background image
Code_Aster
®
Version
5.0
Titrate:
Simple Oscillating SDLD101 under random excitation
Date:
30/08/01
Author (S):
J. PIGAT
Key
:
V2.01.101-B
Page:
1/6
Manual of Validation
V2.01 booklet: Linear dynamics of the discrete systems
HT-62/01/012/A
Organization (S):
EDF/RNE/AMV













Manual 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 shock absorber, 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 Gaussian noise 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.
background image
Code_Aster
®
Version
5.0
Titrate:
Simple Oscillating SDLD101 under random excitation
Date:
30/08/01
Author (S):
J. PIGAT
Key
:
V2.01.101-B
Page:
2/6
Manual of Validation
V2.01 booklet: Linear dynamics of the discrete systems
HT-62/01/012/A
1
Problem of reference
1.1 Geometry

K
m
DX
K
m
AX


The excitation is a seismic movement of imposed acceleration type
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 = 10
5
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.
background image
Code_Aster
®
Version
5.0
Titrate:
Simple Oscillating SDLD101 under random excitation
Date:
30/08/01
Author (S):
J. PIGAT
Key
:
V2.01.101-B
Page:
3/6
Manual of Validation
V2.01 booklet: Linear dynamics of the discrete systems
HT-62/01/012/A
2
Reference solution
2.1
Method of calculation used for the reference solution
The reference solution is analytical [bib1]. The own pulsation of the oscillator is
K
m
,
that is to say
0
=
=
K
m
100 rad/S, and F
O
= 15,9155 Hz.
Moving absolute, the DSP of the response in noted acceleration
()
G
RR
&&&&
is connected to the DSP of
the excitation
G
EE
&&&&
in acceleration also by:
()
(
)
()
()
()
()
()
G
G
G
J
G
G
G
RR
EE
RR
EE
RR
EE
&&&&
&&&&
&&&&
&&&&
&&&&
&&&&
.
.
.
=
+
-
+
=
-
+






=
04
02
02
2
02
2 2
02
02
2
2
02
2
0
0
2
4
4
2
Moving relative, one a:
Moving differential, one a:

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 “Dynamic response under random excitation in Code_Aster: principles
theoretical and examples of use " - Note HP-61/92.148
background image
Code_Aster
®
Version
5.0
Titrate:
Simple Oscillating SDLD101 under random excitation
Date:
30/08/01
Author (S):
J. PIGAT
Key
:
V2.01.101-B
Page:
4/6
Manual of Validation
V2.01 booklet: Linear dynamics of the discrete systems
HT-62/01/012/A
3 Modeling
With
3.1
Characteristics of modeling
Discrete element in translation of the type
DIS_T


DX
K
m
P1
P2


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 K
X
= 10
6
NR/m
Boundary conditions:
All the ddl are locked except the ddl
DX
P2 node.


3.2
Characteristics of the mesh
A number of nodes: 2
A number of meshs and types: 1 SEG2, 2 POI1

3.3 Functionalities
tested
Controls
MODE_STATIQUE DDL_IMPO
AVEC_CMP
DEFI_INTE_SPEC KANAI_TAJIMI
CONSTANT
DYNA_ALEA_MODAL EXCIT
MODE_STAT
ANSWER
REST_SPEC_PHYS
POST_DYNA_ALEA GOING BEYOND
RAYLEIGH
GAUSS
VANMARCKE
MOMENT
TOO BAD
background image
Code_Aster
®
Version
5.0
Titrate:
Simple Oscillating SDLD101 under random excitation
Date:
30/08/01
Author (S):
J. PIGAT
Key
:
V2.01.101-B
Page:
5/6
Manual of Validation
V2.01 booklet: Linear dynamics of the discrete systems
HT-62/01/012/A
4
Results of modeling A
4.1 Values
tested
Random dynamic response

Identification Reference Aster %
Difference
ABSOLUTE: F = 5. Hz
1.2307
1.2307
0.%
ABSOLUTE: F = 10. Hz
2.7116
2.7116
0.%
ABSOLUTE: F = 15. Hz
47.2154
47.2157
0.%
ABSOLUTE: F = 20. Hz
2.8924
2.8924
0.%
ABSOLUTE: F = 25. Hz
0.47047
0.47047
0.%
RELATIVE: F = 5. Hz
0.01197
0.01197
0.%
RELATIVE: F = 10. Hz
0.04209
0.04209
0.%
RELATIVE: F = 15. Hz
36.9225
36.9258
0.%
RELATIVE: F = 20. Hz
7.1006
7.1006
0.%
RELATIVE: F = 25. Hz
2.7953
2.7953
0.%
DIFFERENTIAL: F = 5. Hz
1.0
1.0
0.%
DIFFERENTIAL: F = 10. Hz
1.0
1.0
0.%
DIFFERENTIAL: F = 15. Hz
1.0
1.0
0.%
DIFFERENTIAL: F = 20. Hz
1.0
1.0
0.%
DIFFERENTIAL: 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 10
2
Spectral moment n°1
2.4524 10
4
Spectral moment n°2
2.5125 10
6
Spectral moment n°3
2.7647 10
8
Spectral moment n°4
3.603 10
10
Standard deviation 22.49
Factor of irregularity
0.8324
Frequency connects (Hz)
15.86
Numbers average passages by zero a second
31.73
background image
Code_Aster
®
Version
5.0
Titrate:
Simple Oscillating SDLD101 under random excitation
Date:
30/08/01
Author (S):
J. PIGAT
Key
:
V2.01.101-B
Page:
6/6
Manual of Validation
V2.01 booklet: Linear dynamics of the discrete systems
HT-62/01/012/A
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
10
­ 3
Distribution of Gauss
10.97
0.0395
40.55
0.0019
60.10
0.396
10
­ 4
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:
Overall dimension 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.