Code_Aster
®
Version
7.4
Titrate:
Operator
NORM_MODE
Date:
21/01/05
Author (S):
E. BOYERE, O. BOITEAU
Key
:
U4.52.11-G
Page
:
1/8
Instruction manual
U4.5- booklet: Methods of resolution
HT-66/05/004/A
Organization (S):
EDF-R & D/AMA, SINETICS
Instruction manual
U4.5- booklet: Methods of resolution
Document: U4.52.11
Operator
NORM_MODE
1 Goal
To normalize clean modes according to a criterion chosen by the user.
Operators of modal calculation
MODE_ITER_INV
[U4.52.04] and
MODE_ITER_SIMULT
[U4.52.03]
produce a concept of the type
mode_meca
or
mode_meca_c
of which real clean modes or
complexes are standardized in such way that largest of the components which is not one
multiplier of LAGRANGE, is equal to one.
Operator NORM_MODE allows the user to choose another method of standardization by
example masses generalized, generalized rigidity…
According to standardization chosen, the modal parameters (factor of participation, masses
effective,…) are reactualized.
Réentrant operator.
Code_Aster
®
Version
7.4
Titrate:
Operator
NORM_MODE
Date:
21/01/05
Author (S):
E. BOYERE, O. BOITEAU
Key
:
U4.52.11-G
Page
:
2/8
Instruction manual
U4.5- booklet: Methods of resolution
HT-66/05/004/A
2 Syntax
m_out = NORM_MODE (
reuse = m_out
MODE
=
m_in/
[mode_meca]
/
[mode_meca_C]
/STANDARD =/“MASS_GENE”
/
“RIGI_GENE”
/
“TRAN”
/
“TRAN_ROTA”
/
“EUCL”
/
“EUCL_TRAN”
/
NODE
=
N
[node]
NOM_CMP = cmp
[KN]
/
SANS_CMP
=
s_cmp
[l_Kn]
/
AVEC_CMP
=
a_cmp
[l_Kn]
MASS_INER= masstru [tabl_mass_iner]
MODE_SIGNE = _F (
NODE
=
N
[node]
NOM_CMP =
cmp, [kN]
SIGN
=
/
“POSITIVE”
[DEFECT]
/
“NEGATIVE”
)
SENSITIVITY = (
… to see [U4.50.02]….
)
TITRATE
= T
[l_Kn]
INFORMATION
=
/
1
[DEFECT]
/2
);
m_in
=
if m_in is of type [mode_meca] then m_out is of type [mode_meca]
idem with [mode_meca_c]
idem with [mode_flamb]
Code_Aster
®
Version
7.4
Titrate:
Operator
NORM_MODE
Date:
21/01/05
Author (S):
E. BOYERE, O. BOITEAU
Key
:
U4.52.11-G
Page
:
3/8
Instruction manual
U4.5- booklet: Methods of resolution
HT-66/05/004/A
3 Operands
3.1 Operand
MODE
MODE
=
m_in
Name of the concept of the type
mode_ *
which one wants to change the standardization of the clean modes. If
m_out
is identical to
m_in
and if the key word “reuse” is activated with the value m_out
renormalization is done in place.
3.2 Operand
NORMALIZES
(cf [§5])
/STANDARD
=
Reference symbol of the selected standard.
“MASS_GENE”:
The modes are standardized with the unit generalized mass.
“RIGI_GENE”:
The modes are normalized with unit generalized rigidity.
“TRAN”:
The modes are normalized to 1. for largest of the components of translation:
(components:
DX, DY, DZ
).
“TRAN_ROTA”
:
The modes are normalized to 1. for largest of the components of translation and of
rotation (components:
DX, DY, DZ, DRX, DRY, DRZ
).
“EUCL”
:
The modes are standardized to the euclidian norm of the components which are not
multipliers of LAGRANGE (component:
LAGR
).
