J, NOM_CMP_I
and
NOM_CMP_J
define the interspectre excitation.
4.3.1 Operand
DERIVATION
DERIVATION
=
When the size of the excitation is of imposed ddl type (
“DEPL_R”
), this key word allows
to describe if the interspectre excitation must be regarded as a displacement, a speed
or an acceleration imposed. The user specifies then
0
,
1
or
2
.
This key word is optional. By defect, it is equal to
0
.
Note:
In the case of a seismic calculation, the excitation is often an acceleration. This key word
must then be equal to 2.
4.3.2 Operand
SIZE
SIZE
=
This key word makes it possible to say if the excitation is of imposed ddl type (
“DEPL_R”
), imposed effort
(
“EFFO”
), source of flow-volume ('
SOUR_DEBI_VOLU'
), source of flow-mass
('
SOUR_DEBI_MASS'
), source of pressure ('
SOUR_PRESS'
) or fluid source of force
('
SOUR_FORCE'
).
This key word is optional. By defect, it is equal to
“DEPL_R”
and the excitation is of ddl type of
displacement imposed in all the cases except in the case of supports represented by
assembled vectors (key word
CHAM_NO
).
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Titrate:
Operator
DYNA_ALEA_MODAL
Date:
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Key:
U4.53.22-G
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4.3.3 Operands
INTE_SPEC
and
NUME_VITE_FLUI
These key words define L (be) interspectre (S) of excitation.
INTE_SPEC = interexc
interexc
is the concept of the type
tabl
_
intsp
containing the whole of the matrices
interspectrales (spectral concentration of power) of excitation. It is taken into account such as it is
defined in the function associated with the concept, i.e. in particular which one does not interpret
a possible folding up of spectrum.
For a function defined by:
[
]
()
F
F F
S F
1
2
,
given
One will interpret:
()
[
]
()
()
F
F
S F
F
F F
S F
F
F
S F
<
=
=
1
1
2
2
0
0
,
given
If the loop of frequency
[
]
F F
1
2
,
must be reproduced for the negative frequencies, it is necessary:
·
that is to say to give the whole of the spectrum on the axis of realities,
·
that is to say to apply a coefficient 2 to the value of the DSP, possible skirting,
since all calculation is linear in control DYNA_ALEA_MODAL.
NUME_VITE_FLUI = nk
nk
is the sequence number if the concept
tabl
_
intsp
contains several tables of interspectres
(indexed by this parameter).
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Titrate:
Operator
DYNA_ALEA_MODAL
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U4.53.22-G
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4.3.4 Operands NUME_ORDRE_I, NUME_ORDRE_J, NODE, NOM_CMP, CHAM_NO and
MODAL
These key words bind the terms of () the interspectre (S) of excitation and the points of excitation for one
modal excitation or when the parameters of the table were subscripted by sequence numbers.
/
NUME_ORDRE_I = noi1, noi2.
NUME_ORDRE_J = noj1, noj2,…
These lists of sequence number are appairées two by two in order to determine it
term of the matrix interspectrale given.
/
NODE = list_noe
This key word makes it possible to specify the nodes where the multispectral excitation
will be applied. Example
(N1 N5 N7)
.
For all the types of sizes of excitation, except for the sources of
pressure and sources of force,
list_noe
as many terms as it contains
y has couples of indices defining of the interspectres of excitation.
In the case of sources of pressure or sources of force, with each
source is associated a dipole, i.e. two points of application.
list_noe
then has twice more terms than there are couples of indices
defining interspectres.
NOM_CMP = list_cmp
This key word makes it possible to specify the components on which the excitation
multispectral will be applied. Example
(“CLOSE” “DRZ” “PHI”)
.
These components must of course correspond to degrees of
freedom of the nodes of supports.
In all the cases,
list_cmp
the same number of elements has as
list_noe
.
For the fluid sources, it is the ddl
“CLOSE”
who is excited.
MODAL = '' NON' [DEFECT]
The excitation is not modal in this case.
/
CHAM_NO = list_vass
When this key word is present, each support of excitation is a vector
assembled definite before in the command file
.
list_vass
the list of the assembled vectors contains holding place of supports. Size
associated exciter is “EFFO”. It is recommended that the associated intensity
to the effort which one imposes by this skew is given by the interspectre:
assembled vector is primarily used to define a function of form
support of a spectrum of power in effort. It is thus standardized.
This option makes it possible to affect a spectrum of power of effort on one
function of form.
In all the cases,
list_vass
as many terms contains as there is
couples of indices defining of the interspectres.
MODAL = '' NON' [DEFECT]
The excitation is not modal in this case.
/
MODAL = “YES”
The presence of
“YES”
under this key word implies that the interspectre
of excitation is regarded as a modal excitation.
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Titrate:
Operator
DYNA_ALEA_MODAL
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U4.53.22-G
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4.3.5 Operands
NOEUD_I, NOEUD_J, NOM_CMP_I and NOM_CMP_J
These key words bind the terms of () the interspectre (S) of excitation and the points of excitation when them
parameters of the table were subscripted by physical data made up of the couple
(Node-CMP).
/
NOEUD_I = ndi1,
ndi2,…
NOM_CMP_I = cmpi1, cmpi2.
NOEUD_J = ndj1,
ndj2,…
NOM_CMP_J = cmpj1, cmpj2,…
These lists of sequence number are appairées two by two in order to determine it
term of the matrix interspectrale given. The length of the preceding lists must
to correspond to the number of excitations imposed on the structure.
NODE
=
list_noe [l_noeud]
NOM_CMP
= list_comp
[l_cmp]
These two key words have the same significance as in [§4.3.4].
MODAL
=
“NOT” [DEFECT]
The excitation is not modal in this case.

