3. Modeling A

3.1. Characteristics of modeling

The mass-spring system is modelled by an element of type POI1 at node \(\mathrm{NO1}\). It is subject to move along the \(x\) axis. Node \(\mathrm{NO1}\) is positioned at \(O=(0.0.0.)\).

An obstacle of type PLAN_Z (two parallel planes separated by a game) is used to simulate the possible shocks of the mass-spring system against a rigid plane. We choose to take the \(\mathrm{Oy}\) axis as normal to the shock plane, i.e. NORM_OBST: (0., 1., 0.). In order not to be hampered by the bounce of the oscillator symmetrically, we push this one very far away (cf. [Figure. 3.1-a]). We therefore choose to locate the origin of the obstacle in ORIG_OBS: (-1. 0. 0. 0.).

Figure 3.1-a: Modeled Geometry

It remains to define the parameter \(\mathrm{JEU}\) which gives the half-distance between the planes in contact. We want a real draw here, hence \(\mathrm{JEU}:1\). If you want a real game of \(j\), you must, in the case presented, impose \(\mathrm{JEU}:1+j\).

The time integration is carried out with the Euler algorithm and a time step of \({5.10}^{-4}s\). All calculation steps are archived. It is considered that the reduced damping \({\xi }_{i}\) for all the calculated modes is zero.

3.2. Characteristics of the mesh

The mesh consists of a node and a POI1 type mesh.

3.3. Tested sizes and results

For the first two shocks, the calculated values of the moment when the impact occurs, the maximum shock force, the shock time, the impulse and the impact speed are compared to the analytical values. The value of the absolute extremum of the impact force is also tested.

First shock:

Time ( \(s\) )	Reference
INST	1.5630E—02
F_ MAX	9,9500E+03
T_ CHOC	3,1260E—02
IMPULSION	1,9805E+02
V_ IMPACT	—1.

Second shock:

Time ( \(s\) )	Reference
INST	3,6100E—01
F_ MAX	9,9500E+03
T_ CHOC	3,1260E—02
IMPULSION	1,9805E+02
V_ IMPACT	—1,0000E+00

Time ( \(s\) )	Reference
F_ MAX_ABS	9.95E+03