4. B modeling#
4.1. 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 (\(c\mathrm{=}\mathrm{0,01}{c}_{\mathit{critique}}\)) |
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 Fu-Devogelaere
No time \(\Delta t\mathrm{=}{10}^{\mathrm{-}3}s\)
Integration on a modal basis with 2nd order adaptive \(\Delta t\)
No initial time \(\Delta t\mathrm{=}{10}^{\mathrm{-}5}s\)
Maximum pitch \(\Delta t\mathrm{=}{10}^{\mathrm{-}3}s\)
Observation time: \(5s\).
4.2. Characteristics of the mesh#
Number of knots: 2
Number of meshes and type: 1 mesh SEG2
4.3. Tested sizes and results#
Move point \(B\)
Move |
Move |
Move |
||||
Time |
Reference |
DEVOG |
Tolerance |
ADAPT_ORDRE2 |
Tolerance |
|
(\(s\)) |
(\(m\)) |
Aster (\(m\)) |
(%) |
Aster (\(m\)) |
(%) |
|
0.06 |
3.06503 E—4 |
3.06503 E—4 |
3.06503 E—4 |
3.06503 E—4 |
0.5% |
|
0.13 |
—5.93807 E—4 |
—5.93807 E—4 |
0.5% |
—5.93729 E—4 |
0.5% |
|
0.25 |
—1.178772 E—3 |
—1.178772 E—3 |
0.5% |
—1.17890 E—3 |
0.5% |
|
0.69 |
2.91788 E—3 |
2.91788 E—3 |
2.91788 E—3 |
2.91744 E—3 |
0.5% |
|
1.01 |
—3.83901 E—3 |
—3.83901 E—3 |
0.5% |
—3.83567 E—3 |
0.5% |
|
2.32 |
6.68206 E—3 |
6.68206 E—3 |
6.68206 E—3 |
6.68656 E—3 |
0.5% |
|
3.64 |
—8,19821 E—3 |
—8,19821 E—3 |
0.5% |
—8,204 E—3 |
0.5% |
|
4.96 |
9.00847 E—3 |
9.00847 E—3 |
0.5% |
9.0143 E—3 |
0.5% |
Move |
Move |
Move |
||||
Time |
Reference |
RUNGE_KUTTA_54 |
Tolerance |
RUNGE_KUTTA_32 |
Tolerance |
|
(\(s\)) |
(\(m\)) |
Aster (\(m\)) |
(%) |
Aster (\(m\)) |
(%) |
|
0.06 |
3.06503 E—4 |
3.06420E-04 |
3.06420E-04 |
0.5% |
3.06443E-04 |
0.5% |
0.13 |
—5.93807 E—4 |
-5.93619E-04 |
-5.93619E-04 |
-5.93713E-04 |
0.5% |
|
0.25 |
—1.17872 E—3 |
-1.178373E—3 |
0.5% |
-1.17845E—3 |
0.5% |
|
0.69 |
2.91788 E—3 |
2.91701E—3 |
2.91701E—3 |
2.91706E—3 |
0.5% |
|
1.01 |
—3.83901 E—3 |
-3.83786E—3 |
0.5% |
-3.83772E—3 |
0.5% |
|
2.32 |
6.68206 E—3 |
6.68009E—3 |
6.68009E—3 |
6.67939E—3 |
0.5% |
|
3.64 |
—8,19821 E—3 |
-8.19578E—3 |
0.5% |
-8.19318E—3 |
0.5% |
|
4.96 |
9.00847 E—3 |
9.00579E—3 |
0.5% |
9.00479E—3 |
0.5% |
Point B speed
Speed |
Speed |
Speed |
||||
Time |
Reference |
DEVOG |
Tolerance |
ADAPT_ORDRE2 |
Tolerance |
|
(\(s\)) |
(\({\mathit{m.s}}^{-1}\)) |
Aster (\({\mathit{m.s}}^{-1}\)) |
(%) |
Aster (\({\mathit{m.s}}^{-1}\)) |
(%) |
|
0.04 |
8.95997 E—3 |
8.95997 E—3 |
0.5% |
8.9722 E—3 |
0.5% |
|
0.10 |
—2.33271 E—2 |
—2.33271 E—2 |
0.5% |
—2.33499 E—2 |
0.5% |
|
0.22 |
—5.20590 E—2 |
—5.20590 E—2 |
0.5% |
—5.2113 E—2 |
0.5% |
|
0.66 |
1.40500 E—1 |
1.40500 E—1 |
1.40500 E—1 |
0.5% |
1.40591 E—1 |
0.5% |
1.04 |
1.99889 E—1 |
1.99889 E—1 |
1.99889 E—1 |
1.99933 E—1 |
0.5% |
|
2.36 |
—3.39933 E—1 |
—3.39933 E—1 |
0.5% |
—3.39725 E—1 |
0.5% |
|
3.68 |
4.10585 E—1 |
4.10585 E—1 |
4.10585 E—1 |
4.10585 E—1 |
0.5% |
|
5.00 |
—4.4531 E—1 |
—4.45308 E—1 |
0.5% |
—4.44429 E—1 |
0.5% |
Speed |
Speed |
Speed |
||||
Time |
Reference |
RUNGE_KUTTA_54 |
Tolerance |
RUNGE_KUTTA_32 |
Tolerance |
|
(\(s\)) |
(\({\mathrm{m.s}}^{-1}\)) |
Aster (\({\mathrm{m.s}}^{-1}\)) |
(%) |
Aster (\({\mathrm{m.s}}^{-1}\)) |
(%) |
|
0.04 |
8.95997 E—3 |
8.89561E—3 |
0.5% |
8.95719E—3 |
0.5% |
|
0.10 |
—2.33271 E—2 |
-2.33194E—2 |
0.5% |
-2.33211E—2 |
0.5% |
|
0.22 |
—5.20590 E—2 |
-5.20435E—2 |
0.5% |
-5.20573E—2 |
0.5% |
|
0.66 |
1.40500 E—1 |
1.40458E—1 |
0.5% |
1.40475E—1 |
0.5% |
|
1.04 |
1.99889 E—1 |
1.99829E—1 |
1.99829E—1 |
1.99809E—1 |
0.5% |
|
2.36 |
—3.39933 E—1 |
-3.39832E—1 |
0.5% |
-3.39767E—1 |
0.5% |
|
3.68 |
4.10585 E—1 |
4.10463E—1 |
4.10463E—1 |
4.10403E—1 |
0.5% |
|
5.00 |
—4.4531 E—1 |
-4.45308E—1 |
-4.45308E—1 |
-4.45145E—1 |
0.5% |
4.4. notes#
The results are tested at the peak level where the values are the most significant.
The observation period chosen allows you to see the effect of amortization. However, in this interval, the response of point \(B\) still remains transient but we are close to the steady state whose displacement amplitude is \({10}^{\mathrm{-}2}m\).