Code_Aster ®
Version
7.4
Titrate:
Operator MODE_ITER_INV
Date:
31/01/05
Author (S):
E. BOYERE, O. BOITEAU Key
:
U4.52.04-H Page
: 1/14
Organization (S): EDF-R & D/AMA, SINETICS
Handbook of Utilization
U4.5- booklet: Methods of resolution
Document: U4.52.04
Operator MODE_ITER_INV
1 Goal
To calculate clean values and vectors by the method of the iterations opposite. The case of the problem
generalized (calculation of the dynamic type without damping or buckling type of Euler) and the case of
quadratic problem (calculation of the dynamic type with damping) are dealt with. Product a concept
mode_meca_ * (dynamic case) or mode_flamb (case buckling of Euler).
Handbook of Utilization
U4.5- booklet: Methods of resolution
HT-66/05/004/A
Code_Aster ®
Version
7.4
Titrate:
Operator MODE_ITER_INV
Date:
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Author (S):
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:
U4.52.04-H Page
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2 Syntax
mode
[*] = MODE_ITER_INV
# MODAL FACT OF THE CASE
(
MATR_A
=
With
/
[matr_asse_DEPL_R]
/
[matr_asse_PRES_R]
/
[matr_asse_GENE_R]
MATR_B
=
B
/
[matr_asse_DEPL_R]
/
[matr_asse_PRES_R]
/
[matr_asse_GENE_R]
MATR_C
= C
[matr_asse_DEPL_R]
# STANDARD OF PROBLEM
TYPE_RESU
=
/
“DYNAMIQUE”
[DEFAUT]
/
“MODE_FLAMB”
# PHASE HEURISTIC
# STANDARD OF MODAL CALCULATION
CALC_FREQ = _F (OPTION
=/“PROCHE”
/“SEPARE”
/“AJUSTE”
[DEFAUT]
NMAX_FREQ
=
/
0
[DEFAUT]
/
nf
[I]
#
IF TYPE_RESU = “DYNAMIC”
FREQ
=
lfreq
[l_R]
AMOR_REDUIT = lamor
[l_R]
#
IF TYPE_RESU = “MODE_FLAMB”
CHAR_CRIT
=
lcharc
[l_R]
#
IF OPTION = “SEPARE” or “AJUSTE”
NMAX_ITER_SEPARE
=
/
30
[DEFAUT]
/
nis
[I]
PREC_SEPARE
=
/
1.E-4
[DEFAUT]
/
PS
[R]
#
IF OPTION = “ADJUSTS”
NMAX_ITER_AJUSTE
=
/
15
[DEFAUT]
/
denied
[I]
PREC_AJUSTE
:
/
1.E-4
[DEFAUT]
/Pa
[R]
# SENSIBILITE
SENSIBILITE = (
… to see [U4.50.02]….
)
Handbook of Utilization
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Code_Aster ®
Version
7.4
Titrate:
Operator MODE_ITER_INV
Date:
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Author (S):
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:
U4.52.04-H Page
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# FOR PREPROCESSINGS
SEUIL_FREQ
=
/
1.E-2
[DEFAUT]
/
sf
[R]
PREC_SHIFT
=
/
0.05 [DEFAUT]
/
PS
[R]
NMAX_ITER_SHIFT
=/5 [DEFAUT]
/
NS
[I]
NPREC_SOLVEUR
=
/
8
[DEFAUT]
/
ndeci
[I]
)
# PHASE ITERATIONS OPPOSITE
CALC_MODE = _F (OPTION
=/“DIRECT”
[DEFAUT]
/“RAYLEIGH”
NMAX_ITER
=/30 [DEFAUT]
/nim [I]
PREC
=
/1.E-5
[DEFAUT]
/pm
[R]
)
# FOR FINAL VERIFIVATION
VERI_MODE = _F (STOP_ERREUR
=
/
“OUI”
[DEFAUT]
/
“NON”
SEUIL
=/
1.E-2
[DEFAUT]
/R
[R]
)
# DIVERS
INFO
=
/
1
[DEFAUT]
/2
TITER
= Ti
[l_Kn]
);
# GIVEN RESULT
If TYPE_RESU = “MODE_FLAMB”
then [*]
- >
mode_flamb
If MATR_C= [matr_asse_DEPL_R]
then [*]
- >
mode_meca_C
If MATR_A= [matr_asse_DEPL_R]
then [*]
- >
mode_meca
If MATR_A= [matr_asse_PRES_R]
then [*]
- >
mode_acou
If MATR_A= [matr_asse_GENE_R]
then [*]
- >
mode_gene
Handbook of Utilization
U4.5- booklet: Methods of resolution
HT-66/05/004/A
Code_Aster ®
Version
7.4
Titrate:
Operator MODE_ITER_INV
Date:
31/01/05
Author (S):
E. BOYERE, O. BOITEAU Key
:
U4.52.04-H Page
: 4/14
3 Operands
3.1 Principles
