Code_Aster ®
Version
4.0
Titrate:
Forced SDND111 Vibrations of a system mass-arise
Date:
12/01/98
Author (S):
G. JACQUART
Key:
V5.01.111-A Page:
1/6
Organization (S): EDF/EP/AMV
Handbook of Validation
V5.01 booklet: Nonlinear dynamics of the discrete systems
V5.01.111 document
SDND111 - Vibrations forced of a system
mass-arises with fluid force of blade
Summary:
This test implements a system mass-arises specific subjected to a force of fluid blade which deadens it and one
harmonic external force. The fluid non-linearity of blade as well as the algorithm of point fixes which is to them
associated are thus tested. The reference solution is obtained by direct numerical integration out of
Code_Aster for the parabolic profile, with a step of very small time to ensure itself of the convergence of
solution.
Handbook of Validation
V5.01 booklet: Nonlinear dynamics of the discrete systems
HP-51/96/032 - Ind A
Code_Aster ®
Version
4.0
Titrate:
Forced SDND111 Vibrations of a system mass-arise
Date:
12/01/98
Author (S):
G. JACQUART
Key:
V5.01.111-A Page:
2/6
1
Problem of reference
1.1 Geometry
X
Fext (T)
2L
M
·
X
X
F
O
Z
1.2
Material properties
specific mass:
m = 25 kg
stiffness of the spring:
K = 24674 NR/m
width:
2L = 100 mm
density of the fluid:
F = 1000 kg/m3
viscosity:
= 1.E6
· with a parabolic profile of flow in the fluid blade:
= -
=
= -
-
0 0833
0 19992
0 9996 10 6
.
,
.
,
.
.
, = 0
· with a uniform profile of flow in the fluid blade:
= - 0 0833
.
, = 0 1666
.
, = 0, = 0
1.3
Boundary conditions and loadings
The mass is plunged in an incompressible fluid, and an indeformable obstacle is present in X = 0
and displacements only for X > 0 authorize.
1.4 Conditions
initial
Initial distance from the mass to the obstacle:
X = 5 mm
0
Initial speed:
X = 0 m/s
0
Handbook of Validation
V5.01 booklet: Nonlinear dynamics of the discrete systems
HP-51/96/032 - Ind A
Code_Aster ®
Version
4.0
Titrate:
Forced SDND111 Vibrations of a system mass-arise
Date:
12/01/98
Author (S):
G. JACQUART
Key:
V5.01.111-A Page:
3/6
2
Reference solution
2.1
Method of calculation used for the reference solution
The dynamic equation to which the system is subjected is as follows:
2
X
X
X
X X
MX
+ KX = F + + +
+
ext.
X
X
X 3
X 2
This equation cannot be solved in an analytical way, one uses a resolution by a diagram
of integration temporal of the dynamic problem. One can rewrite the system in the form:
2
X
X
X X
T
T
M -
X + KX = F
T
T
+ +
+
X
T
T
ext.
X
X 3
X 2
T
T
T
T
One uses the diagram of Euler modified to integrate this equation in time.
X, X
0
0 given to t0,
To repeat:
2
X
X
X
X
T
I
F
- KX
I
I
+ +
+
ext.
I
3
2
X
X
X
I
I
I
X =
I
M - Xi
T +1 = T + dt
I
I
X +1 = X + dt X
I
I
I
X +1 = X + dt X
I
I
i+1
as long as T
T
i+1 < fine.
2.2
Uncertainty on the solution
Solution approached numerically by step of very small time.
2.3 References
bibliographical
[1]
G.JACQUART “Modélisation of the forces of fluid blade” - HP-61/94/159/A
Handbook of Validation
V5.01 booklet: Nonlinear dynamics of the discrete systems
HP-51/96/032 - Ind A
Code_Aster ®
Version
4.0
Titrate:
Forced SDND111 Vibrations of a system mass-arise
Date:
12/01/98
Author (S):
G. JACQUART
Key:
V5.01.111-A Page:
4/6
3 Modeling
With
3.1
Characteristics of modeling
For modeling, one uses two nodes NO1 and separate NO2 of a distance L = 1m, to which are
affected two discrete elements of type POI1.
