Code_Aster ®
Version
4.0
Titrate:
SDLD02 Système mass-arises with 8 degrees of freedom
Date:
01/12/98
Author (S):
B. QUINNEZ
Key:
V2.01.002-E Page:
1/24
Organization (S): EDF/IMA/MN
Handbook of Validation
V2.01 booklet: Linear dynamics of the discrete systems
Document: V2.01.002
SDLD02 - Système mass-arises with 8 degrees
of freedom
Summary:
This two-dimensional problem consists in seeking the frequencies and the modes of vibration of a structure
mechanics made up of masses and springs. This case-test of Mécanique of Structures corresponds to one
analyze dynamic of a discrete model having a linear behavior.
This test allows a complete validation of the options of modeling of discrete rigidity and mass (without
finite elements) offered by command AFFE_CARA_ELEM [U4.24.01]. Four different modelings are
proposed: two modelings for the discrete elements in translation and two others for the elements
discrete in translation/rotation. In addition, various functionalities of commands MODE_ITER_INV
[U4.52.01] (calculation of values and clean vectors per iteration reverses), MODE_ITER_SIMULT [U4.52.02]
(calculation of the values and vectors clean by the method of Lanczos) and NORME_MODE [U4.64.02] (definition of
normalizes of a clean vector) are tested.
This test refers to a test VPCS, but it was modified. Indeed, the Code_Aster test directs the system
mechanics on an axis 3y = 4x, which makes it possible to validate the input of the data in local reference mark.
Handbook of Validation
V2.01 booklet: Linear dynamics of the discrete systems
HI-75/98/040 - Ind A

Code_Aster ®
Version
4.0
Titrate:
SDLD02 Système mass-arises with 8 degrees of freedom
Date:
01/12/98
Author (S):
B. QUINNEZ
Key:
V2.01.002-E Page:
2/24
1
Problem of reference
1.1 Geometry
U
U
1
2
U
U
3
8

With
m
m
m
m
B
X, U
K
K
K
K
P1
P2
P3
P8
Specific masses: mP = m = m = ...... = m = m
1
P2
P3
P8
Stiffnesses of connection: kAP1 = kP1P2 = kP2P3 = ...... = kP8B = K
1.2
Material properties
Comes out from linear elastic translation
K = 105 NR/m
Specific mass
m = 10 kg
1.3
Boundary conditions and loadings
Embedded points A and b: (U = 0).
1.4 Conditions
initial
Without object for the modal analysis.
Handbook of Validation
V2.01 booklet: Linear dynamics of the discrete systems
HI-75/98/040 - Ind A

Code_Aster ®
Version
4.0
Titrate:
SDLD02 Système mass-arises with 8 degrees of freedom
Date:
01/12/98
Author (S):
B. QUINNEZ
Key:
V2.01.002-E Page:
3/24
2
Reference solution
2.1
Method of calculation used for the reference solution
The reference solution is that given in card SDLD02/89 of the guide VPCS which presents
method of calculation in the following way:
The problem led to seek the eigenvalues and clean vectors of:
(Km
I)
I = 0
K
­ K

0





­ K 2k ­ K


m

K =
.

M =
.






­ K
2k
­ K

m



­ K
K




0
from where:
1
K
N +1- I
F =
I

cos
m

(n+) 1 2
I = 1, 2, ....., N
N = a number of masses
Ti calculated by resolution of the linear system.
2.2
Results of reference
the first 8 Eigen frequencies and the first and eighth clean vectors normalized such as:
T
Test V.P.C.S. provides modes normalized to M = 10. Normalized modes are presented:
·
T
with the unit generalized mass: M = 1; the components of reference are
divided by 10,
·
with the generalized stiffness what amounts dividing the preceding components by I,
· with the largest component of displacement.
2.3
Uncertainty on the solution
Analytical solution.
2.4 References
bibliographical
[1]
Mr. LALANNE, P. BERTHIER, J. DERHAGOPIAN. Mechanics of the linear vibrations. Paris:
MASSON, 2° edition, chapter 3, p. 100-101 (1986)
Handbook of Validation
V2.01 booklet: Linear dynamics of the discrete systems
HI-75/98/040 - Ind A

Code_Aster ®
Version
4.0
Titrate:
SDLD02 Système mass-arises with 8 degrees of freedom
Date:
01/12/98
Author (S):
B. QUINNEZ
Key:
V2.01.002-E Page:
4/24
3 Modeling
With
3.1
Characteristics of modeling
Discrete element of rigidity in translation DIS_T
Y
0.4
0.3
P
P
P
1
P
3
P
6
P
X
2
4
P5
7
P8
X
Characteristics of the elements:
ORIENTATION:
in all the nodes
with an angle = 53.130102°
DISCRET:
with nodal masses all nodes
M_T_D_N
in absolute reference mark
(m = 10.)
matrices of rigidity all meshs
K_T_D_L
in local reference mark
(Kx = 1. 105)
with the nodes ends
K_T_D_N
in local reference mark
(Kx = 1. 105)
Limiting conditions:
DDL_IMPO: (TOUT:“YES” DZ: 0. )
LIAISON_DDL: (such as 3Dy=4Dx in all the nodes)
Names of the nodes: P1, P2,…., P8
Not A = N1
= N2
3.2
Characteristics of the grid
A number of nodes: 8
A number of meshs and types: 7 SEG2
3.3 Functionalities
tested
Commands
Keys
AFFE_CARA_ELEM
DISCRET
GROUP_MA
“K_T_D_L'
[U4.24.01]
NOEUD
“K_T_D_N'
“M_T_D_N'
ORIENTATION
GROUP_NO
“ANG_NAUT”
AFFE_CHAR_MECA
DDL_IMPO
TOUT
[U4.25.01]
LIAISON_DDL
NOEUD
AFFE_MATERIAU
TOUT
[U4.23.02]
AFFE_MODELE
TOUT
“MECANIQUE”
“DIS_T'
[U4.22.01]
GROUP_NO
“DIS_T'
DEFI_MATERIAU
ELAS
[U4.23.01]
MODE_ITER_INV
CALC_FREQ
OPTION
“AJUSTE”
[U4.52.01]
FREQ
CALC_MODE
OPTION
“DIRECT”
RECU_CHAMP
“DEPL”
NUME_ORDRE
[U4.62.01]
FREQ
NORM_MODE
“MASS_GENE”
[U4.64.02]
NORM_MODE
“RIGI_GENE”
[U4.64.02]
Handbook of Validation
V2.01 booklet: Linear dynamics of the discrete systems
HI-75/98/040 - Ind A

