Code_Aster ®
Version
5.0
Titrate:
Simple SDLD101 Oscillateur under random excitation
Date:
30/08/01
Author (S):
J. PIGAT Key
:
V2.01.101-B Page:
1/6
Organization (S): EDF/RNE/AMV
Handbook of Validation
V2.01 booklet: Linear dynamics of the discrete systems
V2.01.101 document
SDLD101 - Simple Oscillator under excitation
random
Summary:
An oscillator simple, made up of a mass connected to a support by a spring and a damping device, is subjected to
a random excitation transmitted by the support, of imposed acceleration type.
This test uses the functionalities of the stochastic analysis and calculates the spectral concentration of power (DSP)
movement of the mass starting from the excitation of the white vibration type data by its DSP also.
The movement is calculated according to various options: relative, absolute, differential movement.
One calculates then the statistical properties of the response while passing in all the options of
random dynamic postprocessing.
Handbook of Validation
V2.01 booklet: Linear dynamics of the discrete systems
HT-62/01/012/A
Code_Aster ®
Version
5.0
Titrate:
Simple SDLD101 Oscillateur under random excitation
Date:
30/08/01
Author (S):
J. PIGAT Key
:
V2.01.101-B Page:
2/6
1
Problem of reference
1.1 Geometry
AX
K
DX
m
The excitation is a seismic movement of type imposed acceleration AX applied to the support in
feel DX.
One is interested in the movement of the mass Mr.
1.2
Material properties
Specific mass:
m = 100 kg
Arises elastic:
K = 105 NR/m
Modal damping:
0 = 0.05
1.3
Boundary conditions and loadings
The problem is unidimensional in direction X, and to 1 degree of freedom: the displacement of
mass Mr.
The excitation is a spectral concentration of power (DSP), of constant acceleration between 0. and 100 Hz.
It is applied to the support.
Handbook of Validation
V2.01 booklet: Linear dynamics of the discrete systems
HT-62/01/012/A
Code_Aster ®
Version
5.0
Titrate:
Simple SDLD101 Oscillateur under random excitation
Date:
30/08/01
Author (S):
J. PIGAT Key
:
V2.01.101-B Page:
3/6
2
Reference solution
2.1
Method of calculation used for the reference solution
K
The reference solution is analytical [bib1]. The own pulsation of the oscillator is
,
m
K
that is to say 0 =
= 100 rad/S, and F
m
O = 15,9155 Hz.
Moving absolute, the DSP of the response in noted acceleration G
()
RR
& & is connected to the DSP of
excitation GEE
& & in acceleration also by:
4 + 4 2 2 2
G () =
0
0
0
.
RR
& &
(2 - 2 2
2
2
2
0
)
G
()
EE
& &
+ 4
0
0
Moving relative, one a:
2
2
G () =
G ().
RR
& &
2 - 2 +
2 J
EE
& &
0
0
0
Moving differential, one a:
G () = G
().
RR
& &
EE
& &
2.2
Results of reference
One tests the DSP of the response for 0, 5, 10, 15, 20 Hz in the three cases of movement: absolute,
relative and differential.
2.3
Uncertainty on the solution
Analytical solution.
2.4 References
bibliographical
[1]
C. DUVAL “Réponse dynamic under random excitation in Code_Aster: principles
theoretical and examples of use " - Note HP-61/92.148
Handbook of Validation
V2.01 booklet: Linear dynamics of the discrete systems
HT-62/01/012/A
Code_Aster ®
Version
5.0
Titrate:
Simple SDLD101 Oscillateur under random excitation
Date:
30/08/01
Author (S):
J. PIGAT Key
:
V2.01.101-B Page:
4/6
3 Modeling
With
3.1
Characteristics of modeling
Discrete element in translation of the type DIS_T
P1
K
P2
DX
m
Characteristics of the elements:
With the nodes P1 and P2: matrices of masses of the type M_T_D_N with m = 100 kg.
Between P1 and P2: a matrix of rigidity of the type K_T_D_L with Kx = 106 NR/m
Boundary conditions:
All the ddl are blocked except ddl DX of the P2 node.
