Code_Aster
®
Version
7.4
Titrate:
Operator
DYNA_LINE_HARM
Date:
17/02/05
Author (S):
H. ANDRIAMBOLOLONA,
O. NICOLAS
Key
:
U4.53.11-G
Page
:
1/8
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: U4.53.11
Operator
DYNA_LINE_HARM
1 Goal
To calculate the dynamic response complexes of a system to a harmonic excitation. Direct calculation
for a structure in physical space, calculation by harmonic under-structuring for several
under structures defined by their modal base in modal co-ordinates.
Product a structure of data of the dyna_harmo type or acou_harmo or harmo_gene.
Code_Aster
®
Version
7.4
Titrate:
Operator
DYNA_LINE_HARM
Date:
17/02/05
Author (S):
H. ANDRIAMBOLOLONA,
O. NICOLAS
Key
:
U4.53.11-G
Page
:
2/8
Instruction manual
U4.5- booklet: Methods of resolution
HT-66/05/004/A
2 Syntax
harm [*]
= DYNA_LINE_HARM
(
MODEL
=
Mo
[model]
CHAM_MATER =
chmat
[cham_mater]
CARA_ELEM
=
carac
[cara_elem]
MATR_MASS
=
m
/
[matr_asse_DEPL_R]
/
[matr_asse_PRES_C]
/
[matr_asse_GENE_R]
MATR_RIGI
=
K
/
[matr_asse_DEPL_R]
/
[matr_asse_DEPL_C]
/
[matr_asse_PRES_C]
/
[matr_asse_GENE_R]
/
MATR_AMOR
=
C
/
[matr_asse_DEPL_R]
/
[matr_asse_PRES_C]
/
[matr_asse_GENE_R]
/AMOR_REDUIT = L
[l_R]
/LIST_AMOR
= C
[listr8]
MATR_IMPE_PHI
=
imp
/
[matr_asse_DEPL_R]
/
[matr_asse_GENE_R]
/
FREQ =
lf
[l_R]
/
LIST_FREQ
=
cf
[listr8]
/
TOUT_CHAM
=
“YES”
[DEFECT]
/
NOM_CHAM =
|
“DEPL”
|
“QUICKLY”
|
“ACCE”
/
SENSITIVITY = (
… to see [U4.50.02]….
)
EXCIT=_F (
/
VECT_ASSE = vecti
/[cham_no_DEPL_R]
/
[cham_no_PRES_C]
/
[vect_asse_GENE]
/
CHARGE
=
chi [char_meca]
TYPE_CHARGE
=
“FIXES”
[DEFECT]
/FONC_MULT_C = hci
[fonction_C]
/COEF_MULT_C = aci
[C]
/
FONC_MULT
=
hi
[function, formula]
/
COEF_MULT
=
have
[R]
PHAS_DEG
=
/
0.
[DEFECT]
/
I
[R]
PUIS_PULS
=/0 [DEFECT]
/
nor
[Is]
)
TITRATE
=
tx
[l_Kn]
);
if MATR_RIGI = [matr_asse_DEPL_R]
then [*] dyna_harmo
[matr_asse_DEPL_C]
dyna_harmo
[matr_asse_PRES_C]
acou_harmo
[matr_asse_GENE_R]
harm_gene
Code_Aster
®
Version
7.4
Titrate:
Operator
DYNA_LINE_HARM
Date:
17/02/05
Author (S):
H. ANDRIAMBOLOLONA,
O. NICOLAS
Key
:
U4.53.11-G
Page
:
3/8
Instruction manual
U4.5- booklet: Methods of resolution
HT-66/05/004/A
3 Recalls
3.1
Equation of dynamic behavior under harmonic excitation
The damping of the structure can be viscous or hysteretic [U1.01.05] [R5.05.04].
This operator solves the equation:
(
)
{}
()
-
-
+
+
=
=
J
J
F
P
I
K
J
I
N
J
I
I
I
3
2
180
1
I
M
C K X
G
E
H ()
E
where
K
represent a matrix
of rigidity (real or complex),
M
represent a matrix
of mass,
C
represent a matrix
of damping,
I
represent a matrix
of acoustic impedance resulting from a formulation in
displacement-pressure-potential,
P
is a point running of the structure.
3.2 Damping
hysteretic
This operator also allows to calculate the harmonic response of a structure with
damping hysteretic.
(
)
()
K
M X
G
.
.e
. ()
-
=
=
2
1
180
H
F
P
I
N
J
I
I
K
I
I
with
K
stamp complex rigidity.
For detailed examples, one will refer to the document [U1.05.01].
This operator is usable in imposed force and imposed (relative reference frame or absolute).
Code_Aster
®
Version
7.4
Titrate:
Operator
DYNA_LINE_HARM
Date:
17/02/05
Author (S):
H. ANDRIAMBOLOLONA,
O. NICOLAS
Key
:
U4.53.11-G
Page
:
4/8
Instruction manual
U4.5- booklet: Methods of resolution
HT-66/05/004/A
4 Operands
4.1 Operand
MODEL
MODEL = Mo
Name of the concept defining the model whose elements are the subject of harmonic calculation.