Code_Aster ®
Version
4.0
Titrate:
SDLD02 Système mass-arises with 8 degrees of freedom
Date:
01/12/98
Author (S):
B. QUINNEZ
Key:
V2.01.002-E Page:
5/24
4
Results of modeling A
4.1 Values
tested
Identification
Reference
Aster
% Difference
tolerance
Number of the mode
valley. relative
clean
1
5.5274
5.5274
0.
10­4
2
10.8868
10.8868
-
-
3
15.9155
15.9155
-
-
4
20.4606
20.4606
-
-
5
24.3840
24.3840
-
-
6
27.5664
27.5664
-
-
7
29.9113
29.9113
-
-
8
31.3474
31.3474
-
-
Normalized mode with 1 with the largest component
Nature of the clean mode
Not
Reference
Aster
P1
­ 0.3473
­ 0.34729
P2
­ 0.6527
­ 0.65270
Translation 1
P3
­ 0.8793
­ 0.87938
(Dy)
P4
­ 1.
­ 1.

P5
­ 1.
­ 1.
1
P6
­ 0.8793
­ 0.87938
P7
­ 0.6527
­ 0.65270
P8
­ 0.3473
­ 0.34729
P1
0.3473
0.34729
P2
­ 0.6527
­ 0.65270
Translation 8
P3
0.8793
0.87938
(Dy)
P4
­ 1.
­ 1.

P5
1.
1.
8
P6
­ 0.8793
­ 0.87938
P7
0.6527
0.65270
P8
­ 0.3473
­ 0.34729
Maximum error lower than: 0.03%.
Handbook of Validation
V2.01 booklet: Linear dynamics of the discrete systems
HI-75/98/040 - Ind A

Code_Aster ®
Version
4.0
Titrate:
SDLD02 Système mass-arises with 8 degrees of freedom
Date:
01/12/98
Author (S):
B. QUINNEZ
Key:
V2.01.002-E Page:
6/24
Mode normalized with the unit generalized mass
Nature of the clean mode
Not
Reference
Aster
P1
­ 4.0781E2
­ 4.0788E2
P2
­ 7.6654E2
­ 7.6657E2
Translation 1
P3
­ 1.0327E1
­ 1.0327E1
(Dy)
P4
­ 1.1743E1
­ 1.1744E1

P5
­ 1.1743E1
­ 1.1744E1
1
P6
­ 1.0327E1
­ 1.0327E1
P7
­ 7.6654E2
­ 7.6657E2
P8
­ 4.0781E2
­ 4.0788E2
P1
4.0781E2
4.0788E2
P2
­ 7.6654E2
­ 7.6657E2
Translation 8
P3
1.0327E1
1.0328E1
(Dy)
P4
­ 1.1743E1
­ 1.1744E1

P5
1.1743E1
1.1744E1
8
P6
­ 1.0327E1
­ 1.0328E1
P7
7.6654E2
7.6657E2
P8
­ 4.0781E2
­ 4.0788E2
Maximum error lower than: 0.03%.
Mode normalized with the unit generalized stiffness
Nature of the clean mode
Not
Reference
Aster
P1
­ 1.1742E3
­ 1.1744E3
P2
­ 2.2072E3
­ 2.2072E3
Translation 1
P3
­ 2.9735E3
­ 2.9738E3
(Dy)
P4
­ 3.3813E3
­ 3.3817E3

P5
­ 3.3813E3
­ 3.3817E3
1
P6
­ 2.9735E3
­ 2.9738E3
P7
­ 2.2072E3
­ 2.2072E3
P8
­ 1.1742E3
­ 1.1744E3
P1
2.0705E4
2.0709E4
P2
­ 3.8918E4
­ 3.8920E4
Translation 8
P3
5.2432E4
5.2436E4
(Dy)
P4
­ 5.9621E4
­ 5.9628E4

P5
5.9621E4
5.9628E4
8
P6
­ 5.2432E4
­ 5.2436E4
P7
3.8918E4
3.8920E4
P8
­ 2.0705E4
­ 2.0709E4
Maximum error lower than: 0.03%.
Handbook of Validation
V2.01 booklet: Linear dynamics of the discrete systems
HI-75/98/040 - Ind A

Code_Aster ®
Version
4.0
Titrate:
SDLD02 Système mass-arises with 8 degrees of freedom
Date:
01/12/98
Author (S):
B. QUINNEZ
Key:
V2.01.002-E Page:
7/24
4.2 Remarks
Calculations carried out by:
MODE_ITER_INV
OPTION:“AJUSTE”
LIST_FREQ:(5., 10., 15., 20., 24., 27., 30., 32.)
CALC_MODE: (OPTION: “DIRECT”)
Contents of the file results:
the first 8 Eigen frequencies, clean vectors and modal parameters
4.3 Parameters
of execution
Version: 3.02.21
Machine: CRAY C90
System:
UNICOS 8.0
Obstruction memory:
8 megawords
Time CPU To use:
6 seconds
Handbook of Validation
V2.01 booklet: Linear dynamics of the discrete systems
HI-75/98/040 - Ind A