3.2
Characteristics of the grid
A number of nodes: 2
A number of meshs and types: 1 SEG2, 2 POI1
3.3 Functionalities
tested
Commands
MODE_STATIQUE DDL_IMPO
AVEC_CMP
DEFI_INTE_SPEC KANAI_TAJIMI
CONSTANT
DYNA_ALEA_MODAL EXCIT
MODE_STAT
REPONSE
REST_SPEC_PHYS
POST_DYNA_ALEA GOING BEYOND
RAYLEIGH
GAUSS
VANMARCKE
MOMENT
DOMMAGE
Handbook of Validation
V2.01 booklet: Linear dynamics of the discrete systems
HT-62/01/012/A
Code_Aster ®
Version
5.0
Titrate:
Simple SDLD101 Oscillateur under random excitation
Date:
30/08/01
Author (S):
J. PIGAT Key
:
V2.01.101-B Page:
5/6
4
Results of modeling A
4.1 Values
tested
Random dynamic response
Identification Reference Aster %
Difference
ABSOLU: F = 5. Hz
1.2307
1.2307
0.%
ABSOLU: F = 10. Hz
2.7116
2.7116
0.%
ABSOLU: F = 15. Hz
47.2154
47.2157
0.%
ABSOLU: F = 20. Hz
2.8924
2.8924
0.%
ABSOLU: F = 25. Hz
0.47047
0.47047
0.%
RELATIF: F = 5. Hz
0.01197
0.01197
0.%
RELATIF: F = 10. Hz
0.04209
0.04209
0.%
RELATIF: F = 15. Hz
36.9225
36.9258
0.%
RELATIF: F = 20. Hz
7.1006
7.1006
0.%
RELATIF: F = 25. Hz
2.7953
2.7953
0.%
DIFFERENTIEL: F = 5. Hz
1.0
1.0
0.%
DIFFERENTIEL: F = 10. Hz
1.0
1.0
0.%
DIFFERENTIEL: F = 15. Hz
1.0
1.0
0.%
DIFFERENTIEL: F = 20. Hz
1.0
1.0
0.%
DIFFERENTIEL: F = 25. Hz
1.0
1.0
0.%
Postprocessing on the response in absolute displacement: spectral moments and parameters
statistics
Identification
Aster
version 5.02
Spectral moment n°0
2.5285 102
Spectral moment n°1
2.4524 104
Spectral moment n°2
2.5125 106
Spectral moment n°3
2.7647 108
Spectral moment n°4
3.603 1010
Standard deviation 22.49
Factor of irregularity
0.8324
Frequency connects (Hz)
15.86
Numbers average passages by zero a second
31.73
Handbook of Validation
V2.01 booklet: Linear dynamics of the discrete systems
HT-62/01/012/A
Code_Aster ®
Version
5.0
Titrate:
Simple SDLD101 Oscillateur under random excitation
Date:
30/08/01
Author (S):
J. PIGAT Key
:
V2.01.101-B Page:
6/6
Postprocessing on the response in absolute displacement: statistical functions
The recorded values are those printed in the file result.
Identification Parameter
Aster
Version 5.02
Nb going beyond a second
10.97
25.00
40.55
1.23
60.10
0.025
Distribution of Rayleigh
10.97
0.0342
40.55
0.0062
60.10
0.187
103
Distribution of Gauss
10.97
0.0395
40.55
0.0019
60.10
0.396
104
Function of distribution of VANMARCKE
40.55
0.0043
10 (seconds)
50.09
0.3291
60.10
0.8688
4.2 Parameters
of execution
Version: 5.02
Machine: SGI ORIGIN 2000
System:
Obstruction memory:
8 megawords
Time CPU To use:
2.65 seconds
5
Summary of the results
It is not astonishing that the results awaited for the random dynamic response are obtained
with an accuracy of 0%. Indeed the DSP of the answers do not result from an iterative process of
resolution, but of an analytical expression bringing into play the modal transfer functions. This
analytical expression coincides with the reference solution for this problem.
For postprocessing, there is no reference solution. The results of version 4.03.09 are
used to check that the results do not evolve/move from one version to another. Calculation has very well
supported the change of platform.
Handbook of Validation
V2.01 booklet: Linear dynamics of the discrete systems
HT-62/01/012/A
Outline document