This operator solves the problem generalized with the eigenvalues according to [R5.01.01]:
To find (, X) such as Ax = Bx, X 0, where A and B are symmetrical matrices with coefficients
realities. This type of problem corresponds, in mechanics, in particular with:
·
The study of the free vibrations of a not deadened and nonrevolving structure. For this
structure, one seeks the smallest eigenvalues or those which are in one
interval given to know if an exiting force can create a resonance. In this case,
matrix A is the matrix of material rigidity, noted K, (possibly increased
stamp geometrical rigidity noted kg, if the structure is prestressed) and B is the matrix
of mass or noted inertia Mr. Les eigenvalues obtained are the squares of the pulsations
associated the sought frequencies.
The system to be solved can be written: (K + K
where = () 2
2 F is the square of
G) X = {
MX
4
1 4
2 3
B
With
pulsation, F the Eigen frequency and X the vector of associated clean displacement.
·
The search for linear mode of buckling. Within the framework of the linearized theory, in
supposing a priori that the phenomena of stability are suitably described by
system of equations obtained by supposing the linear dependence of displacement by
report/ratio at the level of critical load, the search of the mode of buckling X associated it
level of critical load µ = -, brings back itself to a problem generalized to the eigenvalues
form: (K + µ K
=
=
with K stamps material rigidity and
G) X
0
{
Kx
K X
{G
With
B
Kg stamps geometrical rigidity.
Caution:
In the code, one treats only the eigenvalues of the generalized problem, them. For
to obtain the true critical loads, the µ, it is necessary to multiply them by 1.
This operator allows also the study of the dynamic stability of an involved structure
gyroscopic depreciation and effects. That led to the resolution of a modal problem
of a nature higher, known as quadratic [R5.01.02]. Clean values and vectors then are sought
complexes by the method of Lanczos after having carried out a linear reduction of the problem.
·
The problem consists in finding (, X) (C, C NR) such as (2B + C + A) X = 0 where
typically, in linear mechanics, A will be the matrix of rigidity, B the matrix of mass and
C the matrix of damping. The matrices A, B and C are matrices with coefficients
realities. The eigenvalue complexes is connected to the Eigen frequency F and damping
reduced by: = (2) ± (2) 1 - 2
F
I
F
.
Handbook of Utilization
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Code_Aster ®
Version
7.4
Titrate:
Operator MODE_ITER_INV
Date:
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Author (S):
E. BOYERE, O. BOITEAU Key
:
U4.52.04-H Page
: 5/14
To solve these generalized or quadratic modal problems, Code_Aster proposes
various approaches. Beyond their numerical specificities and functional calculuses which are taken again
in the document [R5.01.01], one can synthesize them in the shape of table below (the values
by defect are materialized in fat).
Operator/
Algorithm Key word Advantages
Disadvantages
Perimeter
of application
MODE_ITER_INV
1ère phase
(heuristics)
Calculation of some
Bisection
“SEPARE”
modes
Calculation of some
Bisection +
“AJUSTE”
Better precision
Cost calculation
modes
Secant (gene.)
Muller (quad.)