Code_Aster ®
Version
4.0
Titrate:
SDLD02 Système mass-arises with 8 degrees of freedom
Date:
01/12/98
Author (S):
B. QUINNEZ
Key:
V2.01.002-E Page:
8/24
5 Modeling
B
5.1
Characteristics of modeling
Discrete element of rigidity in translation DIS_T
Y
0.4
0.3
P
P
P
1
P
3
P
6
P
X
2
4
P5
7
P8
X
Characteristics of the elements:
ORIENTATION:
in all the nodes
with an angle = 53.130102°
DISCRET:
nodal masses all nodes
M_T_N
in absolute reference mark
(m = 10.)
matrices of rigidity all meshs
K_T_L
in local reference mark
(Kx = 1. 105)
with the nodes ends
K_T_N
in local reference mark
(Kx = 1. 105)
Limiting conditions:
DDL_IMPO: (TOUT:“YES” DZ: 0. )
LIAISON_DDL: (such as 3Dy=4Dx in all the nodes)
Names of the nodes: : P1, P2,…., P8
5.2
Characteristics of the grid
A number of nodes: 8
A number of meshs and types: 7 SEG2
5.3 Functionalities
tested
Commands
Keys
AFFE_CARA_ELEM
DISCRET
GROUP_MA
“K_T_L'
[U4.24.01]
NOEUD
“K_T_N'
“M_T_N'
ORIENTATION
GROUP_NO
“ANGL_NAUT”
AFFE_MODELE
TOUT
“MECANIQUE”
“DIS_T'
[U4.22.01]
GROUP_NO
“DIS_T'
MODE_ITER_SIMULT
METHODE
“TRI_DIAG”
[U4.52.01]
CALC_FREQ
OPTION
“PLUS_PETITE”
NMAX_FREQ
IMPR_STURM
FREQ_MIN
[U4.73.01]
FREQ_MAX
NORM_MODE
“MASS_GENE”
or
“RIGI_GENE”
[U4.64.02]
NORM_MODE
“AVEC_CMP”
or
“SANS_CMP”
[U4.64.02]
NORM_MODE
NOEUD
CMP
[U4.64.02]
NORM_MODE
“NORME”
“TRAN” or “EUCL”
or “EUCL_TRAN”
[U4.64.02]
Handbook of Validation
V2.01 booklet: Linear dynamics of the discrete systems
HI-75/98/040 - Ind A

Code_Aster ®
Version
4.0
Titrate:
SDLD02 Système mass-arises with 8 degrees of freedom
Date:
01/12/98
Author (S):
B. QUINNEZ
Key:
V2.01.002-E Page:
9/24
6
Results of modeling B
6.1 Values
tested
Identification
Reference
Aster
% Difference
tolerance
Number of the mode
valley. relative
clean
1
5.5274
5.5274
0.
10­4
2
10.8868
10.8868
-
-
3
15.9155
15.9155
-
-
4
20.4606
20.4606
-
-
5
24.3840
24.3840
-
-
6
27.5664
27.5664
-
-
7
29.9113
29.9113
-
-
8
31.3474
31.3474
-
-
Normalized mode with 1 with the largest component
Nature of the clean mode
Not
Reference
Aster
P1
­ 0.3473
­ 0.34729
P2
­ 0.6527
­ 0.65270
Translation 1
P3
­ 0.8793
­ 0.87938
(Dy)
P4
­ 1.
­ 1.

P5
­ 1.
­ 1.
1
P6
­ 0.8793
­ 0.87938
P7
­ 0.6527
­ 0.65270
P8
­ 0.3473
­ 0.34729
P1
0.3473
0.34729
P2
­ 0.6527
­ 0.65270
Translation 8
P3
0.8793
0.87938
(Dy)
P4
­ 1.
­ 1.

P5
1.
1.
8
P6
­ 0.8793
­ 0.87938
P7
0.6527
0.65270
P8
­ 0.3473
­ 0.34729
Maximum error lower than: 0.03%.
Handbook of Validation
V2.01 booklet: Linear dynamics of the discrete systems
HI-75/98/040 - Ind A

Code_Aster ®
Version
4.0
Titrate:
SDLD02 Système mass-arises with 8 degrees of freedom
Date:
01/12/98
Author (S):
B. QUINNEZ
Key:
V2.01.002-E Page:
10/24
Mode normalized with the unit generalized mass
Nature of the clean mode
Not
Reference
Aster
P1
­ 4.0781E2
­ 4.0788E2
P2
­ 7.6654E2
­ 7.6657E2
Translation 1
P3
­ 1.0327E1
­ 1.0327E1
(Dy)
P4
­ 1.1743E1
­ 1.1744E1

P5
­ 1.1743E1
­ 1.1744E1
1
P6
­ 1.0327E1
­ 1.0327E1
P7
­ 7.6654E2
­ 7.6657E2
P8
­ 4.0781E2
­ 4.0788E2
P1
4.0781E2
4.0788E2
P2
­ 7.6654E2
­ 7.6657E2
Translation 8
P3
1.0327E1
1.0328E1
(Dy)
P4
­ 1.1743E1
­ 1.1744E1

P5
1.1743E1
1.1744E1
8
P6
­ 1.0327E1
­ 1.0328E1
P7
7.6654E2
7.6657E2
P8
­ 4.0781E2
­ 4.0788E2
Maximum error lower than: 0.03%.
Mode normalized with the unit generalized stiffness
Nature of the clean mode
Not
Reference
Aster
P1
­ 1.1742E3
­ 1.1744E3
P2
­ 2.2072E3
­ 2.2072E3
Translation 1
P3
­ 2.9735E3
­ 2.9738E3
(Dy)
P4
­ 3.3813E3
­ 3.3817E3

P5
­ 3.3813E3
­ 3.3817E3
1
P6
­ 2.9735E3
­ 2.9738E3
P7
­ 2.2072E3
­ 2.2072E3
P8
­ 1.1742E3
­ 1.1744E3
P1
2.0705E4
2.0709E4
P2
­ 3.8918E4
­ 3.8920E4
Translation 8
P3
5.2432E4
5.2436E4
(Dy)
P4
­ 5.9621E4
­ 5.9628E4

