3. Modeling A

3.1. Characteristics of modeling

The mass-spring system is modelled by a discrete element DIS_T.

Numeric data:

for the mass-spring system:	\(m=\mathrm{450 }\mathrm{kg}\)
for the floor:	\({k}_{\mathrm{0 }}={10}^{\mathrm{5 }}N/m\)
for non-linearity:	\({x}_{\mathrm{0 }}=\mathrm{0,1 }m\); \(a=\mathrm{0,01}\) and \(\omega =\pi /4\).

The time integration is carried out with the Euler algorithm or the Devogelaere algorithm and a time step of 0.02 seconds. The calculations are archived every time step.

We consider reduced damping \({\xi }_{i}\) to zero for all the calculated modes.

3.2. Characteristics of the mesh

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

3.3. Tested sizes and results

We check the natural frequency of the oscillator as well as the relative movements of the node \(\mathrm{NO1}\) at different times (for the integration algorithm EULER).

Frequency (Hz)	Reference
	2.37254

Relative displacement of node \(\mathrm{NO1}\) with the Euler numerical integration algorithm:

Time (s)	Reference
2	0.01
6	—0.01
10	0.01
14	—0.01
18	0.01

Relative displacement of node \(\mathrm{NO1}\) with Devogelaere’s numerical integration algorithm:

Time (s)	Reference
2	0.01
6	—0.01
10	0.01
14	—0.01
18	0.01