*Article* **Friction-Induced Vibration Suppression via the Tuned Mass Damper: Optimal Tuning Strategy**

**Jia Lin Hu <sup>1</sup> and Giuseppe Habib 2,\***


Received: 29 October 2020; Accepted: 16 November 2020; Published: 20 November 2020 -

**Abstract:** Friction-induced vibrations are a significant problem in various engineering applications, while dynamic vibration absorbers are an economical and effective tool for suppressing various kinds of vibrations. In this study, the archetypal mass-on-moving-belt model with an attached dynamic vibration absorber was considered. By adopting an analytical procedure, the optimal tuning of the absorber's parameters was defined. Furthermore, the bifurcations occurring at the loss of stability were analytically investigated; this analysis illustrated that a properly chosen nonlinearity in the absorber's stiffness permits controlling the supercritical or subcritical character of the bifurcation. However, a numerical analysis of the system's dynamics, despite confirming the analytical results, also illustrated that the system's global behavior is only slightly affected by the bifurcation character. Indeed, a dynamic vibration absorber possessing a perfectly linear restoring force function seems to provide the optimal performance; namely, it minimizes the velocity range for which stick–slip oscillations exists.

**Keywords:** friction-induced vibrations; mass-on-moving-belt; dynamic vibration absorber; tuned mass damper; passive vibrations mitigation
