Code_Aster
®
Version
3
Titrate:
FDLV102 Masses added, calculated on a generalized model
Date:
21/07/99
Author (S):
G. ROUSSEAU
Key:
V8.01.102-A
Page:
1/6
Manual of Validation
V8.01 booklet: Fluid
HP-51/96/031 - Ind A
Organization (S):
EDF/EP/AMV
Manual of Validation
V8.01 booklet: Fluid
V8.01.102 document
FDLV102 - Mass added calculated on a model
generalized
Summary:
This test belongs to the field of the fluid interaction/structure, in its aspect inertial coupling: it is about
to calculate a matrix of added mass, starting from a generalized model resulting from a calculation by under-structuring
dynamics. One carries out a modal analysis on the fluid coupled system/structure starting from a calculation by under
structuring, and one compares the result with a modal calculation in direct fluid. One tests thus, for a problem
two-dimensional fluid, the possibility of calculating the terms of added car-mass and mass added of
coupling between substructures deduced between them by rotation and translation (these “deduced” substructures
not being with a grid).
There is currently only one modeling, which consists in assigning to the fluid mesh thermal elements
plans.
Code_Aster
®
Version
3
Titrate:
FDLV102 Masses added, calculated on a generalized model
Date:
21/07/99
Author (S):
G. ROUSSEAU
Key:
V8.01.102-A
Page:
2/6
Manual of Validation
V8.01 booklet: Fluid
HP-51/96/031 - Ind A
1
Problem of reference
1.1 Geometry
O
L
L
D
With
B
C
D
E
F
G
H
I
J
K
L
O1
O2
R
R
K1
K2
K1
K2
K2
K2
K1
K1
X
y
Line of cylinders with circular section connected by springs to a fixed solid mass:
length:
L = L
X
= 2.0 m
width
L = L
y
= 1.0 m
radius of the cylinders:
R= 0.25 m
outdistance between centers of the tubes:
D = 1.0 m
Co-ordinates of the points (in m):
O1
O2
With
B
C
D
X
0.
1.00
0.50
1.50
1.50
0.50
y
0.
0.
0.50
0.50
0.50
0.50
E
F
G
H
I
J
K
L
X
- 0.50
0.
0.
0.25
0.
0.25
0.
0.50
y
0.
0.50
- 0.50
0.
0.25
0.
0.25
0.
1.2
Properties of materials
Fluid: Water
O
=
1000.0 Kg.m
3
Solid: Steel
S
=
7800.0 Kg.m
3
E = 2.E11 AP
= 0.3
Springs connecting the cylinder (substructure n°1 with a grid) to the solid mass:
Discrete element of the type
K_T_D_L
:
K
1
= (1.E7 1. 1.E7) NR/m
K
2
= (1. 1.E8 1.E8) NR/m
1.3
Boundary conditions and loading
Without object for the calculation of added mass.
1.4 Conditions
initial
Without object for the calculation of added mass.
Code_Aster
®
Version
3
Titrate:
FDLV102 Masses added, calculated on a generalized model
Date:
21/07/99
Author (S):
G. ROUSSEAU
Key:
V8.01.102-A
Page:
3/6
Manual of Validation
V8.01 booklet: Fluid
HP-51/96/031 - Ind A
2
Reference solution
2.1
Method of calculation used for the reference solution
Direct modal calculation (without dynamic under-structuring)
Calculation of the clean modes in air:
One calculates with the option
BANDAGE
of the operator
MODE_ITER_SIMULT
the first 4 frequencies
clean of the system in air (system mass-arises):
mode 1:
vibration of the two cylinders in phase according to OX
mode 2:
vibration of the cylinder n°2 according to OY (on the right)
mode 3:
vibration of the two cylinders in opposition of phase according to OX
mode 4:
vibration of the cylinder n°1 according to OY (on the left)
These modes can be analytically given [bib1].
