Code_Aster ®
Version
7.4
Titrate:
Operator DYNA_LINE_HARM


Date:
17/02/05
Author (S):
H. ANDRIAMBOLOLONA, O. Key NICOLAS
:
U4.53.11-G Page
: 1/8

Organization (S): EDF-R & D/AMA

Handbook of Utilization
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.

Handbook of Utilization
U4.5- booklet: Methods of resolution
HT-66/05/004/A

Code_Aster ®
Version
7.4
Titrate:
Operator DYNA_LINE_HARM


Date:
17/02/05
Author (S):
H. ANDRIAMBOLOLONA, O. Key NICOLAS
:
U4.53.11-G Page
: 2/8

2 Syntax

harm [*]
= DYNA_LINE_HARM


(

MODELE
=
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
=
“OUI”
[DEFAUT]




/
NOM_CHAM = | “DEPL”










| “VITE”










| “ACCE”




/
SENSIBILITE = (
… 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
=
“FIXE”
[DEFAUT]







/FONC_MULT_C = hci
[fonction_C]







/COEF_MULT_C = aci
[C]







/
FONC_MULT
=
hi
[function, formula]







/
COEF_MULT
=
have
[R]







PHAS_DEG
=
/
0.
[DEFAUT]












/I
[R]







PUIS_PULS
=/0 [DEFAUT]
/
nor
[Is]






)



TITER
=
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
Handbook of Utilization
U4.5- booklet: Methods of resolution
HT-66/05/004/A

Code_Aster ®
Version
7.4
Titrate:
Operator DYNA_LINE_HARM


Date:
17/02/05
Author (S):
H. ANDRIAMBOLOLONA, O. Key NICOLAS
:
U4.53.11-G Page
: 3/8

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:

(


3
2
J
K

N
J
I


- J
I -
M + J C + K) {Xe} = H (F) I




180
E
G (P)
I
I


I = 1





where K represents 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 current point of the structure.

3.2 Damping
hysteretic

This operator also allows to calculate the harmonic response of a structure with
damping hysteretic.

(
K
I
K - M) X =
N
J
I
I ().
.e
2
180
H
F
.g (P)
I
with K stamps complex rigidity.
i=1

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).
Handbook of Utilization
U4.5- booklet: Methods of resolution
HT-66/05/004/A

Code_Aster ®
Version
7.4
Titrate:
Operator DYNA_LINE_HARM


Date:
17/02/05
Author (S):
H. ANDRIAMBOLOLONA, O. Key NICOLAS
:
U4.53.11-G Page
: 4/8

4 Operands

4.1 Operand
MODELE


MODELE = 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 listr8 type 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].
Handbook of Utilization
U4.5- booklet: Methods of resolution
HT-66/05/004/A

Code_Aster ®
Version
7.4
Titrate:
Operator DYNA_LINE_HARM


Date:
17/02/05
Author (S):
H. ANDRIAMBOLOLONA, O. Key NICOLAS
:
U4.53.11-G Page
: 5/8

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 listr8 type containing the list of the frequencies of calculation.

4.9 Operands
TOUT_CHAM/NOM_CHAM


/
TOUT_CHAM =
“OUI”

/
NOM_CHAM = | “DEPL”







| “VITE”







| “ACCE”

Choice of the fields to calculate to represent the answer: displacement, speed,
acceleration or three.

4.10 Operands
SENSIBLITE


/
SENSIBILITE =

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
correspondent 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) (
G P), 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:

·
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,
·
operator CALC_CHAR_SEISME moving imposed of 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 the ième occurrence of EXCIT.


TYPE_CHARGE = “FIXES”

Is there only to use the routines of the non-linear one.
Handbook of Utilization
U4.5- booklet: Methods of resolution
HT-66/05/004/A

Code_Aster ®
Version
7.4
Titrate:
Operator DYNA_LINE_HARM


Date:
17/02/05
Author (S):
H. ANDRIAMBOLOLONA, O. Key NICOLAS
:
U4.53.11-G Page
: 6/8

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, 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 fonction_C type 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 function type 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
ni= (2 F) nor; by defect ni= 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 blocked degrees of freedom (conditions
kinematics preliminary to the construction of the 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
TITER


TITER = tx

Titrate attached to the concept produced by this operator [U4.03.01].
Handbook of Utilization
U4.5- booklet: Methods of resolution
HT-66/05/004/A

Code_Aster ®
Version
7.4
Titrate:
Operator DYNA_LINE_HARM


Date:
17/02/05
Author (S):
H. ANDRIAMBOLOLONA, O. Key NICOLAS
:
U4.53.11-G Page
: 7/8

5
Example of use in imposed force

# ----------------------------------------------------------------------
# REFERENCE: SFM/VPCS SDLD21 COMMANDS
# ----------------------------------------------------------------------
# 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=
“MASSE”,
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,),);
FIN ();
Handbook of Utilization
U4.5- booklet: Methods of resolution
HT-66/05/004/A

Code_Aster ®
Version
7.4
Titrate:
Operator DYNA_LINE_HARM


Date:
17/02/05
Author (S):
H. ANDRIAMBOLOLONA, O. Key NICOLAS
:
U4.53.11-G Page
: 8/8

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Handbook of Utilization
U4.5- booklet: Methods of resolution
HT-66/05/004/A

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