P5
5.9621E4
5.9628E4
8
P6
­ 5.2432E4
­ 5.2436E4
P7
3.8918E4
3.8920E4
P8
­ 2.0705E4
­ 2.0709E4
Maximum error lower than: 0.03%.
6.2 Remarks
Calculations carried out by:
MODE_ITER_SIMULT
METHODE: “TRI_DIAG”
CALC_FREQ:
OPTION = “PLUS_PETITE”
NMAX_FREQ = 8
Contents of the file results:
the first 8 Eigen frequencies, clean vectors and modal parameters
6.3 Parameters
of execution
Version: 3.02.21
Machine: CRAY C90
System:
UNICOS 8.0
Obstruction memory:
8 megawords
Time CPU To use:
16.686 seconds
Handbook of Validation
V2.01 booklet: Linear dynamics of the discrete systems
HI-75/98/040 - Ind A

Code_Aster ®
Version
4.0
Titrate:
SDLD02 Système mass-arises with 8 degrees of freedom
Date:
01/12/98
Author (S):
B. QUINNEZ
Key:
V2.01.002-E Page:
11/24
7 Modeling
C
7.1
Characteristics of modeling
Transposition of the test of reference to the case of the degrees of freedom of rotation (from torsion + inertia comes out)
by using the discrete element of rigidity in translation/rotation DIS_TR.
Y
0.4
0.3
P
P
P
1
P
3
P
6
P
X
2
4
P5
7
P8
X
Characteristics of the elements:
ORIENTATION:
in all the nodes
with an angle = 53.130102°
DISCRET:
with nodal masses all nodes
M_TR_D_N
in absolute reference mark
(Ixx = 10.)
matrices of rigidity all meshs
K_TR_D_L
in local reference mark
(KRx = 1. 105)
with the nodes
K_TR_D_N
in local reference mark
(KRx = 1. 105)
ends
Limiting conditions:
DDL_IMPO: (TOUT:“YES” DX: 0., DZ: 0., DRZ: 0. )
LIAISON_DDL: (such as 3DRY=4DRY in all the nodes)
Names of the nodes: : P1, P2,…., P8
7.2
Characteristics of the grid
A number of nodes: 8
A number of meshs and types: 7 SEG2
7.3 Functionalities
tested
Commands
Keys
AFFE_CARA_ELEM
DISCRET
GROUP_MA
“K_TR_D_L'
[U4.24.01]
NOEUD
“K_TR_D_N'
“M_TR_D_N'
ORIENTATION
GROUP_NO
“ANGL_NAUT”
AFFE_MODELE
TOUT
“MECANIQUE”
“DIS_TR”
[U4.22.01]
GROUP_NO
“DIS_TR”
MODE_ITER_INV
CALC_FREQ
OPTION
“AJUSTE”
[U4.52.01]
FREQ
CALC_MODE
OPTION
“DIRECT”
NORM_MODE
“MASS_GENE”
or “RIGI_GENE”
[U4.64.02]
Handbook of Validation
V2.01 booklet: Linear dynamics of the discrete systems
HI-75/98/040 - Ind A

Code_Aster ®
Version
4.0
Titrate:
SDLD02 Système mass-arises with 8 degrees of freedom
Date:
01/12/98
Author (S):
B. QUINNEZ
Key:
V2.01.002-E Page:
12/24
8
Results of modeling C
8.1 Values
tested
Identification
Reference
Aster
% Difference
tolerance
Number of the mode
valley. relative
clean
1
5.5274
5.5274
0.
10­4
2
10.8868
10.8868
-
-
3
15.9155
15.9155
-
-
4
20.4606
20.4606
-
-
5
24.3840
24.3840
-
-
6
27.5664
27.5664
-
-
7
29.9113
29.9113
-
-
8
31.3474
31.3474
-
-
Normalized mode with 1 with the largest component
Nature of the clean mode
Not
Reference
Aster
P1
­ 0.3473
­ 0.34729
P2
­ 0.6527
­ 0.65270
Rotation 1
P3
­ 0.8793
­ 0.87938
(DRY)
P4
­ 1.
­ 1.

P5
­ 1.
­ 1.
1
P6
­ 0.8793
­ 0.87938
P7
­ 0.6527
­ 0.65270
P8
­ 0.3473
­ 0.34729
P1
0.3473
0.34729
P2
­ 0.6527
­ 0.65270
Rotation 8
P3
0.8793
0.87938
(DRY)
P4
­ 1.
­ 1.

P5
1.
1.
8
P6
­ 0.8793
­ 0.87938
P7
0.6527
0.65270
P8
­ 0.3473
­ 0.34729
Maximum error lower than: 0.03%.
Mode normalized with the unit generalized mass
Nature of the clean mode
Not
Reference
Aster
P1
­ 4.0781E2
­ 4.0788E2
P2
­ 7.6654E2
­ 7.6657E2
Rotation 1
P3
­ 1.0327E1
­ 1.0327E1
(DRY)
P4
­ 1.1743E1
­ 1.1744E1

P5
­ 1.1743E1
­ 1.1744E1
1
P6
­ 1.0327E1
­ 1.0327E1
P7
­ 7.6654E2
­ 7.6657E2
P8
­ 4.0781E2
­ 4.0788E2
P1
4.0781E2
4.0788E2
P2
­ 7.6654E2
­ 7.6657E2
Rotation 8
P3
1.0327E1
1.0328E1
(DRY)
P4
­ 1.1743E1
­ 1.1744E1

P5
1.1743E1
1.1744E1
8
P6
­ 1.0327E1
­ 1.0328E1
P7
7.6654E2
7.6657E2
P8
­ 4.0781E2
­ 4.0788E2
Maximum error lower than: 0.03%.
Handbook of Validation
V2.01 booklet: Linear dynamics of the discrete systems
HI-75/98/040 - Ind A

