Code_Aster
®
Version
7.0
Titrate:
SDLD313 - System mass-arises to 2 ddl (damping hysteretic)
Date:
23/06/03
Author (S):
O. NICOLAS
Key
:
V2.01.313-A
Page:
1/10
Manual of Validation
V2.01 booklet: Linear dynamics of the discrete systems
HT-66/03/008/A
Organization (S):
EDF-R & D/AMA
Manual of Validation
V2.01 booklet: Linear dynamics of the discrete systems
Document: V2.01.313
SDLD313 - System masses spring with 2 DDL with
damping hysteretic
Summary:
This one-way problem consists in carrying out a harmonic analysis of a mechanical structure
composed of a whole of mass-springs with damping hysteretic and subjected to an excitation
sinusoidal. This test of mechanics of the structures corresponds to a dynamic analysis of a discrete model
having a linear behavior. It includes/understands three modelings.
Via modeling A, one tests the discrete elements in translation (mass, arises), them
options
AMOR_HYST
of
AFFE_CARA_ELEM
.
Via modeling B, one tests the elements of beam (
POU_D_T
), options
AMOR_HYST
of
DEFI_MATERIAU
,
Via modeling C, one tests calculation modal (
MODE_ITER_SIMULT)
complex.
On the first two modelings, one tests the definition of a force of specific excitation harmonic and
the operator of harmonic calculation of answer (
DYNA_LINE_HARM
[U4.54.02]). In addition, several are tested
operators of postprocessing:
RECU_FONCTION
[U4.62.03],
TEST_FONCTION
[U4.72.02],
RECU_CHAMP
[U4.62.01].
Results obtained for the first two modelings (field of displacement for different
frequencies of excitation) are in concord with the results of guide VPCS. Results obtained for
the third modeling are in concord with the semi-analytical results.
Code_Aster
®
Version
7.0
Titrate:
SDLD313 - System mass-arises to 2 ddl (damping hysteretic)
Date:
23/06/03
Author (S):
O. NICOLAS
Key
:
V2.01.313-A
Page:
2/10
Manual of Validation
V2.01 booklet: Linear dynamics of the discrete systems
HT-66/03/008/A
1
Problem of reference
1.1 Geometry
We consider the system represented by the diagram below:
Specific masses:
m
1
& m
2
Stiffnesses of connection:
K
1
& K
2
Damping hysteretic:
1
&
2
1.2
Properties of material
Comes out from linear elastic translation
K
1
= 28000
NR/m
K
2
=
28000 NR/m
Specific mass
M
1
=
10 kg
M
2
=
5 kg
Damping hysteretic
1
=
0.1
2
=
0.0
1.3
Boundary conditions and loadings
Boundary conditions:
Points A, B, C embedded out of DY and DZ
Embedded points a: (DX = 0).
Loading: Force concentrated sinusoidal of variable frequency at the point C
NR
100
constant
Hz
21.0543
F
Hz
C
Not
0
=
=
=
=
0
0
2
sin
4
F
F
T
F
F
X
1.4 Conditions
initial
Without object for the study of the permanent harmonic mode.
m
1
X
1
X
2
m
2
K
1
(1+j *
1
)
K
2
(1+j *
2
)
WITH B C
Code_Aster
®
Version
7.0
Titrate:
SDLD313 - System mass-arises to 2 ddl (damping hysteretic)
Date:
23/06/03
Author (S):
O. NICOLAS
Key
:
V2.01.313-A
Page:
3/10
Manual of Validation
V2.01 booklet: Linear dynamics of the discrete systems
HT-66/03/008/A
2
Reference solution
2.1
Method of calculation
The system of differential equations of the second command coupled is form:
-
-
+
-
-
-
-
+
=
=
=
+
1
1
0
1
1
.
0
2
1
.
0
1
0
1
.
0
1
1
.
0
1
28000
and
5
0
0
0
10
0
0
0
0
with
J
J
J
J
K
M
F
U
K
U
M &&
The solution
with a harmonic excitation
F
=
F
0
E
J
T
J
2
= -
1
(
)
is form
U
=
U
0
E
J
T
, it
who leads to:
(
)
0
0
2
F
M
K
=
-
U
This system is solved for all
.
2.2
Sizes and results of reference
Displacement according to X of the point C for certain frequencies.
Eigen frequencies and damping reduced.
2.3
Uncertainties on the solution
Semi-analytical solution.
2.4 References
bibliographical
[1]
J. PIRANDA: Note of use of the software of modal analysis MODAN - Version 0.2 (1990).
Laboratory of Mechanics Applied - University of Frank County - Besancon (France).