“EUCL_TRAN”
:
The modes are standardized to the euclidian norm of the components which are
components of translation (component:
DX, DY, DZ
).
3.3 Operands
NODE
and
NOM_CMP
NODE = N
Name of the node of standardization
NOM_CMP = cmp
Name of the component of standardization to the node
N
The modes are normalized to 1. for the component
cmp
node
N
.
3.4 Operands
AVEC_CMP
/
SANS_CMP
/AVEC_CMP = a_cmp
a_cmp
list names of the components used for standardization.
The modes are normalized to 1. for largest of the components of the list
a_cmp
some is
the node.
/SANS_CMP = s_cmp
s_cmp
list names of the components which are not used for standardization.
The modes are normalized to 1. for largest of the components which is not in the list
s_cmp
.
Code_Aster
®
Version
7.4
Titrate:
Operator
NORM_MODE
Date:
21/01/05
Author (S):
E. BOYERE, O. BOITEAU
Key
:
U4.52.11-G
Page
:
4/8
Instruction manual
U4.5- booklet: Methods of resolution
HT-66/05/004/A
3.5 Key word
factor
MODE_SIGNE
This key word factor makes it possible to impose for all the modes the sign of a component of a node
stipulated by the user. This key word factor can be used only for the real modes (problem
generalized).
NODE = Nd
Name of the node where the sign of a component is imposed.
NOM_CMP = cmp
Name of the component of the node
N
where the sign is imposed.
SIGN =
/“POSITIVE”
/
“NEGATIVE”
Sign imposed component: “POSITIVE” or “NEGATIVE”.
3.6 Operand
MASS_INER
MASS_INER = masstru
Key word allowing the calculation of the modal parameters
MASS_EFFE_UN_DX,
MASS_EFFE_UN_DY
and
MASS_EFFE_UN_DZ
(unit effective masses in the three directions).
The mass of the structure must be calculated as a preliminary by the operator
POST_ELEM
and the key word
factor
MASS_INER
[U4.81.22] which produces a structure of data which is indicated under
key word MASS_INER of the type counts.
3.7 Operands
SENSIBLITE
SENSITIVITY =
The derivative of the modes normalizes according to the same coefficient of standardization as the modes.
The document [U4.50.02] specifies the operation of the key word.
3.8 Operand
TITRATE
TITRATE =
T
Titrate associated with the concept produced by this operator [U4.03.01].
3.9 Operand
INFORMATION
INFORMATION = 1 or 2
For each mode, the name of the old standard and the name of the new standard are indicated
in the file MESSAGE.
Code_Aster
®
Version
7.4
Titrate:
Operator
NORM_MODE
Date:
21/01/05
Author (S):
E. BOYERE, O. BOITEAU
Key
:
U4.52.11-G
Page
:
5/8
Instruction manual
U4.5- booklet: Methods of resolution
HT-66/05/004/A
4
Formulation of the rules of standardization
The various standards used as well as the definition of the various modal parameters are
listed in the reference material [R5.01.03].
4.1
Real clean modes
For the modes of the type
MODE_MECA_R
(real clean modes) the problem generalized with the values
clean associated is:
(
)
(
)
(
)
0
2
2
2
=
-
=
-
X
M
K
X
M
K
F
where
M
K,
are respectively the matrix of mass and the matrix of rigidity of the mechanical system.
For modelings
“MECHANICAL”
, one defines the components of the clean vector:
·
components of translation
U
T
·
components of rotation
U
R
·
components of the multipliers of LAGRANGE
·
other components (pressure and fluid potential)
p
F
One calls:
·
U
TR
components of translation and rotation,
·
U
components other than multiplying of LAGRANGE.
what leads to
U
U
U
U
T
R
*
=
=
p
F
For the models with components of translation and rotation, the clean mode
I
provided by
algorithms of modal analysis is by defect:
I
I
max
max
=
=
=
*
*
U
U
U
U
TR
TR
what is equivalent to the standardization obtained by the key word `
TRAN_ROTA
'.