Node NO1 represents the mass, node NO2 represents the rigid plan. One is thus applied
condition of embedding to node NO2.
An obstacle of the type BI_PLAN_Z (two parallel plans separated by a play) is used to simulate
connection through the fluid.
One chooses to take OZ for generator of this plan is NORM_OBST: (0. 0. 1.).
Normal stiffness RIGI_NOR is assigned to an arbitrary value, because the contact takes place through
fluid.
It remains to define parameters DIST_1 and DIST_2 which give the half-spacing between the plans in
contact. One takes DIST_1 = DIST_2 = (L-play)/2 = 0.497 Misters.
NB:
These distances are fictitious and do not correspond to physical dimensions of the objects
in contact.
3.2
Characteristics of the grid
A number of nodes: 2
A number of meshs and types: 2
3.3 Functionalities
tested
Commands
Keys
AFFE_CHAM_NO
GRANDEUR
DEPL_R
[U4.26.01]
PROJ_VECT_BASE
VECT_ASSE
[U4.55.02]
PROJ_MATR_BASE
MATR_ASSE
[U4.55.01]
DEFI_OBSTACLE
TYPE
BI_PLAN_Y
[U4.21.07]
DYNA_TRAN_MODAL
CHOC
NOEU_2
[U4.54.03]
DYNA_TRAN_MODAL
CHOC
LAME_FLUIDE
[U4.54.03]
DYNA_TRAN_MODAL
CHOC
ALPHA
[U4.54.03]
DYNA_TRAN_MODAL
CHOC
BETA
[U4.54.03]
DYNA_TRAN_MODAL
CHOC
CHI
[U4.54.03]
DYNA_TRAN_MODAL
CHOC
DELTA
[U4.54.03]
Handbook of Validation
V5.01 booklet: Nonlinear dynamics of the discrete systems
HP-51/96/032 - Ind A
Code_Aster ®
Version
4.0
Titrate:
Forced SDND111 Vibrations of a system mass-arise
Date:
12/01/98
Author (S):
G. JACQUART
Key:
V5.01.111-A Page:
5/6
4
Results of modeling A
4.1 Values
tested
The displacements tested at the moments of cancellation speed give the following comparisons:
Identification
Reference
Aster
% Difference
(m)
(m)
For the parabolic profile:
Ux (t=0.13)
3.71678E3
3.71527E3
0.041
Ux (t=0.2684)
5.22565E3
5.20065E3
0.478
Ux (t=0.3902)
3.99499E3
3.99034E3
0.116
Ux (t=0.531)
4.68796E3
4.64597E3
0.896
For the uniform profile:
Ux (t=0.1282)
3.54435E3
3.54283E3
0.019
Ux (t=0.2651)
5.99203E3
5.96578E3
0.438
Ux (t=0.3876)
3.78488E3
3.78001E3
0.129
Ux (t=0.5263)
5.66919E3
5.61641E3
0.931
4.2 Remarks
One observes in this case a very good precision in the reproduction by the calculation of displacement
structure (less than 0.9% of difference with the quasi-analytical solution).
4.3 Parameters
of execution
Version: 3.05
Machine: CRAY C90
System:
UNICOS 8.0
Obstruction memory:
16 megawords
Time CPU To use:
250 seconds
Handbook of Validation
V5.01 booklet: Nonlinear dynamics of the discrete systems
HP-51/96/032 - Ind A
Code_Aster ®
Version
4.0
Titrate:
Forced SDND111 Vibrations of a system mass-arise
Date:
12/01/98
Author (S):
G. JACQUART
Key:
V5.01.111-A Page:
6/6
5
Summary of the results
Good agreement between the results obtained and the values of reference.
Handbook of Validation
V5.01 booklet: Nonlinear dynamics of the discrete systems
HP-51/96/032 - Ind A