Calculation ASTER provides for the Eigen frequencies in air:
mode 1:
F
1
= 17.3555 Hz
mode 2:
F
2
= 18.2034 Hz
mode 3:
F
3
= 42.6760 Hz
mode 4:
F
4
= 57.5418 Hz
Calculation of the matrix of mass added on modal basis:
On this modal basis, one calculates the matrix of added mass of command 4 with the operator
CALC_MATR_AJOU
[U4.55.10] option
“MASS_AJOU”
key word
MODE_MECA
(terms of the triangular one
inferiors):
m11 = 300.67 kg/m
m12 = 0.001 kg/m
m13 = 269.98 kg/m
m14 = 0.009 kg/m
m22 = 269.98 kg/m
m23 = 0.009 kg/m
m24 = 31.05 kg/m
m33 = 301.71 kg/m
m34 = 0.011 kg/m
m44 = 269.86 kg/m
Addition of this matrix to the matrix of generalized mass:
One adds the matrix thus determined to the matrix of generalized mass (operator
COMB_MATR_ASSE
[U4.53.01]) then one calculates the Eigen frequencies of the structure immersed with
the operator
MODE_ITER_SIMULT
option
PLUS_PETITE
[U4.52.01].
Calculation finds the Eigen frequencies following:
mode 1:
f'
1
= 15.8782 Hz
mode 2:
f'
2
= 16.7811 Hz
mode 3:
f'
3
= 39.0389 Hz
mode 4:
f'
4
= 53.0488 Hz
2.2
Results of reference
Eigen frequencies determined by ASTER in a direct calculation.
2.3 References
bibliographical
[1]
R.J GIBERT - Vibrations of the Structures. Interactions with fluids. Eyrolles (1988).
Code_Aster
®
Version
3
Titrate:
FDLV102 Masses added, calculated on a generalized model
Date:
21/07/99
Author (S):
G. ROUSSEAU
Key:
V8.01.102-A
Page:
4/6
Manual of Validation
V8.01 booklet: Fluid
HP-51/96/031 - Ind A
3 Modeling
With
3.1
Characteristics of modeling
Thermal formulation planes for fluid (TRIA3 and SEG2)
Plane and discrete deformation formulation for solid (TRIA3 and SEG2)
Cutting =
40 meshs TRIA3 according to the axis of
X
20 meshs TRIA3 according to the axis of
y
120 meshs SEG2 on the contour of the two cylinders
4 meshs SEG2 on the contour of the two cylinders representing them
meshs of the springs
Boundary conditions:
DDL_IMPO: (GROUP_NO: PBLOC1 DX: 0. DY: 0. DZ: 0.)
DDL_IMPO: (GROUP_NO: PBLOC2 DX: 0. DY: 0. DZ: 0.)
DDL_IMPO: (GROUP_NO: PBLOC3 DX: 0. DY: 0. DZ: 0.)
DDL_IMPO: (GROUP_NO: PBLOC4 DX: 0. DY: 0. DZ: 0.)
