4. B modeling

4.1. 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:

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

4.2. Characteristics of the mesh

Number of knots: 10

Number of meshes and types: 9 SEG2

To test REST_SPEC_TEMP, we will compare several approaches (on a modal and physical basis) by testing the \(\mathrm{DX}\) component at the point \({P}_{4}\) of displacement, speed and acceleration.

Two methods are thus tested:

• calculation on a modal basis, then after REST_SPEC_TEMP, back to physical basis with RECU_FONCTION on the RESU_GENE,

• calculation on a physical basis directly.

Each time we test the option TOUT_CHAM =” OUI “or by calculating the three kinematic fields separately with NOM_CHAM =” DEPL “,” VITE “or” ACCE “.

By these different paths we must find the same results because the modal base is complete (this is not a problem because we have a low number of physical degrees of freedom).

Rather than testing only at particular times, comparisons (on a physical basis) are made by analyzing the sum over all the times of the absolute values of the maximum (at each step) of the differences between the temporal solutions (obtained by FFT inverse with REST_SPEC_TEMP). This norm must always be strictly zero.

Given the number of additional operations associated with the REST_SPEC_TEMP tests, the CPU time of B modeling is significantly increased, compared to other models that do not include these tests.

4.3. Tested sizes and results

Real and imaginary parts of component \(\mathrm{DX}\) 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

For the tests on REST_SPEC_TEMP, all the norms on the maximum values of the differences between the solutions calculated for the fields of displacement, speed and acceleration are strictly zero: we therefore have the same results on a modal or physical basis and regardless of the mode of use of REST_SPEC_TEMP.

4.4. 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.