Code_Aster
®
Version
6.4
Titrate:
Structure of data
MODE_MECA
and
MODE_MECA_C
Date:
24/06/03
Author (S):
O. NICOLAS
Key:
U5.01.23-D
Page:
1/6
Instruction manual
U5.0- booklet: Structure of data
result
HT-66/03/002/A
Organization (S):
EDF-R & D/AMA
Instruction manual
U5.0- booklet: Structure of data
result
Document: U5.01.23
Structure of data
mode_meca
and
mode_meca_C
1 Significance
Structure of data gathering the results coming from a linear modal calculation (clean modes
realities or complexes).
2
Operators producing this structure of data
Operator Reference
Creation
Amendment
MODE_ITER_INV
[U4.52.04] Yes
Not
MODE_ITER_SIMULT
[U4.52.03] Yes
Not
NORM_MODE
[U4.52.11] Yes
Yes
EXTR_MODE
[U4.52.12] Yes
Yes
MACRO_MODE_MECA
[U4.52.02] Yes
Not
Code_Aster
®
Version
6.4
Titrate:
Structure of data
MODE_MECA
and
MODE_MECA_C
Date:
24/06/03
Author (S):
O. NICOLAS
Key:
U5.01.23-D
Page:
2/6
Instruction manual
U5.0- booklet: Structure of data
result
HT-66/03/002/A
3
Operators using this structure of data
Operator Reference
PROJ_MATR_BASE
[U4.63.12]
PROJ_VECT_BASE
[U4.63.13]
DEFI_BASE_MODALE
[U4.64.02]
CALC_AMOR_MODAL
[U4.52.13]
CALC_FLUI_STRU
[U4.66.02]
CALC_MATR_AJOU
[U4.66.01]
COMB_SISM_MODAL
[U4.84.01]
DYNA_ALEA_MODAL
[U4.53.22]
IMPR_CLASSI
[U7.04.21]
MACRO_MADMACS
[U7.03.21]
MACRO_PROJ_BASE
[U4.63.11]
MODI_BASE_MODALE
[U4.66.21]
REST_BASE_PHYS
[U4.63.21]
REST_SPEC_PHYS
[U4.63.22]
4 Variables
access
Variable of access
Significance
Type
NUME_ORDRE
Sequence number of the required field (position of the mode in
calculated part of the spectrum)
I
FREQ
Frequency of the mode
R
NUME_MODE
Position of the mode in the total spectrum
I
Characteristic:
NUME_ORDRE > 0
Code_Aster
®
Version
6.4
Titrate:
Structure of data
MODE_MECA
and
MODE_MECA_C
Date:
24/06/03
Author (S):
O. NICOLAS
Key:
U5.01.23-D
Page:
3/6
Instruction manual
U5.0- booklet: Structure of data
result
HT-66/03/002/A
5 Parameters
associated
Parameters Significance
Type
NORMALIZES
Normalizes clean mode
K24
OMEGA2
Square of the pulsation
R
AMOR_REDUIT
Reduced damping
R
ERROR
Modal error
R
MASS_GENE
Mass generalized of the mode
R
RIGI_GENE
Generalized stiffness of the mode
R
AMOR_GENE
Generalized damping of the mode
R
MASS_EFFE_DX
Effective modal mass in direction DX (translation)
R
MASS_EFFE_DY
Effective modal mass in the direction DY (translation)
R
MASS_EFFE_DZ
Effective modal mass in direction DZ (translation)
R
MASS_EFFE_DRX
Effective modal mass in direction DRX (rotation)
R
MASS_EFFE_DRY
Effective modal mass in direction DRY (rotation)
R
MASS_EFFE_DRZ
Effective modal mass in direction DRZ (rotation)
R
FACT_PARTICI_DX
Factor of participation in direction DX (translation)
R
FACT_PARTICI_DY
Factor of participation in the direction DY (translation)
R
FACT_PARTICI_DZ
Factor of participation in direction DZ (translation)
R
FACT_PARTICI_DRX
Factor of participation in direction DRX (rotation)
R
FACT_PARTICI_DRY
Factor of participation in direction DRY (rotation)
R
FACT_PARTICI_DRZ
Factor of participation in direction DRZ (rotation)
R
MASS_EFFE_UN_DX
Unit effective modal mass in direction DX
(translation)
R
MASS_EFFE_UN_DY
Unit effective modal mass in the direction DY
(translation)
R
MASS_EFFE_UN_DZ
Unit effective modal mass in direction DZ (translation)
R
MASS_EFFE_UN_DRX
Unit effective modal mass in direction DRX (rotation)
R
MASS_EFFE_UN_DRY
Unit effective modal mass in direction DRY (rotation)
R
MASS_EFFE_UN_DRZ
Unit effective modal mass in direction DRZ (rotation)
R
MASS_GENE_DX
Mass generalized in direction DX (translation)
R
MASS_GENE_DY
Mass generalized in the direction DY (translation)
R
MASS_GENE_DZ
Mass generalized in direction DZ (translation)
R
Note:
The parameters which relate to the degrees of freedom of rotation are not calculated.
Code_Aster
®
Version
6.4
Titrate:
Structure of data
MODE_MECA
and
MODE_MECA_C
Date:
24/06/03
Author (S):
O. NICOLAS
Key:
U5.01.23-D
Page:
4/6
Instruction manual
U5.0- booklet: Structure of data
result
HT-66/03/002/A
6 Fields
accessible
The list of the accessible fields being long, one returns the reader to the document [U5.01.01] which
synthesize in the form of tables the list of the accessible fields for the various structures of
data.