4.2 Operand
CHAM_MATER
CHAM_MATER = chmat
Name of the concept defining the affected material field on the model
Mo
.
4.3 Operand
CARA_ELEM
CARA_ELEM = carac
Name of the concept defining the characteristics of the elements of beam, hulls, etc…
4.4 Operand
MATR_MASS
MATR_MASS = m
Name of the concept stamps assembled corresponding to the matrix of mass of the system.
4.5 Operand
MATR_RIGI
MATR_RIGI = K
Name of the concept stamps assembled corresponding to the matrix of rigidity of the system.
4.6 Operand
MATR_AMOR
/
AMOR_REDUIT
/
LIST_AMOR
/MATR_AMOR = C
Name of the concept stamps assembled corresponding to the matrix of viscous damping of
system.
/AMOR_REDUIT = L
List of all reduced depreciation: (
1
,
2
,…,
N
).
/LIST_AMOR = C
Name of the concept of the type
listr8
containing the list of reduced depreciation.
4.7 Operand
MATR_IMPE_PHI
MATR_IMPE_PHI = imp
Name of the concept stamps assembled corresponding to the matrix of impedance for a system
fluid-structure whose formulation is in displacement-pressure-potential (
U,
p
) [R4.02.02].
Code_Aster
®
Version
7.4
Titrate:
Operator
DYNA_LINE_HARM
Date:
17/02/05
Author (S):
H. ANDRIAMBOLOLONA,
O. NICOLAS
Key
:
U4.53.11-G
Page
:
5/8
Instruction manual
U4.5- booklet: Methods of resolution
HT-66/05/004/A
4.8 Operands
FREQ/LIST_FREQ
/
FREQ = lf
List of all the frequencies of calculation: (
f1, f2,…, fn
).
/
LIST
_FREQ = cf
Name of the concept of the type
listr8
containing the list of the frequencies of calculation.
4.9 Operands
TOUT_CHAM
/
NOM_CHAM
/
TOUT_CHAM =
“YES”
/
NOM_CHAM =
|
“DEPL”
|
“QUICKLY”
|
“ACCE”
Choice of the fields to calculate to represent the answer: displacement, speed,
acceleration or three.
4.10 Operands
SENSIBLITE
/
SENSITIVITY =
Activate the calculation of derived from the field from displacement, speed and acceleration compared to
a significant parameter of the problem.
The document [U4.50.01] specifies the operation of the key word.
4.11 Word
key
EXCIT
EXCIT
Operand allowing to define several excitations. Maybe by indicating an assembled vector
agent with a loading, is loads which will lead to the calculation and the assembly of one
second member. For each occurrence of the key word factor, one defines a component of
the excitation in the form (
H () ()
F
P
G
,
phase).
4.11.1 Operands
VECT_ASSE/LOAD/TYPE_CHARGE
Allow to define
G ()
P
) space discretization of the loading, in the form of a field with
nodes corresponding to one or more loads of force or imposed movement.
/
VECT_ASSE = vecti
Name of the concept produced by:
·
the operator
ASSE_VECTEUR
in imposed force or imposed of
displacement in an absolute reference frame. The amplitudes of the excitation can be
defined in the concepts of the type charges corresponding,
·
the operator
CALC_CHAR_SEISME
moving imposed displacement, speed
or acceleration corresponding to the vector assembled in a relative reference frame: in
this case the loads should contain only conditions kinematics (
DDL_IMPO
of zero value).
/
CHARGE = chi
chi
name of the concept of loading specified by I
ème
occurrence of
EXCIT
.
TYPE_CHARGE = “FIXES”
Is there only to use the routines of the non-linear one.
Code_Aster
®
Version
7.4
Titrate:
Operator
DYNA_LINE_HARM
Date:
17/02/05
Author (S):
H. ANDRIAMBOLOLONA,
O. NICOLAS
Key
:
U4.53.11-G
Page
:
6/8
Instruction manual
U4.5- booklet: Methods of resolution
HT-66/05/004/A
4.11.2 Operands
FONC_MULT_C
/
COEF_MULT_C
/
FONC_MULT
/
COEF_MULT
Allow to define
H ()
F
law of evolution, complex or real, of the frequency, applied to
all components of the field to the node associated with this occurrence. Several possibilities
are offered:
/
FONC_MULT_C = hci
Name of the concept of the type
fonction_C
defining a function
H ()
F
complex of
frequency
F
,
/
COEF_MULT_C = aci
Coefficient complexes multiplying loading, independent of the loading,
/
FONC_MULT = hi
Concept of the type
function
defining a function
H ()
F
real of the frequency
F
,
/
COEF_MULT = have
Multiplying real coefficient of the loading, independent of the loading.
4.11.3 Operand
PUIS_PULS
PUIS_PULS = nor
Allows to define the power of the pulsation when the loading is a function of the frequency
nor
=
(2
F
)
nor
;
by defect
nor
= 0.
