Code_Aster
®
Version
4.0
Titrate:
SDND111 Vibrations forced of a system mass-arises
Date:
12/01/98
Author (S):
G. JACQUART
Key:
V5.01.111-A
Page:
1/6
Manual of Validation
V5.01 booklet: Nonlinear dynamics of the discrete systems
HP-51/96/032 - Ind A
Organization (S):
EDF/EP/AMV
Manual of Validation
V5.01 booklet: Nonlinear dynamics of the discrete systems
V5.01.111 document
SDND111 - Forced vibrations 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 pitch of very small time to ensure itself of the convergence of
solution.
Code_Aster
®
Version
4.0
Titrate:
SDND111 Vibrations forced of a system mass-arises
Date:
12/01/98
Author (S):
G. JACQUART
Key:
V5.01.111-A
Page:
2/6
Manual of Validation
V5.01 booklet: Nonlinear dynamics of the discrete systems
HP-51/96/032 - Ind A
1
Problem of reference
1.1 Geometry
Z
X
X
X
·
F
O
2L
M
Fext (T)
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/m
3
viscosity:
= 1.E6
·
with a parabolic profile of flow in the fluid blade:
= -
=
= -
=
-
0 0833
0 19992
0 9996 10
0
6
.
,
.
,
.
.
,
·
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:
5 mm
Initial speed:
0 m/s
X
X
0
0
=
=
Code_Aster
®
Version
4.0
Titrate:
SDND111 Vibrations forced of a system mass-arises
Date:
12/01/98
Author (S):
G. JACQUART
Key:
V5.01.111-A
Page:
3/6
Manual of Validation
V5.01 booklet: Nonlinear dynamics of the discrete systems
HP-51/96/032 - Ind A
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:
MX
KX
F
X
X
X
X
X
X
X X
X
ext.
+
=
+ + +
+
2
3
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:
M
X
X
KX
F
X
X
X
X
X X
X
T
T
T
ext.
T
T
T
T
T
T
T
-
+
=
+ +
+
2
3
2
One uses the diagram of Euler modified to integrate this equation in time.
X X
0
0
,
given to T
0
,
To repeat:
X
F
KX
X
X
X
X
X X
X
M
X
T
T
dt
X
X
dt X
X
X
dt X
I
ext.
I
I
I
I
I
T
I
I
I
I
I
I
I
I
I
I
I
=
-
+ +
+
-
= +
=
+
=
+
+
+
+
+
2
3
2
1
1
1
1
as long as
T
T
I
end
+
<
1
.
2.2
Uncertainty on the solution
Solution approached numerically by pitch of very small time.
2.3 References
bibliographical
[1]
G.JACQUART “Modeling of the forces of fluid blade” - HP-61/94/159/A
Code_Aster
®
Version
4.0
Titrate:
SDND111 Vibrations forced of a system mass-arises
Date:
12/01/98
Author (S):
G. JACQUART
Key:
V5.01.111-A
Page:
4/6
Manual of Validation
V5.01 booklet: Nonlinear dynamics of the discrete systems
HP-51/96/032 - Ind A
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 the parameters
DIST_1
and
DIST_2
who 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 mesh
A number of nodes: 2
A number of meshs and types: 2
3.3 Functionalities
tested
Controls
Keys
AFFE_CHAM_NO
SIZE
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
SHOCK
NOEU_2
[U4.54.03]
DYNA_TRAN_MODAL
SHOCK
LAME_FLUIDE
[U4.54.03]
DYNA_TRAN_MODAL
SHOCK
ALPHA
[U4.54.03]
DYNA_TRAN_MODAL
SHOCK
BETA
[U4.54.03]
DYNA_TRAN_MODAL
SHOCK
CHI
[U4.54.03]
DYNA_TRAN_MODAL
SHOCK
DELTA
[U4.54.03]
Code_Aster
®
Version
4.0
Titrate:
SDND111 Vibrations forced of a system mass-arises
Date:
12/01/98
Author (S):
G. JACQUART
Key:
V5.01.111-A
Page:
5/6
Manual of Validation
V5.01 booklet: Nonlinear dynamics of the discrete systems
HP-51/96/032 - Ind A
4
Results of modeling A
4.1 Values
tested
The displacements tested at the moments of cancellation speed give the following comparisons:
Identification
Reference
(m)
Aster
(m)
% Difference
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
Overall dimension memory:
16 megawords
Time CPU To use:
250 seconds
Code_Aster
®
Version
4.0
Titrate:
SDND111 Vibrations forced of a system mass-arises
Date:
12/01/98
Author (S):
G. JACQUART
Key:
V5.01.111-A
Page:
6/6
Manual of Validation
V5.01 booklet: Nonlinear dynamics of the discrete systems
HP-51/96/032 - Ind A
5
Summary of the results
Good agreement between the results obtained and the values of reference.