Improvement of
Initialization by
“PROCHE”
Resumption of values
No the capture
some estimates
the user
clean estimated
of multiplicity
by another
process.
Cost calculation of this
phase quasi-no one
2nd phase
(method of
powers properly
said)
Basic method
Powers
“DIRECT”
Very good
Not very robust
opposite
construction of
clean vectors
Option of acceleration
Quotient of
“RAYLEIGH”
Improve
Cost calculation
Rayleigh
convergence
Not carried in
quadratic
MODE_ITER_SIMULT
Calculation of part of
Bathe & Wilson
“JACOBI”
Little
robust
spectrum
Not carried in
quadratic
Lanczos
“TRI_DIAG”
Little
robust
(Newman- Pipano)
IRAM
(Sorensen)
Increased “SORENSEN” Robustesse. Not carried in
Better
quadratic
calculation complexities
and memory.
Control
quality of the modes.
Table 3.1-1: Summary of the modal methods of Code_Aster
When it is a question of determining some simple eigenvalues discriminated well or to refine
some estimates, operator MODE_ITER_INV, is often clearly shown. On the other hand, for
to capture a part significant of the spectrum, one A resorts to MODE_ITER_SIMULT, via the methods
known as “of subspace”.
It is the first class of method which will interest us here.
It consists in coupling a heuristic phase of localization of the eigenvalues (determination
of an approximate value of each eigenvalue contained in an interval given by one
technique of bisection, refined or not, by a method of the secant, in generalized, or by
a method of Muller into quadratic), with a phase of iterations opposite itself
(accelerated by a quotient of Rayleigh or not), which will improve these estimates all in
exhuming the associated clean vectors.
Handbook of Utilization
U4.5- booklet: Methods of resolution
HT-66/05/004/A
Code_Aster ®
Version
7.4
Titrate:
Operator MODE_ITER_INV
Date:
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Author (S):
E. BOYERE, O. BOITEAU Key
:
U4.52.04-H Page
: 6/14
It is completely recommended besides to benefit from the strong points of the two classes from
method by refining the clean vectors obtained by MODE_ITER_SIMULT, via
MODE_ITER_INV (OPTION=' PROCHE'). That will make it possible to reduce the standard of the final residue
(cf [§3.6.2]).
Note:
One strongly advises a preliminary reading of the reference materials [R5.01.01]
[R5.01.02]. It gives to the user the properties and the limitations, theoretical and practical, of
modal methods approached while connecting these considerations, which can sometimes appear one
little éthérées, with a precise parameter setting of the options.
3.2 Operands
MATR_A, _B, _C
MATR_A
= A
Stamp assembly of the type [matr_asse_ * _R] of the system generalized or quadratic with
to solve.
MATR_B
= B
Stamp assembly of the type [matr_asse_ * _R] of the system generalized or quadratic with
to solve.
MATR_C
= C
Stamp assembly of the type [matr_asse_ * _R] of the quadratic system to solve.
3.3 Word
key
TYPE_RESU
TYPE_RESU =/“DYNAMIC”
[DEFAUT]
/“MODE_FLAMB”
This key word makes it possible to define the nature of the modal problem to treat: search for frequencies of
vibration (traditional case of dynamics with or without damping) or search for loads
critical (case of the theory of linear buckling). According to this class of membership, them
results are displayed and stored differently in the structure of data:
·
In dynamics, the frequencies are ordered by order ascending of the module of their
variation with the shift (cf [§2.9] [§4.4] [R5.01.01]). It is the value of the variable of access
NUM_ORDRE of the structure of data. The other variable of access, NUME_MODE, is equal to
the true modal position in the spectrum of the eigenvalue (determined by the test of
Sturm cf [§2.5] [§2.6] [R5.01.01]).
·
In buckling, the eigenvalues are stored by order ascending algebraic.
variables NUM_ORDRE and NUM_MODE take the same value equal to this command.
3.4 Word
key
CALC_FREQ
CALC_FREQ
=_F (…
Key word factor for the definition of the parameters of the first phase of calculation (localization of
eigenvalues).
