*2.3. Friction Force*

The applied friction law is described by an exponential decaying function, as done for instance in [1], i.e.,

$$
\mu(v\_{\rm rel}) = \left(\mu\_{\rm d} + (\mu\_{\rm s} - \mu\_{\rm d})\operatorname{e}^{-\frac{\left|\mathcal{U}\_{\rm rel}\right|}{\mathcal{U}\_{\rm D}}}\right) \operatorname{sgn}\left(v\_{\rm rel}\right) \tag{10}
$$

where the relative velocity is *v*rel = *v* − *x* ˜′ 1 . The values assumed by *µ* for a range of relative velocities for *µ*<sup>s</sup> = 1, *µ*<sup>d</sup> = 0.5 and *v*<sup>0</sup> = 0.5 are represented in Figure 3. The values for the friction law adopted in the present study are the same utilized in [1]. Nevertheless, as illustrated below, the optimization of the absorber parameters does not strictly depend on the considered friction law.

**Figure 3.** The weakening friction law with *µ*<sup>s</sup> = 1, *µ*<sup>d</sup> = 0.5, *v*<sup>0</sup> = 0.5.