4.4 Word
key
ANSWER
ANSWER = _F (
Key word factor for the definition of all the parameters concerning the answer.
The three following key words describe the type of the answer.
4.4.1 Operand
DERIVATION
DERIVATION
=
This key word has the same direction as for the key word factor
EXCIT
[§4.3.1].
4.4.2 Operand
OPTION
OPTION
=
If this key word is specified with
“DIAG”
, then all nondiagonal functions of
the interspectre answer are initialized to zero without being calculated. Only the autospectres are
calculated. In the contrary case (
“ALL”
), all the functions of the interspectre answer are
calculated.
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4.4.3 Operands
FREQ_MIN
/
FREQ_MAX
/
NOT
/
FREQ_EXCIT
/
NB_POIN_MODE
These key words are used to describe the frequential discretization in which the answer will be given.
FREQ_MIN = fmin
FREQ_MAX = fmax
fmin
and
fmax
are the two terminals of the interval of frequency.
not
is the minimum pitch of
discretization.
NOT = not
If values of
fmin
and
fmax
are given,
not
is worth then by defect
fmax
fmin
-
100
.
If not one takes
fmax
the greatest Eigen frequency of the dynamic modes retained for
calculation.
Then the discretization covers the field
[
]
0
2
;
*
fmax
,
not
fmax
*
= 2 100
.
On the other hand, if
not
is present, one makes sure that the pitch of discretization of the answer is
everywhere lower than
not
.
FREQ_EXCIT =
/
“WITH”
/
“WITHOUT”
If the user gives the argument
“WITH”
under the key word
FREQ_EXCIT
, then frequencies
excitation are integrated into the discretization of the answer (default option). If it gives
the argument
“WITHOUT”
, they will be ignored. This key word is put at “WITHOUT” in the event of presence
key word FREQ_MIN.
NB_POIN_MODE = N [defect = 50]
The response is refined to the place of the Eigen frequencies in order to ensure good
description of the response to the place of the peaks.
The key word
NB_POIN_MODE
allows to define the number of pitches of frequency per frequency
proper taking into account. By defect, there are 50 pitches per Eigen frequency. This key word is not
taken into account if FREQ_MIN is given.
Each function of the interspectre will have by defect a mode of interpolation of the type
'
LINEAIRE'
and a mode of prolongation out of the field of discretization of the type
“EXCLUDED”
.
4.5 Operand
TITRATE
TITRATE = title
titrate
is the title of calculation. It will be printed at the head results. See [U4.03.01].
4.6 Operand
INFORMATION
INFORMATION
=
Specify the options of impression on the file
MESSAGE
.
1
no impression
2
point out the selected options of calculation.
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Titrate:
Operator
DYNA_ALEA_MODAL
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U4.53.22-G
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5 Remarks
of use
·
Need for a static and standard mode of dynamic modes:
In the case of excitation in imposed displacement, the dynamic modes are calculated in supports
locked and the presence of the static mode is obligatory.
In the other cases, the dynamic modes are calculated in free supports, and the presence of one
static mode is not justified any more.
dimension of the matrix interspectrale = a number of static modes + a number of modes
dynamic taken into account.
Thus, for a structure with five dynamic modes, excited in displacement by two supports,
dimension of the matrix interspectrale of modal answer is 7.
If the excitation is given in imposed force, there are not static modes and the dimension of
stamp interspectrale is 5.
·
Use of the key word
MODAL
under the key word factor
EXCIT
:
In the case of use of the key word
MODAL
under the key word factor
EXCIT
to introduce
directly the matrix of modal response like excitation, it is necessary to give again under the key words
EXCIT
BASE_MODALE
and
MODE_STAT
all the arguments which had been used to create the matrix
interspectrale modal (nodes and ddls supports).

6
Phase of checking
The coherence of the data is checked:
·
a number of modal depreciation = a number of modes selected.
·
a number of nodes of supports equal to the component count (for the excitation).
·
a number of couples of indices retained in the interspectre excitation = a number of supports or
a number of points of excitation.
·
in the case of sources of pressure: a number of nodes supports equal to twice the number
couples of indices retained in the interspectre of excitation.
·
the presence of one
mode_stat
is checked in the cases of excitation by a size of the type
DEPL_R
.
·
fmax
fmin
.

7 Example
DYNALEA1=DYNA_ALEA_MODAL (
BASE_MODALE=_F (
MODE_MECA = FREQ1,
NUME_ORDRE = 1,
AMOR_REDUIT = 0.05),
MODE_STAT=MODESTA1,
EXCIT=_F (
DERIVATION = 2,
INTE_SPEC = INTEREXC,
NUME_ORDRE_I = 1,
NUME_ORDRE_J = 1,
NODE = “P1”,
NOM_CMP = “DX”),
REPONSE=_F (
DERIVATION = 2)
)