For the generalized problem, the localization of the eigenvalues is generally carried out by one
dichotomic separation of the frequencies (for options “AJUSTE” and “SEPARE”), followed of one
method of the secant (for the option: “AJUSTE”).
For the quadratic problem, this localization is carried out by a resolution of the problem not
deadened (generalized problem) followed by a method of Muller (for the option: “AJUSTE”).
Handbook of Utilization
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Code_Aster ®
Version
7.4
Titrate:
Operator MODE_ITER_INV
Date:
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Author (S):
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:
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3.4.1 Operand
OPTION
OPTION
=
“PROCHE”
One seeks the mode to which the eigenvalue is closest to a given value. This
value is indicated by:
·
the argument lfreq of key word FREQ for a generalized problem of dynamic type
(TYPE_RESU = “DYNAMIC”).
·
the argument lcharc of key word CHAR_CRIT for a generalized problem of type
linear buckling (TYPE_RESU = “MODE_FLAMB”).
·
the arguments lfreq and lamor of key word FREQ and AMOR_REDUIT for a problem
quadratic of dynamic type (TYPE_RESU = “DYNAMIQUE”).
There is as many search of modes than of terms in this list (or these lists). If one
wish to calculate a multiple mode, one should not use this option because only one will be found
only mode.
“SEPARE”
One separates the eigenvalues by a method of bisection based on the criterion of Sturm.
The terminals of the interval of search are:
·
arguments of the list lfreq of key word FREQ for a generalized problem or
quadratic of dynamic type (TYPE_RESU = “DYNAMIQUE”).
·
arguments of the list lcharc of key word CHAR_CRIT for a problem
generalized of linear buckling type (TYPE_RESU = “MODE_FLAMB”).
“AJUSTE”
[DEFAUT]
After having separated the Eigen frequencies, as for option “SEPARE” one carries out
additional iterations either by the method of the secant (generalized problem) or by
method of Muller (quadratic problem) to obtain a better precision on the value
clean.
3.4.2 Operand
FREQ
FREQ = lfreq
For a problem of search for eigenvalue of dynamic type (TYPE_RESU =
“DYNAMIQUE”), this key word corresponds to the list of the frequencies of which the use depends on
the selected OPTION.
If option “PROCHE”: it is the list of the frequencies whose one seeks the mode nearest.
The list has at least 1 element and is ordered by ascending order.
If option “SEPARE” or “AJUSTE”: they are the terminals of the intervals of search
FREQ: (f1, f2,…, fn-1, fn)
One will seek to separate the frequencies in the intervals
[f1, f2], [f2, f3]…. [fn-2, fn-1], [fn-1, fn]
The list has at least 2 elements. The frequencies are positive. It is checked that the frequencies
are given in the ascending order.
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:
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3.4.3 Operand
AMOR_REDUIT
AMOR_REDUIT = lamor
For the quadratic problem of dynamic type (TYPE_RESU = “DYNAMIQUE”), and if the option
PROCHE was chosen, one can initialize the method of the iterations opposite starting from a value
clean initial complex. To build this complex value, the list of the arguments is used
given under key words FREQ (list of frequencies) and AMOR_REDUIT (list of depreciation).
These two lists must have the same number of arguments.
3.4.4 Operand
CHAR_CRIT
CHAR_CRIT = lcharc
For a problem of search for eigenvalue of buckling type of Euler
(TYPE_RESU = “MODE_FLAMB”), this key word corresponds to the list of the critical loads of which
the use depends on the selected OPTION.
If option “PROCHE”: it is the list of the critical loads whose one seeks the mode more
near. The list has at least 1 element.
If option “SEPARE” and “AJUSTE”: they are the terminals of the intervals of search
CHAR_CRIT: (1, 2,…, n-1, N)
One will seek to separate the critical loads in the intervals
[1, 2], [2, 3]…. [N2, n-1], [n-1, N]
The list has at least 2 elements. The critical loads are negative or positive. One checks
that the critical loads are given in the ascending order.