Code_Aster ®
Version
4.0
Titrate:
SDLD02 Système mass-arises with 8 degrees of freedom
Date:
01/12/98
Author (S):
B. QUINNEZ
Key:
V2.01.002-E Page:
13/24
Mode normalized with the unit generalized stiffness
Nature of the clean mode
Not
Reference
Aster
P1
­ 1.1742E3
­ 1.1744E3
P2
­ 2.2072E3
­ 2.2072E3
Rotation 1
P3
­ 2.9735E3
­ 2.9738E3
(DRY)
P4
­ 3.3813E3
­ 3.3817E3

P5
­ 3.3813E3
­ 3.3817E3
1
P6
­ 2.9735E3
­ 2.9738E3
P7
­ 2.2072E3
­ 2.2072E3
P8
­ 1.1742E3
­ 1.1744E3
P1
2.0705E4
2.0709E4
P2
­ 3.8918E4
­ 3.8920E4
Rotation 8
P3
5.2432E4
5.2436E4
(DRY)
P4
­ 5.9621E4
­ 5.9628E4

P5
5.9621E4
5.9628E4
8
P6
­ 5.2432E4
­ 5.2436E4
P7
3.8918E4
3.8920E4
P8
­ 2.0705E4
­ 2.0709E4
Maximum error lower than: 0.03%.
8.2 Remarks
Calculations carried out by:
MODE_ITER_INV
OPTION: “AJUSTE”
LIST_FREQ: (5., 10., 15., 20., 24., 27., 30., 32.)
CALC_MODE: (OPTION: “DIRECT”)
Contents of the file results:
the first 8 Eigen frequencies, clean vectors and modal parameters
8.3 Parameters
of execution
Version: 3.02.21
Machine: CRAY C90
System:
UNICOS 8.0
Obstruction memory:
8 megawords
Time CPU To use:
5.8 seconds
Handbook of Validation
V2.01 booklet: Linear dynamics of the discrete systems
HI-75/98/040 - Ind A

Code_Aster ®
Version
4.0
Titrate:
SDLD02 Système mass-arises with 8 degrees of freedom
Date:
01/12/98
Author (S):
B. QUINNEZ
Key:
V2.01.002-E Page:
14/24
9 Modeling
D
9.1
Characteristics of modeling
Transposition of the test of reference to the case of the degrees of freedom of rotation (from torsion + inertia comes out)
by using the discrete element of rigidity in translation/rotation: DIS_TR.
Y
0.4
0.3
P
P
P
1
P
3
P
6
P
X
2
4
P5
7
P8
X
Characteristics of the elements:
ORIENTATION:
in all the nodes
with an angle = 53.130102°
DISCRET:
with nodal masses all nodes
M_TR_N
in absolute reference mark
(Ixx = 10.)
matrices of rigidity all meshs
K_TR_L
in local reference mark
(KRx = 1. 105)
with the nodes
K_TR_N
in local reference mark
(KRx = 1. 105)
ends
Limiting conditions:
DDL_IMPO: (TOUT:“YES” DX: 0., DY: 0., DZ: 0., DRZ: 0. )
LIAISON_DDL: (such as 3DRY=4DRY in all the nodes)
Names of the nodes: P1, P2,…., P8
9.2
Characteristics of the grid
A number of nodes: 8
A number of meshs and types: 7 SEG2
9.3 Functionalities
tested
Commands
Keys
AFFE_CARA_ELEM
DISCRET
GROUP_MA
“K_TR_L'
[U4.24.01]
NOEUD
“K_TR_N'
“M_TR_N'
ORIENTATION
GROUP_NO
“ANGL_NAUT”
AFFE_MODELE
TOUT
“MECANIQUE”
“DIS_TR”
[U4.22.01]
GROUP_NO
“DIS_TR”
MODE_ITER_INV
CALC_FREQ
OPTION
“AJUSTE”
[U4.52.01]
FREQ
CALC_MODE
OPTION
“DIRECT”
RECU_CHAMP
“DEPL”
NUME_ORDRE
[U4.62.01]
FREQ
NORM_MODE
“MASS_GENE”
or
“RIGI_GENE”
[U4.64.02]
Handbook of Validation
V2.01 booklet: Linear dynamics of the discrete systems
HI-75/98/040 - Ind A

Code_Aster ®
Version
4.0
Titrate:
SDLD02 Système mass-arises with 8 degrees of freedom
Date:
01/12/98
Author (S):
B. QUINNEZ
Key:
V2.01.002-E Page:
15/24
10
Results of modeling D
10.1 Values
tested
Identification
Reference
Aster
% Difference
tolerance
Number of the mode
valley. relative
clean
1
5.5274
5.5274
0.
10­4
2
10.8868
10.8868
-
-
3
15.9155
15.9155
-
-
4
20.4606
20.4606
-
-
5
24.3840
24.3840
-
-
6
27.5664
27.5664
-
-
7
29.9113
29.9113
-
-
8
31.3474
31.3474
-
-
Normalized mode with 1 with the largest component
Nature of the clean mode
Not
Reference
Aster
P1
­ 0.3473
­ 0.34729
P2
­ 0.6527
­ 0.65270
Rotation 1
P3
­ 0.8793
­ 0.87938
(DRY)
P4
­ 1.
­ 1.

P5
­ 1.
­ 1.
1
P6
­ 0.8793
­ 0.87938
P7
­ 0.6527
­ 0.65270
P8
­ 0.3473
­ 0.34729
P1
0.3473
0.34729
P2
­ 0.6527
­ 0.65270
Rotation 8
P3
0.8793
0.87938
(DRY)
P4
­ 1.
­ 1.