4.11.4 Operand
PHAS_DEG
PHAS_DEG =
I
Allows to define the phase of each component of the excitation in degrees compared to one
single reference of phase; by defect
I
= 0.
4.11.5 Notice
For a problem with imposed movement, one defines the locked degrees of freedom (conditions
kinematics preliminary to the construction of
cham_no
); one can then choose an excitation:
·
in imposed displacement N = 0,
= 0°
·
in imposed speed N = 1,
= 90°
·
in imposed acceleration N = 2,
= 180°
4.12 Operand
TITRATE
TITRATE = tx
Titrate attached to the concept produced by this operator [U4.03.01].
Code_Aster
®
Version
7.4
Titrate:
Operator
DYNA_LINE_HARM
Date:
17/02/05
Author (S):
H. ANDRIAMBOLOLONA,
O. NICOLAS
Key
:
U4.53.11-G
Page
:
7/8
Instruction manual
U4.5- booklet: Methods of resolution
HT-66/05/004/A
5
Example of use in imposed force
# ----------------------------------------------------------------------
# REFERENCE: SFM/VPCS SDLD21 CONTROLS
# ----------------------------------------------------------------------
# SYSTEM MASSE-RESSORT A 8 DEGREES OF FREEDOM WITH DAMPING
# VISCOUS PROPORTIONAL (HARMONIC ANSWER)
# 9 SPRINGS 8 MASSES -- K =1.E+5 M =10 --
# ----------------------------------------------------------------------
BEGINNING (CODE=_F (NOM=' SDLD21A '),);
# ----------------------------------------------------------------------
MA = LIRE_MAILLAGE ();
MO =
AFFE_MODELE (MAILLAGE= MA,
AFFE= (_F (TOUT=' OUI', PHENOMENE=' MECANIQUE',
MODELISATION=' DIS_T',),
_F (GROUP_NO= MASSES, MODELISATION=' DIS_T',),),);
CARELEM = AFFE_CARA_ELEM (MODELE= MO,
DISCRET= (_F (GROUP_MA=
“SPRING”, CARA=' K_T_D_L',
VALE= (1.E+5,1., 1.),),
_F (GROUP_NO= MASSES, CARA=' M_T_D_N', VALE= 10.,),
_F (GROUP_MA=
DEADENED, CARA=' A_T_D_L',
VALE= (50., 1., 1.),),),),);
#
CH =AFFE_CHAR_MECA (MODELE= MO,
DDL_IMPO=
(_F (GROUP_NO=
“A_ET_B”,
DX=0., DY=0., DZ=0.,),
_F (GROUP_NO=
“MASS”,
DY=0., DZ=0.,),),
FORCE_NODALE=_F (
NOEUD=
“P4”,
FX=
1.,),);
MELR = CALC_MATR_ELEM (MODELE= MO, CHARGE= CH, OPTION=' RIGI_MECA',
CARA_ELEM=
CARELEM,
)
;
MELM = CALC_MATR_ELEM (MODELE= MO, CHARGE= CH, OPTION=' MASS_MECA',
CARA_ELEM=
CARELEM,
)
;
MELC = CALC_MATR_ELEM (MODELE= MO, CHARGE= CH, OPTION=' AMOR_MECA',
CARA_ELEM=
CARELEM,
)
;
VECT = CALC_VECT_ELEM (CHARGE= CH,
OPTION=' CHAR_MECA');
# ----------------------------------------------------------------------
NUM = NUME_DDL (MATR_RIGI= MELR,);
MATASSR = ASSE_MATRICE (MATR_ELEM= MELR, NUME_DDL= NUM,);
MATASSM = ASSE_MATRICE (MATR_ELEM= MELM, NUME_DDL= NUM,);
MATASSC = ASSE_MATRICE (MATR_ELEM= MELC, NUME_DDL= NUM,);
VECTASS = ASSE_VECTEUR (VECT_ELEM= VECT, NUME_DDL= NUM,);
# ------------------------------------------------------------------
# EXCITATION BY a SINUSOIDAL FORCE Of CRETE AMPLITUDE FX = 1.N
# AT THE P4 POINT
# (AMPLITUDE INDEPENDENT OF THE FREQUENCY)
LIFREQ = DEFI_LIST_REEL (DEBUT=5.,
INTERVALLE=_F (JUSQU_A=40., NOMBRE=70,),);
DYNAHARM = DYNA_LINE_HARM
(MATR_MASSE= MATASSM, MATR_RIGI= MATASSR, MATR_AMOR= MATASSC,
LIST_FREQ = LIFREQ, EXCIT=_F (VECT_ASSE= VECTASS, COEF_MULT= 1.,)
,
);
IMPR_RESU (MODELE=MO, RESU=_F (RESULTAT= DYNAHARM,),);
END ();
Code_Aster
®
Version
7.4
Titrate:
Operator
DYNA_LINE_HARM
Date:
17/02/05
Author (S):
H. ANDRIAMBOLOLONA,
O. NICOLAS
Key
:
U4.53.11-G
Page
:
8/8
Instruction manual
U4.5- booklet: Methods of resolution
HT-66/05/004/A
Intentionally white left page.