Code_Aster
®
Version
7.0
Titrate:
SDLD313 - System mass-arises to 2 ddl (damping hysteretic)
Date:
23/06/03
Author (S):
O. NICOLAS
Key
:
V2.01.313-A
Page:
4/10
Manual of Validation
V2.01 booklet: Linear dynamics of the discrete systems
HT-66/03/008/A
3 Modeling
With
3.1
Characteristics of modeling
Discrete element of rigidity in translation
y
X
WITH B
C
Characteristics of the elements
DISCRETE
:
with nodal masses
M_T_D_N
and matrices of rigidity
K_T_D_L
Limiting conditions:
in all the nodes
DDL_IMPO:
(ALL:“YES” DY: 0. , DZ: 0. )
with the node end A
(GROUP_NO: WITH DX: 0. )
Names of the nodes:
Not A = N1
With
= N1
Not B = N2
B = N2
Not C = N3
C = N3
3.2
Characteristics of the mesh
A number of nodes: 3
A number of meshs and types: 2 SEG2
3.3 Functionalities
tested
Controls
DISCRETE AFFE_CARA_ELEM GROUP_MA
GROUP_MA
“K_T_D_L'
AMOR_HYST
“A_T_D_L'
AFFE_MODELE ALL
GROUP_NO
“MECHANICAL” “DIS_T'
“DIS_T'
AFFE_CHAR_MECA DDL_IMPO
FORCE_NODALE
GROUP_NO
NODE
DEFI_LIST_REEL BEGINNING
INTERVAL
RECU_FONCTION LIST_FREQ
Code_Aster
®
Version
7.0
Titrate:
SDLD313 - System mass-arises to 2 ddl (damping hysteretic)
Date:
23/06/03
Author (S):
O. NICOLAS
Key
:
V2.01.313-A
Page:
5/10
Manual of Validation
V2.01 booklet: Linear dynamics of the discrete systems
HT-66/03/008/A
3.4
Sizes tested and results
Parts real and imaginary of the component
DX
displacement of the point C.
Frequency Reference
Aster %
Difference
0.00
7.1075E-03
3.5360E-04
7.1074964639321E-03
3.5360678925035E-04
1.08E-04
3.36870E+00 9.388216E-03
7.31196E-04
9.3882649899583E-03
7.3120610001073E-04
5.31E-04
6.48480E+00 5.0269E-03
7.07103E-02
5.0349198344062E-03
7.0708581052416E-02
0.012
8.00060E+00 9.54931E-03
2.2154E-03
9.5490053525137E-03
2.2153458282190E-03
0.003
1.18746E+01 4.23259E-05
3.57193E-04
4.2266734408325E-05
3.5719325443817E-04
0.016
1.34747E+01 2.35524E-03
5.01765E-04
2.3552527130123E-03
5.0176685846530E-04
5.34E-04
1.55802E+01 1.6395374E-02
6.871471E-02
1.6420641488151E-02
6.8704047854161E-02
0.039
2.10543E+01 1.88977E-03
5.53314E-06
1.8897660707219E-03
5.5328629109043E-06
2.08E-04
3.5 Remarks
Contents of the file results:
Values of the displacement of the component
DX
point C for all the frequencies of 0 with
2.10543E+01Hz by pitch of 3.3687.
Code_Aster
®
Version
7.0
Titrate:
SDLD313 - System mass-arises to 2 ddl (damping hysteretic)
Date:
23/06/03
Author (S):
O. NICOLAS
Key
:
V2.01.313-A
Page:
6/10
Manual of Validation
V2.01 booklet: Linear dynamics of the discrete systems
HT-66/03/008/A
4 Modeling
B
4.1
Characteristics of modeling
Continuous element of beam type in traction
y
X
WITH B
C
Characteristics of the elements
DISCRETE
: masses
nodal
M_T_D_N
BEAM:
matrices of rigidity
POU_D_T
Limiting conditions:
in all the nodes
DDL_IMPO:
(ALL:“YES” DY: 0. , DZ: 0. )
with the node end A
(GROUP_NO: WITH DX: 0. )
Names of the nodes:
Not A = N1
With
= N1
Not B = N2
B = N2
Not C = N3
C = N3
4.2
Characteristics of the mesh
A number of nodes: 3
A number of meshs and types: 2 SEG2
4.3 Functionalities
tested
Controls
DISCRETE AFFE_CARA_ELEM
GROUP_MA “M_T_D_L'
DEFI_MATERIEU ELAS
AMOR_HYST
AFFE_MODELE ALL
GROUP_NO
“MECHANICAL” “POU_D_T'
“DIS_T'
AFFE_CHAR_MECA DDL_IMPO
FORCE_NODALE
GROUP_NO
NODE
CALC_MATR_ELEM RIGI_MECA_HYST
DEFI_LIST_REEL BEGINNING
INTERVAL
RECU_FONCTION LIST_FREQ
Code_Aster
®
Version
7.0
Titrate:
SDLD313 - System mass-arises to 2 ddl (damping hysteretic)
Date:
23/06/03
Author (S):
O. NICOLAS
Key
:
V2.01.313-A
Page:
7/10
Manual of Validation
V2.01 booklet: Linear dynamics of the discrete systems
HT-66/03/008/A
4.4
Sizes tested and results
Parts real and imaginary of the component
DX
displacement of the point C.