P5
1.
1.
8
P6
­ 0.8793
­ 0.87938
P7
0.6527
0.65270
P8
­ 0.3473
­ 0.34729
Maximum error lower than: 0.03%.
Mode normalized with the unit generalized mass
Nature of the clean mode
Not
Reference
Aster
P1
­ 4.0781E2
­ 4.0788E2
P2
­ 7.6654E2
­ 7.6657E2
Rotation 1
P3
­ 1.0327E1
­ 1.0327E1
(DRY)
P4
­ 1.1743E1
­ 1.1744E1

P5
­ 1.1743E1
­ 1.1744E1
1
P6
­ 1.0327E1
­ 1.0327E1
P7
­ 7.6654E2
­ 7.6657E2
P8
­ 4.0781E2
­ 4.0788E2
P1
4.0781E2
4.0788E2
P2
­ 7.6654E2
­ 7.6657E2
Rotation 8
P3
1.0327E1
1.0328E1
(DRY)
P4
­ 1.1743E1
­ 1.1744E1

P5
1.1743E1
1.1744E1
8
P6
­ 1.0327E1
­ 1.0328E1
P7
7.6654E2
7.6657E2
P8
­ 4.0781E2
­ 4.0788E2
Maximum error lower than: 0.03%.
Handbook of Validation
V2.01 booklet: Linear dynamics of the discrete systems
HI-75/98/040 - Ind A

Code_Aster ®
Version
4.0
Titrate:
SDLD02 Système mass-arises with 8 degrees of freedom
Date:
01/12/98
Author (S):
B. QUINNEZ
Key:
V2.01.002-E Page:
16/24
Mode normalized with the unit generalized stiffness
Nature of the clean mode
Not
Reference
Aster
P1
­ 1.1742E3
­ 1.1744E3
P2
­ 2.2072E3
­ 2.2072E3
Rotation 1
P3
­ 2.9735E3
­ 2.9738E3
(DRY)
P4
­ 3.3813E3
­ 3.3817E3

P5
­ 3.3813E3
­ 3.3817E3
1
P6
­ 2 9735E3
­ 2.9738E3
P7
­ 2.2072E3
­ 2.2072E3
P8
­ 1.1742E3
­ 1.1744E3
P1
2.0705E4
2.0709E4
P2
­ 3.8918E4
­ 3.8920E4
Rotation 8
P3
5.2432E4
5.2436E4
(DRY)
P4
­ 5.9621E4
­ 5.9628E4

P5
5.9621E4
5.9628E4
8
P6
­ 5.2432E4
­ 5.2436E4
P7
3.8918E4
3.8920E4
P8
­ 2.0705E4
­ 2.0709E4
Maximum error lower than: 0.03%.
10.2 Remarks
Calculations carried out by:
MODE_ITER_INV
OPTION: “AJUSTE”
LIST_FREQ: (5., 10., 15., 20., 24., 27., 30., 32.)
CALC_MODE: (OPTION: “DIRECT”)
Contents of the file results:
the first 8 Eigen frequencies, clean vectors and modal parameters
10.3 Parameters
of execution
Version: 3.02.21
Machine: CRAY C90
System:
UNICOS 8.0
Obstruction memory:
8 megawords
Time CPU To use:
5.6 seconds
Handbook of Validation
V2.01 booklet: Linear dynamics of the discrete systems
HI-75/98/040 - Ind A

Code_Aster ®
Version
4.0
Titrate:
SDLD02 Système mass-arises with 8 degrees of freedom
Date:
01/12/98
Author (S):
B. QUINNEZ
Key:
V2.01.002-E Page:
17/24
11 Modeling
E
11.1 Characteristics of modeling
Discrete element of rigidity in translation 2d_DIS_T
Y
0.4
0.3
P
P
P
1
P
3
P
6
P
X
2
4
P5
7
P8
X
Characteristics of the elements:
ORIENTATION:
in all the nodes
with an angle = 53.130102°
DISCRET:
with nodal masses all nodes
M_T_D_N
in absolute reference mark
(m = 10.)
matrices of rigidity all meshs
K_T_D_L
in local reference mark
(Kx = 1. 105)
with the nodes ends
K_T_D_N
in local reference mark
(Kx = 1. 105)
Limiting conditions:
LIAISON_DDL: (such as 3Dy=4Dx in all the nodes)
Names of the nodes: P1, P2,…., P8
Not A = N1
= N2
11.2 Characteristics of the grid
A number of nodes: 8
A number of meshs and types: 7 SEG2
11.3 Functionalities
tested
Commands
Keys
AFFE_CARA_ELEM
DISCRET
GROUP_MA
“K_T_D_L'
[U4.24.01]
NOEUD
“K_T_D_N'
“M_T_D_N'
ORIENTATION
GROUP_NO
“ANG_NAUT”
AFFE_CHAR_MECA
DDL_IMPO
TOUT
[U4.25.01]
LIAISON_DDL
NOEUD
AFFE_MATERIAU
TOUT
[U4.23.02]
AFFE_MODELE
TOUT
“MECANIQUE”
“2d_DIS_T'
[U4.22.01]
GROUP_NO
“2d_DIS_T'
DEFI_MATERIAU
ELAS
[U4.23.01]
MODE_ITER_INV
CALC_FREQ
OPTION
“AJUSTE”
[U4.52.01]
FREQ
CALC_MODE
OPTION
“DIRECT”
RECU_CHAMP
“DEPL”
NUME_ORDRE
[U4.62.01]
FREQ
NORM_MODE
“MASS_GENE”
[U4.64.02]
NORM_MODE
“RIGI_GENE”
[U4.64.02]
Handbook of Validation
V2.01 booklet: Linear dynamics of the discrete systems
HI-75/98/040 - Ind A

Code_Aster ®
Version
4.0
Titrate:
SDLD02 Système mass-arises with 8 degrees of freedom
Date:
01/12/98
Author (S):
B. QUINNEZ
Key:
V2.01.002-E Page:
18/24
12
Results of modeling E
12.1 Values
tested
Identification
Reference
Aster
% Difference
tolerance
Number of the mode
valley. relative
clean
1
5.5274
5.5274
0.
10­4
2
10.8868
10.8868
-
-
3
15.9155
15.9155
-
-
4
20.4606
20.4606
-
-
5
24.3840
24.3840
-
-
6
27.5664
27.5664
-
-
7
29.9113
29.9113
-
-
8
31.3474
31.3474
-
-
Normalized mode with 1 with the largest component
Nature of the clean mode
Not
Reference
Aster
P1
­ 0.3473
­ 0.34729
P2
­ 0.6527
­ 0.65270
Translation 1
P3
­ 0.8793
­ 0.87938
(Dy)
P4
­ 1.
­ 1.