3.4.5 Operand
NMAX_FREQ
NMAX_FREQ = nf
(0)
[DEFAUT]
Numbers maximum eigenvalues to calculate. This operand is ignored for the option
“PROCHE”.
For the other options, if the user does not inform this key word, all eigenvalues
contained in the intervals specified by the user are calculated. If not, NMAX_FREQ
first eigenvalues, therefore lowest, are calculated
3.4.6 Operands of the bisection (if OPTION = “SEPARE” or “AJUSTE”)
NMAX_ITER_SEPARE = nis
(30)
[DEFAUT]
PREC_SEPARE
= PS
(1.10-4)
[DEFAUT]
Parameters of adjustment of the iteration count and the precision of separation for
dichotomizing search. These operands are ignored for option “PROCHE” (Cf. [R5.01.01
§3.2.1]).
Note:
At the time of the first passages, it is strongly advised not to modify these parameters which
the mysteries of the algorithm concern rather and which are initialized empirically with values
standards.
Handbook of Utilization
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Code_Aster ®
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Titrate:
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Date:
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:
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3.4.7 Operands of the secant (if OPTION = “AJUSTE”)
NMAX_ITER_AJUSTE
=
denied
(15)
[DEFAUT]
PREC_AJUSTE =
Pa (1.10-4)
[DEFAUT]
Parameters of adjustment of the iteration count and the precision of separation for the method
secant. These operands are used only for option “AJUSTE” (Cf. [R5.01.01 §3.2.2]).
Note:
At the time of the first passages, it is strongly advised not to modify these parameters which
the mysteries of the algorithm concern rather and which are initialized empirically with values
standards.
3.4.8 Operands
SEUIL_FREQ, PREC_SHIFT and NMAX_ITER_SHIFT
PREC_SHIFT = PS
(0.05)
[DEFAUT]
SEUIL_FREQ = sf
(0.01)
[DEFAUT]
NMAX_ITER_SHIFT = NS
(5)
[DEFAUT]
For three possible options “PLUS_PETITE”, “BANDE” or “CENTER”, one carries out one
2
factorization LDLT of matrix (A - (2 F *) B). F * depends on the method used. If F * is
detected as being an Eigen frequency or being located near Eigen frequencies
(loss of more than decimal ndeci=8 during the factorization of the matrices), the frequency F * is
then modified (cf §2.6 and 2.9 [R5.01.01]):
F -
F
(1 PS) or F +
=
× -
= F × (1+ PS
*
*
*
*
)
2
If (A - (2 F *) B) is not factorisable LDLT and (F
sf
*
), one carries out
following modification: F - = - sf
*
. It is considered whereas F * is associated a mode of body
rigid. The modification of this frequency makes it possible a priori to enter all the modes of
rigid body. One does not carry out more NS modifications of the value F *.
In the case of linear buckling, the transposition is immediate by replacing F * (frequency
2
2
of vibration) by * (critical load), (2 F *) by * and sf by (2 sf).
Note:
At the time of the first passages, it is strongly advised not to modify these parameters which
the mysteries of the algorithm concern rather and which are initialized empirically with values
standards.
Handbook of Utilization
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Titrate:
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Date:
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:
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3.4.9 Operand
NPREC_SOLVEUR
NPREC_SOLVEUR
= ndeci (8)
[DEFAUT]
ndeci represents the number of decimals which one is authorized to lose during the factorization of
2
stamp shiftée (A - (2 F *) B) or (A - B). If one loses more decimal ndeci, the matrix
is regarded as noninvertible (cf [§2.6] and [§2.9] [R5.01.01]).
Note:
At the time of the first passages, it is strongly advised not to modify this parameter which
rather relate to a mystery of the algorithm and which is initialized empirically with a value
standard.
3.5 Word
key
CALC_MODE
CALC_MODE
=_F (…
Key word factor for the definition of the parameters of calculation of the second phase of calculation
(method of the powers opposite).