Name of the nodes:
E = PBLOC1
F = PBLOC3
L = PBLOC2
G = PBLOC4
3.2
Characteristics of the mesh
A number of nodes: 1 881
A number of meshs and types: 3.580 TRIA3, 124 SEG2
3.3 Functionalities
tested
Controls
Keys
AFFE_MODELE
“THERMAL”
“PLANE”
[U4.22.01]
CALC_MATR_AJOU
OPTION “MASS_AJOU”
MODELE_GENE
DIST_REFE
[U4.55.10]
NUME_DDL_GENE
“FULL”
STORAGE
[U4.55.07]
MODE_ITER_SIMULT
“TAPE”
concept
matr_asse_gene_r
FREQ
[U4.52.01]
COMB_MATR_ASSE
COMB_R
concept
matr_asse_gene_r
[U4.53.01]
Code_Aster
®
Version
3
Titrate:
FDLV102 Masses added, calculated on a generalized model
Date:
21/07/99
Author (S):
G. ROUSSEAU
Key:
V8.01.102-A
Page:
5/6
Manual of Validation
V8.01 booklet: Fluid
HP-51/96/031 - Ind A
4
Results of modeling A
4.1 Values
tested
Identification
Reference
direct calculation
Aster
calculation with
under-structuring
% difference
Command of the clean mode I: 1
15.8782
15.8782
+0.0000
Command of the clean mode I: 2
16.7811
16.7815
+0.00002
Command of the clean mode I: 3
39.0389
39.0289
0.0002
Command of the clean mode I: 4
53.0488
53.0586
0.0002
4.2 Remarks
Calculations of modes carried out by:
MODE_ITER_SIMULT option:“tape” List_freq: (2. 70. )
4.3 Parameters
of execution
Version: 3.05.24
Machine: CRAY C98
System:
UNICOS 8.0
Overall dimension memory:
8 megawords
Time CPU to use:
22 seconds
Code_Aster
®
Version
3
Titrate:
FDLV102 Masses added, calculated on a generalized model
Date:
21/07/99
Author (S):
G. ROUSSEAU
Key:
V8.01.102-A
Page:
6/6
Manual of Validation
V8.01 booklet: Fluid
HP-51/96/031 - Ind A
5 Recall
Course of the calculation of mass added by modal synthesis
·
Calculation of the clean modes of substructure 1 (cylinder of left with a grid) with interfaces
locked by
MODE_ITER_SIMULT
[U4.52.02]
·
Definition of two dynamic interfaces type CRAIG-BAMPTON (displacement unit
imposed):
“EAST”: to the point PBLOC2 = L corresponds
“CUS”: to the point PBLOC4 = G corresponds
·
Definitions of 2 modal bases associated these interfaces: operator
DEFI_INTERF_DYNA
[U4.55.03]:
BAMO1:
two dynamic modes and a constrained mode: unit displacement
on PBLOC2 = L
BAMO2:
two dynamic modes and a constrained mode: unit displacement
on PBLOC4 = G
·
Definitions of 2 macronutrients associated with these modal bases: operator
MACR_ELEM_DYNA
[U4.55.05]
·
Definition of the generalized model: operator
DEFI_MODELE_GENE
[U4.55.06]:
Sous_structure_1: “CYLINDR0”: corresponds to the cylinder of left (with a grid)
Sous_structure_2: “CYLINDR1”: corresponds to the cylinder of straight line (nonwith a grid)
This second substructure is deduced from the first by rotation from - 90°.
ANGL_NAUT
: (- 90., 0., 0.)
Connection: “IS” and “CUS”
This definition of the two substructures allows
DEFI_MODELE_GENE
to calculate
translation enters the two substructures.
·
Creation of a profile line of full sky starting from the definite generalized model: operator
NUME_DDL_GENE
[U4.55.07]
·
Assembly of the matrices of generalized stiffness and mass: operator
ASSE_MATR_GENE
[U4.55.08]
·
Calculation of the matrix of mass added starting from the definite Generalized Model:
The modal bases attached to each of the two substructures define
fields with the nodes of displacement to the site of the 1ère substructure in
mesh. The operator
CALC_MATR_AJOU
[U4.55.10] transports the field to the nodes
corresponding to the modal base of the second substructure via the translation and
rotation defined higher to assign it to the site of the second substructure
in the mesh. The calculation of the added mass is thus carried out following this displacement
of field to the nodes: one can thus calculate the mass added on the 1ère substructure,
mass added on the second substructure as well as the term of coupling between
two substructures, taking into account the fluid environment of each one of under
structures.
·
Summation of the matrix of assembled mass generalized with the matrix of added mass:
COMB_MATR_ASSE
[U4.53.01]
·
Calculation of the clean modes of the immersed total structure:
MODE_ITER_SIMULT
[U4.52.02].