7 Definition of the modal parameters associated
mode_meca
The clean modes of a structure (not deadened) are defined by the modal equation:
K
M
I
I
I
=
2
mode being the couple
(
)
I
I
I
I
2
2
,
,
or
according to whether one considers the square of the pulsation, or
associated frequency.
7.1
Property of orthogonality of the clean modes
The modes are:
M
- orthogonal and
K
- orthogonal, from where relations
iT
J
ij
iT
J
ij
R
M
K
=
=
.
,
.
7.2 Parameters
generalized
7.2.1 Mass and stiffness generalized
One defines the generalized mass and the stiffness of a clean mode of a structure by:
µ
I
iT
I
I
iT
I
K
=
=
M
K
mass generalized (
)
generalized stiffness (
)
MASS_ GENE
RIGI_ GENE
and we have the relation:
K
I
I
I
=
µ
2
Note:
From the physical point of view, the generalized mass (which is a positive value) can be interpreted
like the mass moving
µ
I
U FD
U
2
where is displacement
and more precisely one can note than the potential energy of deformation of the ième mode is:
1
2
iT
I
K
and that the kinetic energy of the structure vibrating according to its ième mode is:
1
2
2
I
iT
I
M
Note:
Owing to the fact that the clean modes are defined except for a constant, mass and stiffness
generalized depend on the standardization of the mode.
Code_Aster
®
Version
6.4
Titrate:
Structure of data
MODE_MECA
and
MODE_MECA_C
Date:
24/06/03
Author (S):
O. NICOLAS
Key:
U5.01.23-D
Page:
5/6
Instruction manual
U5.0- booklet: Structure of data
result
HT-66/03/002/A
7.2.2 Generalized unit displacement
One calls generalized unit displacement or masses generalized of the mode
I
in the direction
(unit)
D
quantity
Q
U
U
D
id
iT
D
D
=
M
where
is the vector unit in the direction
.
Generalized displacement is of unspecified sign, even of zero value and is depend on
normalizes clean mode.
The concept of generalized displacement is not limited to the translations but can be extended to
rotations by considering the following definition:
Q
I
iT
D
=
MR. U
*
where
U
D *
is the matrix whose terms are the matrices
U
K
where
K
is a node of the mesh
(supporting rotations).
Let us clarify the matrix
U
K
, if all the nodes of the mesh support 3 ddl translation
and 3 ddl of rotation; matrices
U
K
are the following matrices 6x6:
(
)
U
K
K
ka
K
K
K
K
K
K
K
Z
y
Z
X
y
X
X
y Z
K
=
-
-
-
1 0 0 0
0 1 0
0
0 0 1
0
0 0 0 1
0
0
0 0 0 0
1
0
0 0 0 0
0
1
with
co-ordinates of the node
,
,
.
Let us note that implicitly we consider here that the center of rotation (center of gravity of
structure) is confused with the origin of the co-ordinates.
7.3
Factors of participation
One notes
has
id
the factor of participation of the ième mode in the direction
D
, by definition:
has
Q
U
id
id
I
iT
D
iT
I
=
=
µ
M
M
7.4
Effective modal mass and unit effective modal mass
One notes
m
id
effective modal mass of the ième mode in the direction
D
, by definition:
(
)
m
Q
U
id
id
I
iT
D
iT
I
=
=
2
2
µ
M
M
Property [R4.05.03]:
The sum of the effective modal masses in a direction is equal to the total mass (
M
T
)
structure.
Code_Aster
®
Version
6.4
Titrate:
Structure of data
MODE_MECA
and
MODE_MECA_C
Date:
24/06/03
Author (S):
O. NICOLAS
Key:
U5.01.23-D
Page:
6/6
Instruction manual
U5.0- booklet: Structure of data
result
HT-66/03/002/A
One will thus use rather the concept of effective modal mass unit associated the mode, which is
fraction (percentage) of the total mass which is excited by the ième mode in the unit direction
D
(
)
m
m
M
M
U
id
id
T
T
iT
D
iT
I
*
=
=
1
2
M
M
The effective modal mass and the effective unit modal mass are independent of
standardization of the clean mode.
7.5
Modal parameters independent of the standardization of the modes
As an indication, we give the list of the modal values independent of standardization of
modes.
·
the reduced factor of participation
-
Q
id
I
I
I
I
µ
.
max
max
where
is largest of the components of
·
stiffness associated with the reduced factor of participation:
-
=
Q
Q
id
I
I
id
I
I
µ
µ
.
max
max
1
2
·
unit effective modal mass
m
M
Q
id
T
id
I
*
=
1
2
µ
8 Definition of the modal parameters associated
MODE_MECA_C
The clean modes of a deadened structure are defined by the modal equation
(
)
()
()
I
I
I
I
E
I
I
I
I
I
E
I
I
I
I
R
R
2
0
M
C K
+
+
=
-
=
-
=
mode being the triplet
where
is the pulsation of the system
is reduced damping
the clean vector or mode of vibration
,
,
This problem can be put in a form of “generalized problem”
With
B
.
.
Z
Z
=
where
With
K
M
B
C
M
M
=
-
= -
-
-
=
=
O
O
O
Z
y
y
,
,
,
Consequently, it is possible to define the concepts of mass and generalized stiffness, like factor of
participation and effective modal mass by taking the matrix
With
like rigidity stamps and
stamp
B
like stamps of mass.