3.5.1 Operand
OPTION
OPTION
=
Definition of alternative for the opposite iteration itself (cf [R5.01.01 §3.3]):
“DIRECT”
Iteration reverses standard (only allowed option for the problem
[DEFAUT]
quadratic),
“RAYLEIGH”
Iteration reverses with quotient of Rayleigh (without effect on the problem
quadratic).
3.5.2 Operand
NMAX_ITER
NMAX_ITER = nim
(30)
[DEFAUT]
Numbers maximum iterations for the search of the clean vectors.
3.5.3 Operand
PREC
PREC = pm
(1.10-5)
[DEFAUT]
The iteration continues as much as the relative variation of standard on the clean modes, between two reiterated,
is higher than pm.
3.6 Operands
SENSIBLITE
SENSIBILITE =
Activate the calculation of derived from the modes compared to a significant parameter of the problem.
It is it should be noted that at present, the derivative of the multiple modes is not available, because it
pose theoretical and practical problems particular.
The document [U4.50.02] specifies the operation of the key word.
Handbook of Utilization
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:
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3.7 Word
key
VERI_MODE
VERI_MODE = _F (…
Key word factor for the definition of the parameters of the checking of the clean modes ([§2.9]
[R5.01.01]).
Note:
·
At the time of the first passages, it is strongly advised not to modify these parameters which
the mysteries of the algorithm concern rather and which are initialized empirically with
values standards.
·
Contrary to its alter-ego, MODE_ITER_SIMULT, this key word factor does not comprise
key word of type STURM and PREC_SHIFT. The phase of postprocessing and checking
do not comprise indeed a test of Sturm which would be redundant with the first part
heuristics. Methods of the type “power” being less robust than those of type
“subspace”, the default value of the threshold R is less demanding (10-2 instead of 10-6).
3.7.1 Operand
STOP_ERREUR
STOP_ERREUR =/
“OUI”
[DEFAUT]
/
“NON”
Allows to indicate to the operator if it must stop (“OUI”) or continue (“NON”) if
one of criteria SEUIL or STURM is not checked.
By defect the concept of output is not produced.
3.7.2 Operand
SEUIL
- 2
SEUIL = R (1.10
)
[DEFAUT]
Tolerance level for the standard of error relating of the mode to the top of which the mode is
regarded as forgery.
The standard of relative error of the mode is:
(A -)
B X 2, for 0 for the generalized problem and
Ax 2
(2B + C - A) X 2,
Ax
for the quadratic problem
2
3.8 Operand
INFO
INFO
=/
1
[DEFAUT]
/2
Indicate the level of impression in file MESSAGE.
1: Impression on file “MESSAGE” of the eigenvalues, their modal position, of
reduced damping, of the standard of error a posteriori and certain useful parameters
to follow the course of calculation.
2: Impression rather reserved for the developers.
3.9 Operand
TITER
TITER = Ti
Titrate attached to the concept produced by this operator [U4.03.01].
Handbook of Utilization
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:
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4 Phase
of execution
4.1 Checking
The matrices A and B (and C), arguments of key words MATR_A and MATR_B (and MATR_C), must
to be coherent between them (i.e. to be based on the same classification and the same mode of
storage).
The operator checks that for options “SEPARE” and “AJUSTE”, the list of the values of
arguments of key word FREQ has, at least, two terms.
It checks also a certain coherence of the parameters of the various algorithms.
4.2 Execution
For option “AJUSTE”, if separation is not possible and that in a given interval there is
more than one value of Eigen frequency, one does not apply the method of adjustment with this interval.
On the other hand, one will carry out during the calculation of the modes of the réorthogonalisations compared to
modes preceding contents in the interval (this makes it possible to calculate modes associated with one
multiple frequency).
For option “SEPARE”, having obtained an interval determining an Eigen frequency, one takes for
the calculation of the mode medium of the interval. During the calculation of the mode, the value of the Eigen frequency
is still refined. It is the result of the opposite iteration itself.
5
Modal parameters/Norme of the modes/Position modal
At output of this operator, the real or complex clean modes are standardized with largest
components which is not a multiplier of Lagrange. To choose another standard, it is necessary
to use command NORM_MODE [U4.52.11].