P5
­ 1.
­ 1.
1
P6
­ 0.8793
­ 0.87938
P7
­ 0.6527
­ 0.65270
P8
­ 0.3473
­ 0.34729
P1
0.3473
0.34729
P2
­ 0.6527
­ 0.65270
Translation 8
P3
0.8793
0.87938
(Dy)
P4
­ 1.
­ 1.

P5
1.
1.
8
P6
­ 0.8793
­ 0.87938
P7
0.6527
0.65270
P8
­ 0.3473
­ 0.34729
Maximum error lower than: 0.03%.
Handbook of Validation
V2.01 booklet: Linear dynamics of the discrete systems
HI-75/98/040 - Ind A

Code_Aster ®
Version
4.0
Titrate:
SDLD02 Système mass-arises with 8 degrees of freedom
Date:
01/12/98
Author (S):
B. QUINNEZ
Key:
V2.01.002-E Page:
19/24
Mode normalized with the unit generalized mass
Nature of the clean mode
Not
Reference
Aster
P1
­ 4.0781E2
­ 4.0788E2
P2
­ 7.6654E2
­ 7.6657E2
Translation 1
P3
­ 1.0327E1
­ 1.0327E1
(Dy)
P4
­ 1.1743E1
­ 1.1744E1

P5
­ 1.1743E1
­ 1.1744E1
1
P6
­ 1.0327E1
­ 1.0327E1
P7
­ 7.6654E2
­ 7.6657E2
P8
­ 4.0781E2
­ 4.0788E2
P1
4.0781E2
4.0788E2
P2
­ 7.6654E2
­ 7.6657E2
Translation 8
P3
1.0327E1
1.0328E1
(Dy)
P4
­ 1.1743E1
­ 1.1744E1

P5
1.1743E1
1.1744E1
8
P6
­ 1.0327E1
­ 1.0328E1
P7
7.6654E2
7.6657E2
P8
­ 4.0781E2
­ 4.0788E2
Maximum error lower than: 0.03%.
Mode normalized with the unit generalized stiffness
Nature of the clean mode
Not
Reference
Aster
P1
­ 1.1742E3
­ 1.1744E3
P2
­ 2.2072E3
­ 2.2072E3
Translation 1
P3
­ 2.9735E3
­ 2.9738E3
(Dy)
P4
­ 3.3813E3
­ 3.3817E3

P5
­ 3.3813E3
­ 3.3817E3
1
P6
­ 2.9735E3
­ 2.9738E3
P7
­ 2.2072E3
­ 2.2072E3
P8
­ 1.1742E3
­ 1.1744E3
P1
2.0705E4
2.0709E4
P2
­ 3.8918E4
­ 3.8920E4
Translation 8
P3
5.2432E4
5.2436E4
(Dy)
P4
­ 5.9621E4
­ 5.9628E4

P5
5.9621E4
5.9628E4
8
P6
­ 5.2432E4
­ 5.2436E4
P7
3.8918E4
3.8920E4
P8
­ 2.0705E4
­ 2.0709E4
Maximum error lower than: 0.03%.
12.2 Remarks
Calculations carried out by:
MODE_ITER_INV
OPTION:“AJUSTE”
LIST_FREQ:(5., 10., 15., 20., 24., 27., 30., 32.)
CALC_MODE: (OPTION: “DIRECT”)
Contents of the file results:
the first 8 Eigen frequencies, clean vectors and modal parameters
12.3 Parameters
of execution
Version: 3.02.21
Machine: CRAY C90
System:
UNICOS 8.0
Obstruction memory:
8 megawords
Time CPU To use:
6 seconds
Handbook of Validation
V2.01 booklet: Linear dynamics of the discrete systems
HI-75/98/040 - Ind A

Code_Aster ®
Version
4.0
Titrate:
SDLD02 Système mass-arises with 8 degrees of freedom
Date:
01/12/98
Author (S):
B. QUINNEZ
Key:
V2.01.002-E Page:
20/24
13 Modeling
F
13.1 Characteristics of modeling
Discrete element of rigidity in translation/rotation: 2d_DIS_TR
Y
0.4
0.3
P
P
P
1
P
3
P
6
P
X
2
4
P5
7
P8
X
Characteristics of the elements:
ORIENTATION:
in all the nodes
with an angle = 53.130102°
DISCRET:
with nodal masses all nodes
M_T_D_N
in absolute reference mark
(m = 10.)
matrices of rigidity all meshs
K_T_D_L
in local reference mark
(Kx = 1. 105)
with the nodes ends
K_T_D_N
in local reference mark
(Kx = 1. 105)
Limiting conditions:
DDL_IMPO: (TOUT:“YES” DRZ: 0. )
LIAISON_DDL: (such as 3Dy=4Dx in all the nodes)
Names of the nodes: P1, P2,…., P8
Not A = N1
= N2
13.2 Characteristics of the grid
A number of nodes: 8
A number of meshs and types: 7 SEG2
13.3 Functionalities
tested
Commands
Keys
AFFE_CARA_ELEM
DISCRET
GROUP_MA
“K_T_D_L'
[U4.24.01]
NOEUD
“K_T_D_N'
“M_T_D_N'
ORIENTATION
GROUP_NO
“ANG_NAUT”
AFFE_CHAR_MECA
DDL_IMPO
TOUT
[U4.25.01]
LIAISON_DDL
NOEUD
AFFE_MATERIAU
TOUT
[U4.23.02]
AFFE_MODELE
TOUT
“MECANIQUE”
“2d_DIS_TR”
[U4.22.01]
GROUP_NO
“2d_DIS_TR”
DEFI_MATERIAU
ELAS
[U4.23.01]
MODE_ITER_INV
CALC_FREQ
OPTION
“AJUSTE”
[U4.52.01]
FREQ
CALC_MODE
OPTION
“DIRECT”
RECU_CHAMP
“DEPL”
NUME_ORDRE
[U4.62.01]
FREQ
NORM_MODE
“MASS_GENE”
[U4.64.02]
NORM_MODE
“RIGI_GENE”
[U4.64.02]
Handbook of Validation
V2.01 booklet: Linear dynamics of the discrete systems
HI-75/98/040 - Ind A