With the key word `
TRAN
'the mode obtained is defined by:
I
I
max
=
=
U
U
T
T
*
For the models with components of translation only, standardization is by defect:
I
max
max
T
T
U
U
U
U
=
=
*
*
what is equivalent to the standardization obtained by the key word
“TRAN”
.
Code_Aster
®
Version
7.4
Titrate:
Operator
NORM_MODE
Date:
21/01/05
Author (S):
E. BOYERE, O. BOITEAU
Key
:
U4.52.11-G
Page
:
6/8
Instruction manual
U4.5- booklet: Methods of resolution
HT-66/05/004/A
Standardization by defect led to the following generalized parameters:
·
generalized rigidity
T
I
I
I
K
=
·
mass generalized
T
I
I
I
M
=
µ
·
from where the own pulsation
µ
I
I
I
2
=
Standardization with the unit generalized mass is obtained by the key word
“MASS_GENE”
:
iM
I
I
=
µ
from where
T
iM
iM
M
= 1.
and
T
iM
iM
I
K
=
2
That with unit generalized rigidity is obtained by the key word
“RIGI_GENE”
:
iK
I
I
=
from where
T
iK
iK
I
M
= 1
2
.
and
T
iK
iK
K
= 1.
The standardization of the mode suitable for the euclidian norm
“EUCL”
is obtained naturally by:
()
I
U
J
J
*
*
=
=
U
U
U
U
2
The standardization of the mode suitable for the euclidian norm
“EUCL_TRAN”
is:
()
I
U
*
T
*
jT
J
T
U
U
U
U
=
=
2
4.2
Complex clean modes
For the modes of the type
MODE_MECA_C
(complex clean modes) resulting from a resolution of one
quadratic problem with the eigenvalues
2
M
C K 0
+
+ =
where
C
is the matrix
of damping of the mechanical system, one normalizes the modes
compared to the linearized problem
associated:
0
M
MR. C
M 0
0
K
0
+ -
=
The clean mode is normalized with the unit generalized mass (
“MASS_GENE”)
, if
I
satisfied:
(
)
T
I
T
I
I
I
0
M
MR. C
= 1.
Code_Aster
®
Version
7.4
Titrate:
Operator
NORM_MODE
Date:
21/01/05
Author (S):
E. BOYERE, O. BOITEAU
Key
:
U4.52.11-G
Page
:
7/8
Instruction manual
U4.5- booklet: Methods of resolution
HT-66/05/004/A
with unit generalized rigidity (
“RIGI_GENE”)
, if
I
satisfied:
(
)
T
I
T
I
I
I
-
=
M 0
0
K
1.
For the other standards, the definitions are equivalent to those defined for the real modes, it is enough
to replace the scalar product by the square product.
5
Real modes examples
For the modes of the type
mode_meca
(real clean modes) resulting from a resolution of a problem
generalized with the eigenvalues
(
)
0
=
-
X
M
K
:
·
to normalize a clean vector
X
to unit generalized rigidity is equivalent so that
X
satisfies
1
=
X
K
X
T
Standardization with duplication of the concept
mode_meca
:
mo_2
=
NORM_MODE
(MODE
=
mo_1,
NORME=
“RIGI_GENE”
);
·
to normalize a clean vector
X
to the unit generalized mass is equivalent so that
X
satisfies
1
=
X
M
X
T
Standardization “places from there” at the unit generalized mass:
Mo
=
NORM_MODE
(reuse = Mo,
MODE
=
Mo,
NORMALIZES
=
“MASS_GENE”
);
Code_Aster
®
Version
7.4
Titrate:
Operator
NORM_MODE
Date:
21/01/05
Author (S):
E. BOYERE, O. BOITEAU
Key
:
U4.52.11-G
Page
:
8/8
Instruction manual
U4.5- booklet: Methods of resolution
HT-66/05/004/A
Intentionally white left page.