In the case of a dynamic calculation, the structure of data mode_meca_ *, contains, in addition to
frequencies of vibration and the associated modal deformations, the modal parameters (mass
generalized, generalized stiffness, factor of participation, mass effective). One will find the definition of
these parameters in [R5.01.03].
In the case of a linear calculation of buckling, the structure of data mode_flamb, only contains
critical loads and associated deformations.
In the case of a dynamic calculation, the modal position of the modes corresponds to the position of the mode
in the whole of the spectrum defined by the matrices A and B.
In the case of a linear calculation of buckling, the modal positions of the critical loads are
allotted of 1 to nf (nf being the number of calculated critical loads) by classifying the loads
critical by order ascending in absolute value. All the modal positions are thus positive.
For option PROCHE, the positions modal are allotted of 1 to nf (nf being the number of values
clean calculated), by taking the eigenvalues in the order of the list indicated under FREQ or
CHAR_CRIT.
Handbook of Utilization
U4.5- booklet: Methods of resolution
HT-66/05/004/A
Code_Aster ®
Version
7.4
Titrate:
Operator MODE_ITER_INV
Date:
31/01/05
Author (S):
E. BOYERE, O. BOITEAU Key
:
U4.52.04-H Page
: 13/14
6
Impression of the results
To display the modal parameters associated with each mode and the co-ordinates with the modes, it is necessary
to use operator IMPR_RESU [U4.91.01] in the following way:
·
Display of the modal parameters only in the form of table:
IMPR_RESU
(RESU =_F (RESULTAT = mode,
TOUT_PARA
=
“OUI”,
TOUT_CHAM
=
“NON”
)
)
;
·
Display of the modal parameters and the clean vectors:
IMPR_RESU
(RESU =_F (RESULTAT = mode,
TOUT_PARA
=
“OUI”,
TOUT_CHAM
=
“OUI”
)
)
;
7 Examples
Are mass and rigidity two matrices beforehand assembled by operator ASSE_MATRICE
starting from elementary matrices of mass (OPTION = “MASS_MECA”) and of rigidity (OPTION =
“RIGI_MECA”).
One calculates the modes of Eigen frequency included/understood in tape 50 Hz with 150 Hz with the operator
MODE_ITER_INV as follows:
mode
= MODE_ITER_INV
(MATR_A= rigidity,
MATR_B= masses,
CALC_FREQ=_F
(
OPTION = “ADJUSTS”,
FREQ = (50. , 150. ))
);
One calculates the modes of Eigen frequency closest to frequencies 20 Hz and 50 Hz with
operator MODE_ITER_INV as follows:
mode
= MODE_ITER_INV
(MATR_A= rigidity,
MATR_B= masses,
CALC_FREQ=_F
(
OPTION = “NEAR”,
FREQ = (50. , 150. )),
CALC_MODE =_F (OPTION = “RAYLEIGH”)
);
The acceleration of convergence by using the coefficient of Rayleigh was selected.
Handbook of Utilization
U4.5- booklet: Methods of resolution
HT-66/05/004/A
Code_Aster ®
Version
7.4
Titrate:
Operator MODE_ITER_INV
Date:
31/01/05
Author (S):
E. BOYERE, O. BOITEAU Key
:
U4.52.04-H Page
: 14/14
8 Remarks
of use
The cost of this operator can be high bus:
·
each dichotomy requires a factorization (if OPTION = “SEPARE”),
·
each iteration of secant (if OPTION = “AJUSTE”) requires also a factorization.
It can be more judicious to make:
·
a search for eigenvalues by operator MODE_ITER_SIMULT [U4.52.03],
·
then to refine the results obtained by MODE_ITER_INV by using option “PROCHE” of
CALC_FREQ and the option “RAYLEIGH” of CALC_MODE to improve the clean vectors.
Handbook of Utilization
U4.5- booklet: Methods of resolution
HT-66/05/004/A
Outline document