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Code_Aster
®
Version
7.4
Titrate:
Operator
DEFI_INTE_SPEC
Date:
10/02/05
Author (S):
S. CAMBIER,
G. JACQUART
Key
:
U4.36.02-G
Page
:
1/8
Instruction manual
U4.3- booklet: Function
HT-66/05/004/A
Organization (S):
EDF-R & D/AMA, EDF-Pole Industry/CNPE of Tricastin













Instruction manual
U4.3- booklet: Function
Document: U4.36.02





Operator
DEFI_INTE_SPEC








1 Goal
To define a matrix interspectrale.
The terms of the matrix are defined by:
·
constants (white Gaussian noise),
·
existing complex functions,
·
the analytical formula of KANAI-TAJIMI.
Product a structure of data of the tabl_intsp type.
background image
Code_Aster
®
Version
7.4
Titrate:
Operator
DEFI_INTE_SPEC
Date:
10/02/05
Author (S):
S. CAMBIER,
G. JACQUART
Key
:
U4.36.02-G
Page
:
2/8
Instruction manual
U4.3- booklet: Function
HT-66/05/004/A
2 Syntax

int
[tabl_intsp] = DEFI_INTE_SPEC
(
DIMENSION
=
/
1
[DEFECT]
/N
[I]

/
PAR_FONCTION =_F (
NUME_ORDRE_I
= I [I]
NUME_ORDRE_J
= J [I]
FUNCTION
=fonct
[fonction_C]
)
/
KANAI_TAJIMI =_F (
NUME_ORDRE_I
= I [I]
NUME_ORDRE_J
= J [I]
FREQ_MIN =/0.
[DEFECT]
/
fmin [R]
FREQ_MAX =/100. [DEFECT]
/
fmax [R]
NOT
=
/
1.
[DEFECT]
/
not
[R]
/VALE_R
= valr [R]
/
VALE_C
=
valc [C]
AMOR_REDUIT=
/0.60 [DEFECT]
/
amor [R]
FREQ_MOY =/5.
[DEFECT]
/
fmoy [R]
Interpol =
I
“FLAX”
[DEFECT]
I
“LOG”
I
“NOT”
PROL_GAUCHE=
/“EXCLUDED” [DEFECT]
/
“CONSTANT”
/
“LINEAR”
PROL_DROITE=
/“EXCLUDED” [DEFECT]
/
“CONSTANT”
/
“LINEAR”
)
background image
Code_Aster
®
Version
7.4
Titrate:
Operator
DEFI_INTE_SPEC
Date:
10/02/05
Author (S):
S. CAMBIER,
G. JACQUART
Key
:
U4.36.02-G
Page
:
3/8
Instruction manual
U4.3- booklet: Function
HT-66/05/004/A

/
CONSTANT:
(
NUME_ORDRE_I
=/I [I]
NUME_ORDRE_J
=/J [I]

FREQ_MIN
=
/
0.
[DEFECT]
/
fmin [R]
FREQ_MAX =/100. [DEFECT]
/
fmax [R]
NOT
=
/
1.
[DEFECT]
/
not
[R]

/VALE_R
=/1.
[DEFECT]
/
valr [R]
/
VALE_C
=
valc [C]

Interpol =
I
“FLAX”
[DEFECT]
I
“LOG”
I
“NOT”
PROL_GAUCHE =/“EXCLUDED” [DEFECT]
/
“CONSTANT”
/
“LINEAR”
PROL_DROITE =/“EXCLUDED” [DEFECT]
/
“CONSTANT”
/
“LINEAR”
)
TITRATE
=
titrate
[l_Kn]
INFORMATION =
/
1
[DEFECT]
/2
)
;
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Code_Aster
®
Version
7.4
Titrate:
Operator
DEFI_INTE_SPEC
Date:
10/02/05
Author (S):
S. CAMBIER,
G. JACQUART
Key
:
U4.36.02-G
Page
:
4/8
Instruction manual
U4.3- booklet: Function
HT-66/05/004/A
3 Operands
3.1 Operand
DIMENSION
DIMENSION
= N
Dimension of the matrix interspectrale, stored in a table of interspectres (
tabl_intsp
).
3.2 Word
key
PAR_FONCTION
/
PAR_FONCTION
=
Key word factor, makes it possible to define a term (
I
,
J
) of the matrix interspectrale from
concepts of the type
fonction_C
already definite.
NUME_ORDRE_I
= I
NUME_ORDRE_J
= J
Couples indices (line, column) of the matrix on which one will affect a function.
FUNCTION: fonct
fonct
is a concept of the type
fonction_C.
3.3 Word
key
KANAI_KAJIMI
/
KANAI_TAJIMI
=
Key word factor, makes it possible to define a function of the matrix interspectrale like a noise
white filtered by an oscillator [bib2].
One gives the three parameters of the filter of KANAI_TAJIMI: damping, frequency and
level.
3.3.1 Operands
AMOR_REDUIT/FREQ_MOY/VALE_R/VALE_C
AMOR_REDUIT = amor
FREQ_MOY = fmoy
/VALE_R
= valr
/
VALE_C
=
valc
fmoy
and
amor
are the Eigen frequency and the reduced damping of the filter. The level can
to be given in the complex or real form.
3.3.2 Operands
INTERPOL/PROL_GAUCHE/PROL_DROITE
One gives for each function the conventional parameters which condition the interpolation and
the extrapolation of the produced function. The possibilities as well as the default values are pointed out
on page 2. For more details to see them [§3.4] and [§3.5].
Interpol
PROL_GAUCHE
PROL_DROITE
3.3.3 Operands
FREQ_MIN/FREQ_MAX/NOT
One gives the parameters of the frequential discretization.
FREQ_MIN = fmin
FREQ_MAX = fmax
NOT
=
not
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Code_Aster
®
Version
7.4
Titrate:
Operator
DEFI_INTE_SPEC
Date:
10/02/05
Author (S):
S. CAMBIER,
G. JACQUART
Key
:
U4.36.02-G
Page
:
5/8
Instruction manual
U4.3- booklet: Function
HT-66/05/004/A
3.4 Operands
PROL_DROITE
and
PROL_GAUCHE
PROL_DROITE
and
PROL_GAUCHE =
Define the type of prolongation on the right (on the left) of the field of definition of the variable:
·
“CONSTANT” for a prolongation with the last (or first) value of
function,
·
“LINEAR” for a prolongation along the first definite segment
(
PROL_GAUCHE)
or of the last definite segment (
PROL_DROITE
),
·
“EXCLUDED”
if the extrapolation of the values apart from the field of definition of
parameter is prohibited (in this case if a calculation requires a value
function out of the field of definition, the code will stop in
fatal error).
For example:
·
PROL_DROITE = “CONSTANT”, PROL_GAUCHE = “CONSTANT”

