1. Reference problem

1.1. Geometry

The structure is a rigid skate modelled by a single node. The skate is equipped with a return spring. It is subject to an external harmonic force \({F}_{\mathit{ext}}(t)\mathrm{=}a\mathrm{sin}(2\pi ft)\). It carries a condition of normal shock against a rigid plan, treated by penalization.

Figure 1.1-a : Geometry

1.2. Material properties

Properties of the structure:

\(m=156\mathrm{kg}\)

\({k}_{\mathit{rappel}}\mathrm{=}2\mathrm{\cdot }{10}^{6}N\mathrm{/}m\)

Properties of the rubber bump stop:

\({k}_{\mathrm{choc}}={10}^{10}N/m\)

\({c}_{\mathrm{choc}}=0\mathrm{Ns}/m\)

\({\mathrm{jeu}}_{\mathrm{choc}}=1\mathrm{mm}\)

1.3. Initial conditions, limits and loading

The skate starts with zero initial conditions: \({x}_{0}={x}_{t=0}=0\) and \(\dot{x}{}_{0}=\dot{x}{}_{t=0}=0\).

It only moves in one direction.

The external force is sinusoidal: \({F}_{\mathrm{ext}}(t)=\mathrm{Fa}\cdot \mathrm{sin}(2\pi ft)\), with \(\mathrm{Fa}=3\cdot {10}^{3}N\) and \(f=5\mathrm{Hz}\).