Code_Aster ®
Version
4.0
Titrate:
SDLD02 Système mass-arises with 8 degrees of freedom
Date:
01/12/98
Author (S):
B. QUINNEZ
Key:
V2.01.002-E Page:
21/24
14
Results of modeling F
14.1 Values
tested
Identification
Reference
Aster
% Difference
tolerance
Number of the mode
valley. relative
clean
1
5.5274
5.5274
0.
10­4
2
10.8868
10.8868
-
-
3
15.9155
15.9155
-
-
4
20.4606
20.4606
-
-
5
24.3840
24.3840
-
-
6
27.5664
27.5664
-
-
7
29.9113
29.9113
-
-
8
31.3474
31.3474
-
-
Normalized mode with 1 with the largest component
Nature of the clean mode
Not
Reference
Aster
P1
­ 0.3473
­ 0.34729
P2
­ 0.6527
­ 0.65270
Translation 1
P3
­ 0.8793
­ 0.87938
(Dy)
P4
­ 1.
­ 1.

P5
­ 1.
­ 1.
1
P6
­ 0.8793
­ 0.87938
P7
­ 0.6527
­ 0.65270
P8
­ 0.3473
­ 0.34729
P1
0.3473
0.34729
P2
­ 0.6527
­ 0.65270
Translation 8
P3
0.8793
0.87938
(Dy)
P4
­ 1.
­ 1.

P5
1.
1.
8
P6
­ 0.8793
­ 0.87938
P7
0.6527
0.65270
P8
­ 0.3473
­ 0.34729
Maximum error lower than: 0.03%.
Handbook of Validation
V2.01 booklet: Linear dynamics of the discrete systems
HI-75/98/040 - Ind A

Code_Aster ®
Version
4.0
Titrate:
SDLD02 Système mass-arises with 8 degrees of freedom
Date:
01/12/98
Author (S):
B. QUINNEZ
Key:
V2.01.002-E Page:
22/24
Mode normalized with the unit generalized mass
Nature of the clean mode
Not
Reference
Aster
P1
­ 4.0781E2
­ 4.0788E2
P2
­ 7.6654E2
­ 7.6657E2
Translation 1
P3
­ 1.0327E1
­ 1.0327E1
(Dy)
P4
­ 1.1743E1
­ 1.1744E1

P5
­ 1.1743E1
­ 1.1744E1
1
P6
­ 1.0327E1
­ 1.0327E1
P7
­ 7.6654E2
­ 7.6657E2
P8
­ 4.0781E2
­ 4.0788E2
P1
4.0781E2
4.0788E2
P2
­ 7.6654E2
­ 7.6657E2
Translation 8
P3
1.0327E1
1.0328E1
(Dy)
P4
­ 1.1743E1
­ 1.1744E1

P5
1.1743E1
1.1744E1
8
P6
­ 1.0327E1
­ 1.0328E1
P7
7.6654E2
7.6657E2
P8
­ 4.0781E2
­ 4.0788E2
Maximum error lower than: 0.03%.
Mode normalized with the unit generalized stiffness
Nature of the clean mode
Not
Reference
Aster
P1
­ 1.1742E3
­ 1.1744E3
P2
­ 2.2072E3
­ 2.2072E3
Translation 1
P3
­ 2.9735E3
­ 2.9738E3
(Dy)
P4
­ 3.3813E3
­ 3.3817E3

P5
­ 3.3813E3
­ 3.3817E3
1
P6
­ 2.9735E3
­ 2.9738E3
P7
­ 2.2072E3
­ 2.2072E3
P8
­ 1.1742E3
­ 1.1744E3
P1
2.0705E4
2.0709E4
P2
­ 3.8918E4
­ 3.8920E4
Translation 8
P3
5.2432E4
5.2436E4
(Dy)
P4
­ 5.9621E4
­ 5.9628E4

P5
5.9621E4
5.9628E4
8
P6
­ 5.2432E4
­ 5.2436E4
P7
3.8918E4
3.8920E4
P8
­ 2.0705E4
­ 2.0709E4
Maximum error lower than: 0.03%.
14.2 Remarks
Calculations carried out by:
MODE_ITER_INV
OPTION:“AJUSTE”
LIST_FREQ:(5., 10., 15., 20., 24., 27., 30., 32.)
CALC_MODE: (OPTION: “DIRECT”)
Contents of the file results:
the first 8 Eigen frequencies, clean vectors and modal parameters
14.3 Parameters
of execution
Version: 3.02.21
Machine: CRAY C90
System:
UNICOS 8.0
Obstruction memory:
8 megawords
Time CPU To use:
6 seconds
Handbook of Validation
V2.01 booklet: Linear dynamics of the discrete systems
HI-75/98/040 - Ind A

Code_Aster ®
Version
4.0
Titrate:
SDLD02 Système mass-arises with 8 degrees of freedom
Date:
01/12/98
Author (S):
B. QUINNEZ
Key:
V2.01.002-E Page:
23/24
15
Summary of the results
For all the options of modeling of the discrete elements of rigidity and mass offered by
AFFE_CARA_ELEM the solutions obtained are those of the reference solution (frequencies and modes
clean with various standardizations).
Handbook of Validation
V2.01 booklet: Linear dynamics of the discrete systems
HI-75/98/040 - Ind A

Code_Aster ®
Version
4.0
Titrate:
SDLD02 Système mass-arises with 8 degrees of freedom
Date:
01/12/98
Author (S):
B. QUINNEZ
Key:
V2.01.002-E Page:
24/24
Intentionally white left page.
Handbook of Validation
V2.01 booklet: Linear dynamics of the discrete systems
HI-75/98/040 - Ind A