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 (\({k}_{\mathrm{N1N2}}=\mathrm{10k}\), \({k}_{\mathrm{N2N3}}=k/10\))
	linear amortization	A_T_D_L

Boundary conditions: at node \(\mathrm{N1}\) DDL_IMPO \(\mathrm{DX}=\mathrm{DY}=\mathrm{DZ}=0\).

Node names: \(A=\mathrm{N1}\), \(C=\mathrm{N2}\), \(B=\mathrm{N3}\).

Calculation methods:

• Integration into physical space with Newmark (\(\alpha =\mathrm{0,25}\), \(\delta =\mathrm{0,5}\))

No time \(\Delta t={10}^{-3}s\)

• Full modal integration with Euler

No time \(\Delta t={10}^{-3}s\) then modal recombination

• Full modal integration with 2nd order adaptive \(\Delta t\)

No initial time \(\Delta t={10}^{-3}s\) then modal recombination

• Integration on a complete modal basis with \(\Delta t\) adaptive by the Runge-Kutta order method (32). Relative error tolerance is \({10}^{-5}\).

• Full modal integration with \(\Delta t\) adaptive using the Runge-Kutta order method (54). Relative error tolerance is \({10}^{-6}\).

Observation time: \(\mathrm{2,5}s\).

4.2. Characteristics of the mesh

Number of knots: 3

Number of meshes and type: 2 meshes SEG2

4.3. Tested sizes and results

• Move (\(m\)) from point \(B\)

Time	Reference
(\(s\))
0.19	2.9334 E-3
0.38	1.0959 E-3
0.57	2.2468 E-3
0.76	1.5260 E-3
0.95	1.9773 E-3
1.19	-1.2107 E-3
1.38	7.5880 E-4
1.57	-4.7553 E-4
1.76	2.9796 E-4
1.95	-1.8668 E-4
2.14	1.1694 E-4
2.33	-7.3246 E-5

• Speed (\({\mathrm{m.s}}^{-1}\)) of point \(B\)

Time	Reference
(\(s\))
0.09	2.4261 E-2
0.28	-1.5210 E-2
0.47	9.5332 E-3
0.66	-5.9745 E-3
0.85	3.7438 E-3
1.08	-2.6037 E-2
1.27	1.6302 E-2
1.46	-1.0204 E-2
1.66	6.387-E-3
1.85	-4.0059 E-3
2.04	2.5114 E-3
2.23	-1.5743 E-3
2.42	9.8676 E-4

4.4. notes

The results are tested at the level of the respective peaks of movement and speed where the values are the most significant.