X
1
X
2
X
n-1
X
N
X
y

·
PROL_DROITE = “LINEAR”, PROL_GAUCHE = “EXCLUDED”

X
1
X
2
X
n-1
X
N
X
y
Note:
The type of prolongation and interpolation are independent one of the other.
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Code_Aster
®
Version
7.4
Titrate:
Operator
DEFI_INTE_SPEC
Date:
10/02/05
Author (S):
S. CAMBIER,
G. JACQUART
Key
:
U4.36.02-G
Page
:
6/8
Instruction manual
U4.3- booklet: Function
HT-66/05/004/A
3.5 Operand
Interpol
Interpol
=
Type of interpolation of the function enters the values of the field of definition of the function: one
type for the interpolation of the parameter and for the interpolation of the function. This is obtained in
providing a list of texts among:
Interpol
=
(“FLAX”,
“LOG”)
“FLAX”
:
linear,
“LOG”
:
logarithmic curve,
“NOT”
:
one does not interpolate (and thus the program will stop if for the value is asked
function for a value of the parameter where it was not defined).
Note:
If only one value is specified, it is taken into account at the same time by the interpolation of
parameter and of the function.
INTERPOL = “LOG”
is equivalent to (
“LOG”, “LOG”)
.
3.6 Word
key
CONSTANT
/
CONSTANT
=
Key word factor which makes it possible to define a function of the matrix interspectrale like a noise
white (constant).
All the key words under this key word factor have the same direction as for the key word factor
Safe KANAI_TAJIMI
AMOR
and
FREQ_MOY
who do not have a direction here.
3.7 Operand
TITRATE
TITRATE
= title
titrate
is the title of calculation to print results at the head. See [U4.03.01].
3.8 Operand
INFORMATION
INFORMATION
=
1
:
no impression.
2
:
impression of the characteristics of the definite matrix interspectrale.


4
Phase of Checking
·
Checking of coherence enters the number of functions and the dimension of the matrix
(square) - (see remark of use).
·
Checking of the coherence of the indices.


5 Remark
of use
·
If
N
is the dimension of the matrix, the aforementioned being square
- it is necessary
(
)
N N
*
/
+1 2
fonction_C
, corresponding to the higher triangular part of
stamp, only stored.
·
To print the contents of the matrix, the operator should be used
IMPR_TABLE
[U4.91.03].
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Code_Aster
®
Version
7.4
Titrate:
Operator
DEFI_INTE_SPEC
Date:
10/02/05
Author (S):
S. CAMBIER,
G. JACQUART
Key
:
U4.36.02-G
Page
:
7/8
Instruction manual
U4.3- booklet: Function
HT-66/05/004/A
6 Example
To define a interspectre (matrix 1 X 1) in constant value
1.
100
0
Hz
INTEREXC
=
DEFI_INTE_SPEC
(
DIMENSION=1,
INFO=2,
CONSTANT=_F (
NUME_ORDRE_I=1,
NUME_ORDRE_J=1,
FREQ_MIN=0.,
FREQ_MAX=100.,
PAS=1.,
PROL_GAUCHE=' CONSTANT',
PROL_DROITE=' CONSTANT',
INTERPOL=' LIN',
VALE_C= (“IH”, 1., 0.),
),
);
To define the interspectre of a white Gaussian noise filtered by an oscillator represented by the filter of
KANAI-TAJIMI:
INTKTJ1
=
DEFI_INTE_SPEC
(
DIMENSION=1,
INFO=2,
KANAI_TAJIMI=_F (
NUME_ORDRE_I=1,
NUME_ORDRE_J=1,
FREQ_MOY=15.,
AMOR=0.05,
VALE_R=1.,
INTERPOL=' LIN',
PROL_GAUCHE=' CONSTANT',
PROL_DROITE=' CONSTANT',
FREQ_MIN=0.,
FREQ_MAX=30.,
PAS=5.,
),
);
The 3 parameters of the filter were given:
damping = 0.05
frequency = 15. Hz
level = 1.
background image
Code_Aster
®
Version
7.4
Titrate:
Operator
DEFI_INTE_SPEC
Date:
10/02/05
Author (S):
S. CAMBIER,
G. JACQUART
Key
:
U4.36.02-G
Page
:
8/8
Instruction manual
U4.3- booklet: Function
HT-66/05/004/A
7 Bibliography
[1]
J.S. BENDAT, J. WILEGSON: “Spectral Engineering application off correlation and analysis”.
[2]
C. DUVAL “Dynamic response under random excitations in Code_Aster: principles
theoretical and examples of use ". Note DER HP-61/92-148