3. Modeling A

3.1. Characteristics of modeling

Discreet translational rigidity element

Characteristics of the elements

DISCRET:	with nodal masses	M_T_D_N
	and stiffness matrices	K_T_D_L
	and damping matrices	A_T_D_L

Boundary conditions:

in all nodes	DDL_IMPO	(TOUT =” OUI “DY= 0., DZ= 0.)
at the end nodes		(GROUP_NO =AB DX= 0.)

Node names:

\(\mathrm{Point}A=\mathrm{N1}\)	\({P}_{1}=\mathrm{N2}\)
\(\mathit{Point}B\mathrm{=}\mathit{N10}\)	\({P}_{2}=\mathrm{N3}\)
	…
	\({P}_{8}=\mathrm{N9}\)

3.2. Characteristics of the mesh

Number of knots: 10

Number of meshes and types: 9 SEG2

3.3. Tested sizes and results

Real and imaginary parts of component \(\mathit{DX}\) of the displacement of point \({P}_{4}\).

Frequency	Reference
5.00	1.0237E—4 —8.5187E—6
5.50	4.5066E—4 —7.7914E—4
6.00	—9.4101E—5 —1.0585E—5
10.00	8.4143E—7 —1.0335E—6
15.00	1.2656E—5 —5.6652E—6
20.00	2.9784E—6 —6.6970E—6
25.00	—1.2536E—6 —5.2703E—6
30.00	—2.0904E—6 —5.4821E—6
35.00	—4.5447E—6 —1.1190E—6
39.50	—2.6895E—6 —3.0505E—7

Real and imaginary parts of the \(\mathrm{DX}\) component of the speed of point \({P}_{4}\).

Frequency	Reference
5.00	2.6762E—4 3.2160E—3
5.50	2.6925E—2 1.5574E—2
6.00	3.9904E—4 —3.5475E—3
10.00	6.4937E—5 5.2869E—5
15.00	5.3393E—4 1.1928E—3
20.00	8.4157E—4 3.7428E—4
25.00	8.2786E—4 —1.9691E—4
30.00	1.0333E—3 —3.9403E—4
35.00	2.4608E—4 —9.9943E—4
39.50	7.5709E—5 —6.6749E—4

Real and imaginary parts of the \(\mathit{DX}\) component of the acceleration of point \({P}_{4}\).

Frequency	Reference
5.00	—1.0103E—1 8.4076E—3
5.50	—5.3819E—1 9.3047E—1
6.00	1.3374E—1 1.5044E—2
10.00	—3.3218E—3 4.0801E—3
15.00	—1.1242E—1 5.0322E—2
20.00	—4.7033E—2 1.0575E—1
25.00	3.0931E—2 1.3004E—1
30.00	7.4273E—2 1.9478E—1
35.00	2.1979E—1 5.4116E—2
39.50	1.6566E—1 1.8789E—2

3.4. notes

Contents of the results file:

The values of the displacement of component \(\mathrm{DX}\) from point \({P}_{4}\) for all frequencies from \(5\) to \(40\mathrm{Hz}\) in steps of \(0.5\) (Initial test case of VPCS).

The values of the speed and acceleration of the \(\mathrm{DX}\) component of the point \({P}_{4}\) for some vibration frequencies.