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Version
5.0
Titrate:
SDLD23 Système of masses and springs under random excitation
Date:
30/08/01
Author (S):
J. PIGAT
Key: V2.01.023-B Page:
1/6
Organization (S): EDF/RNE/AMV
Handbook of Validation
V2.01 booklet: Linear dynamics of the discrete systems
V2.01.023 document
SDLD23 - Système of masses and springs
under random excitation
Summary:
This test is in the course of validation within the framework of the VPCS.
It comprises a whole of eight specific masses and nine springs excited by an imposed random force
on one of the masses.
The excitation is of white vibration type. It is given by the spectral concentration of power of the exiting force.
The movement of the excited mass is calculated by a stochastic approach according to different
frequential discretizations for the answer.
One also calculates in postprocessing the spectral moments of the answer.
Handbook of Validation
V2.01 booklet: Linear dynamics of the discrete systems
HT-62/01/012/A
Code_Aster ®
Version
5.0
Titrate:
SDLD23 Système of masses and springs under random excitation
Date:
30/08/01
Author (S):
J. PIGAT
Key: V2.01.023-B Page:
2/6
1
Problem of reference
1.1 Geometry
dx
K
P1
K
P2
K
P
K
8
m
m
C
C
C
C
The excitation is a seismic movement of type forces imposed applied to the P4 point in the direction dx.
One is interested in the DSP of displacement of the P4 node.
1.2
Material properties
Specific masses:
m = 10 kg
Elastic springs:
K = 105 NR/m
Damping devices:
C = 50 NR/(m/s)
1.3
Boundary conditions and loadings
The problem is unidimensional in direction X (1 ddl by mass).
The excitation is a DSP of constant force of level 1, between 3 and 13 Hz.
1
DSP
(N2/Hz)
3
13
Frequency (Hz)
Handbook of Validation
V2.01 booklet: Linear dynamics of the discrete systems
HT-62/01/012/A
Code_Aster ®
Version
5.0
Titrate:
SDLD23 Système of masses and springs under random excitation
Date:
30/08/01
Author (S):
J. PIGAT
Key: V2.01.023-B Page:
3/6
2
Reference solution
2.1
Method of calculation used for the reference solution
The solution taken for reference results from test SDLD23 of guide VPCS [bib1].
2.2
Results of reference
Peak of the response to the first Eigen frequency.
Values of the first spectral moments for various discretizations.
2.3 Reference
Guide VPCS.
Handbook of Validation
V2.01 booklet: Linear dynamics of the discrete systems
HT-62/01/012/A
Code_Aster ®
Version
5.0
Titrate:
SDLD23 Système of masses and springs under random excitation
Date:
30/08/01
Author (S):
J. PIGAT
Key: V2.01.023-B Page:
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3 Modeling
With
3.1
Characteristics of modeling
Discrete element in translation of the type DIS_T
Modeling respects the geometry.
Characteristics of the elements:
With the P1 nodes in P8: matrices of masses of the type M_T_D_N with m = 10 kg.
Elements of spring: a matrix of stiffness of the type K_T_D_L with Kx = 105 NR/m
Elements of damping: a matrix of damping of the type A_T_D_L with cx = 50 NR/m
Boundary conditions:
All the DDL are blocked except the DDL dx.
Modal damping is calculated by the operator of modal calculation, it is reinjected like
modal damping in random dynamic calculation.
3.2
Characteristics of the grid
A number of nodes: 10
A number of meshs and types: 9 SEG2, 10 POI1
3.3 Functionalities
tested
Commands
DEFI_INTE_SPEC PAR_FONCTION
DYNA_ALEA_MODAL BASE_MODALE AMOR
EXCIT
GRANDEUR
“EFFO”
REPONSE
REST_SPEC_PHYS
POST_DYNA_ALEA MOMENT
Handbook of Validation
V2.01 booklet: Linear dynamics of the discrete systems
HT-62/01/012/A
Code_Aster ®
Version
5.0
Titrate:
SDLD23 Système of masses and springs under random excitation
Date:
30/08/01
Author (S):
J. PIGAT
Key: V2.01.023-B Page:
5/6
4
Results of modeling A
4.1 Values
tested
DSP of displacement to the P4 node
Identification Reference Aster %
Difference
ABSOLU: F = 5.5259 Hz
0.1059E5
0.1059E5
0%
Spectral moments for the discretization by defect (50 points per peak)
Identification Reference Aster %
Difference
Spectral moment n°0
1.585 107 1.618
107 2.11%
Spectral moment n°2
1.902 104 1.942
104 2.12%
Spectral moment n°4
2.322 101 2.370
101 2.09%
Spectral moment n°6
2.941 102 3.001
102 2.05%
Spectral moment n°8
4.143 105 4.226
105 2.00%
Spectral moments for the discretization with regular step 0.25 Hz (40 steps)
Identification Reference Aster %
Difference
Spectral moment n°0
1.585 107 2.339
107 47.61%
Spectral moment n°2
1.902 104 2.790
104 46.73%
Spectral moment n°4
2.322 101 3.368
101 45.05%
Spectral moment n°6
2.941 102 4.173
102 41.91%
Spectral moment n°8
4.143 105 5.600
105 35.17%
Spectral moments for the discretization with regular step 0.05 Hz (200 steps)
Identification Reference Aster %
Difference
Spectral moment n°0
1.585 107 1.577
107 0.44%
Spectral moment n°2
1.902 104 1.893
104 0.46%
Spectral moment n°4
2.322 101 2.311
101 0.48%
Spectral moment n°6
2.941 102 2.928
102 0.43%
Spectral moment n°8
4.143 105 4.130
105 0.30%
Spectral moments for the discretization with regular step 0.025 Hz (400 steps)
Identification Reference Aster %
Difference
Spectral moment n°0
1.585 107 1.585
107 0.02%
Spectral moment n°2
1.902 104 1.902
104 0.01%
Spectral moment n°4
2.322 101 2.322
101 0.02%
Spectral moment n°6
2.941 102 2.941
102 0.00%
Spectral moment n°8
4.143 105 4.144
105 0.03%
4.2 Parameters
of execution
Version: 5.02
Machine: SGI ORIGIN 2000
System:
Obstruction memory: 8 megawords,
time CPU User:
3.60 seconds
Handbook of Validation
V2.01 booklet: Linear dynamics of the discrete systems
HT-62/01/012/A
Code_Aster ®
Version
5.0
Titrate:
SDLD23 Système of masses and springs under random excitation
Date:
30/08/01
Author (S):
J. PIGAT
Key: V2.01.023-B Page:
6/6
5
Summary of the results
The preceding tables highlight the importance of the smoothness of the discretization
frequential of the DSP response for the calculation of the spectral moments.
The user can choose the step: the frequency band is then discretized in a uniform way and it or
the peaks can be badly represented: it is the case with 40 steps of 0.25 Hz, which involves an error
of more than 40% at the spectral time.
More one refines the discretization, better is the result.
To avoid refining unnecessarily far from the peaks, one proposes a discretization by rather broad defect
supplemented by a refinement of 50 points of discretization around each peak.
In the case of this test which includes/understands one peak, this discretization by defect makes it possible to estimate
spectral moments with a precision of about 2%.
Handbook of Validation
V2.01 booklet: Linear dynamics of the discrete systems
HT-62/01/012/A
Outline document