Frequency Reference
Aster %
Difference
0.00
7.1075E-03
3.5360E-04
7.1074964639321E-03
3.5360678925035E-04
1.08E-04
3.36870E+00 9.388216E-03
7.31196E-04
9.3882649899583E-03
7.3120610001073E-04
5.31E-04
6.48480E+00 5.0269E-03
7.07103E-02
5.0349198344064E-03
7.0708581052416E-02
0.012
8.00060E+00 9.54931E-03
2.2154E-03
9.5490053525137E-03
2.2153458282190E-03
0.003
1.18746E+01 4.23259E-05
3.57193E-04
4.2266734408325E-05
3.5719325443817E-04
0.016
1.34747E+01 2.35524E-03
5.01765E-04
2.3552527130123E-03
5.0176685846530E-04
5.34E-04
1.55802E+01 1.6395374E-02
6.871471E-02
1.6420641488152E-02
6.8704047854161E-02
0.039
2.10543E+01 1.88977E-03
5.53314E-06
1.8897660707219E-03
5.5328629109043E-06
2.08E-04
4.5 Remarks
Contents of the file results:
Values of the displacement of the component
DX
point C for all the frequencies of 0 with
2.10543E+01Hz by pitch of 3.3687.
Code_Aster
®
Version
7.0
Titrate:
SDLD313 - System mass-arises to 2 ddl (damping hysteretic)
Date:
23/06/03
Author (S):
O. NICOLAS
Key
:
V2.01.313-A
Page:
8/10
Manual of Validation
V2.01 booklet: Linear dynamics of the discrete systems
HT-66/03/008/A
5 Modeling
C
5.1
Characteristics of modeling
Discrete element of rigidity in translation
y
X
WITH B
C
Characteristics of the elements
DISCRETE
:
with nodal masses
M_T_D_N
and matrices of rigidity
K_T_D_L
Limiting conditions:
in all the nodes
DDL_IMPO:
(ALL:“YES” DY: 0. , DZ: 0. )
with the node end A
(GROUP_NO: WITH DX: 0. )
Names of the nodes:
Not A = N1
With
= N1
Not B = N2
B = N2
Not C = N3
C = N3
5.2
Characteristics of the mesh
A number of nodes: 3
A number of meshs and types: 2 SEG2
5.3 Functionalities
tested
Controls
DISCRETE AFFE_CARA_ELEM GROUP_MA
GROUP_MA
“K_T_D_L'
AMOR_HYST
“A_T_D_L'
AFFE_MODELE ALL
GROUP_NO
“MECHANICAL” “DIS_T'
“DIS_T'
AFFE_CHAR_MECA DDL_IMPO
FORCE_NODALE
GROUP_NO
NODE
MODE_ITER_SIMULT SORENSEN
“COMPLEX”
DEFI_LIST_REEL BEGINNING
INTERVAL
RECU_FONCTION LIST_FREQ
Code_Aster
®
Version
7.0
Titrate:
SDLD313 - System mass-arises to 2 ddl (damping hysteretic)
Date:
23/06/03
Author (S):
O. NICOLAS
Key
:
V2.01.313-A
Page:
9/10
Manual of Validation
V2.01 booklet: Linear dynamics of the discrete systems
HT-66/03/008/A
5.4
Sizes tested and results
Eigen frequencies and reduced depreciation.
Eigen frequencies:
Sequence number
Reference
Aster %
Difference
1
6.4537 6.44568
0.124
2 15.5806 1.55612
0.124
Reduced depreciation:
Sequence number
Reference
Aster %
Difference
1
0.05 0.05
1.39E-14
2 0.05 0.05
2.78E-14
Code_Aster
®
Version
7.0
Titrate:
SDLD313 - System mass-arises to 2 ddl (damping hysteretic)
Date:
23/06/03
Author (S):
O. NICOLAS
Key
:
V2.01.313-A
Page:
10/10
Manual of Validation
V2.01 booklet: Linear dynamics of the discrete systems
HT-66/03/008/A
6
Summary of the results
The results obtained are excellent.