5. C modeling#
5.1. Characteristics of modeling#
Discrete elements of stiffness, damping and mass.
Characteristics of the elements:
DISCRET: |
nodal mass |
M_T_D_N |
linear stiffness |
K_T_D_L |
|
linear amortization |
A_T_D_L (\(c={10}^{-5}{c}_{\mathrm{critique}}\)) |
Boundary conditions: at node \(\mathrm{N1}\) DDL_IMPO DX = DY = DZ = 0.
Node names: \({P}_{1}=\mathrm{N1}\), \({P}_{2}=\mathrm{N2}\).
Calculation methods:
Integration on a modal basis with Newmark (\(\alpha =\mathrm{0,25}\), \(\delta =\mathrm{0,5}\))
No time \(\Delta t={10}^{-\mathrm{3s}}\)
Integration on a modal basis with Euler
No time \(\Delta t={10}^{-\mathrm{3s}}\)
Observation time: \(5s\).
5.2. Characteristics of the mesh#
Number of knots: 2
Number of meshes and type: 1 mesh SEG2
5.3. Tested sizes and results#
Moving point B
Move |
Move |
Move |
||||
Time |
Reference |
NEWMARK |
Tolerance |
EULER |
Tolerance |
|
(\(s\)) |
(\(m\)) |
Aster (\(m\)) |
(%) |
Aster (\(m\)) |
(%) |
|
0.06 |
3.1105 E—4 |
3.10936 E—4 |
3.10936 E—4 |
0.5% |
3.1181 E—4 |
0.5% |
0.13 |
—6,13250 E—4 |
—6,13016 E—4 |
0.5% |
—6,13380 E—4 |
0.5% |
|
0.25 |
—1.25380 E—3 |
—1.25304 E—3 |
0.5% |
—1.25418 E—3 |
0.5% |
|
0.69 |
3.44945 E—3 |
3.44691 E—3 |
0.5% |
3.45069 E—3 |
0.5% |
|
1.01 |
—4.88729 E—3 |
—4.89081 E—3 |
0.5% |
—4.88547 E—3 |
0.5% |
|
2.32 |
1.12876 E—2 |
1.12475 E—2 |
1.12475 E—2 |
0.5% |
1.13069 E—2 |
0.5% |
3.64 |
—1.77960 E—2 |
—1.77100 E—2 |
0.5% |
—1.78360 E—2 |
0.5% |
|
4.96 |
2.43613 E—2 |
2.42198 E—2 |
2.42198 E—2 |
0.5% |
2.44242 E—2 |
0.5% |
Point B speed
Speed |
Speed |
Speed |
||||
Time |
Reference |
NEWMARK |
Tolerance |
EULER |
Tolerance |
|
(\(s\)) |
(\({\mathrm{m.s}}^{-1}\)) |
Aster (\({\mathrm{m.s}}^{-1}\)) |
(%) |
Aster (\({\mathrm{m.s}}^{-1}\)) |
(%) |
|
0.04 |
9.09284 E—3 |
9.08897 E—3 |
0.5% |
9.08230 E—3 |
0.5% |
|
0.10 |
—2.39724 E—2 |
—2.39637 E—2 |
0.5% |
—2.40269 E—2 |
0.5% |
|
0.22 |
—5.49964 E—2 |
—5.49680 E—2 |
0.5% |
—5.48752 E—2 |
0.5% |
|
0.66 |
1.64958 E—1 |
1.64879 E—1 |
1.64879 E—1 |
1.64882 E—1 |
0.5% |
|
1.04 |
2.56456 E—1 |
2.56547 E—1 |
2.56547 E—1 |
0.5% |
2.57280 E—1 |
0.5% |
2.36 |
—5.79010 E—1 |
—5.80019 E—1 |
0.5% |
—5.81033 E—1 |
0.5% |
|
3.68 |
8.97631 E—1 |
9.00729 E—1 |
9.00729 E—1 |
0.5% |
9.00668 E—1 |
0.5% |
5.00 |
—1.21164 |
—1.21829 |
—1.21829 |
0.5% |
—1.21531 |
0.5% |
5.4. notes#
The results are tested at the peak level where the values are the most significant.
In the observation interval, we remain very much below the steady state in resonance whose displacement amplitude is \(10m\).