Inherent Non-Linear Damping in Resonators with Inertia Amplification

TL;DR

This paper reveals that non-linear kinematic couplings in inertia-amplified resonators inherently cause amplitude-dependent damping, which is analytically derived and experimentally validated, impacting their use in vibration control.

Contribution

It provides the first analytical derivation of amplitude-dependent damping in inertia-amplified resonators and validates it with experimental evidence.

Findings

Damping increases with vibration amplitude.

Non-linear couplings induce inherent damping.

Experimental results confirm theoretical predictions.

Abstract

Inertia amplification is a mechanism coupling degrees of freedom within a vibrating structure. Its goal is to achieve an apparent high dynamic mass and, accordingly, a low resonance frequency. Such structures have been described for use in locally resonant metamaterials and phononic crystals to lower the starting frequency of a band gap without adding mass to the system. This study shows that any non-linear kinematic coupling between translational or rotational vibrations leads to the appearance of amplitude-dependent damping. The analytical derivation of the equation of motion of a resonator with inertia amplification creates insight in the damping process, and shows that the vibration damping increases with its amplitude. The theoretical study is validated by experimental evidence from two types of inertia-amplification resonators. Finally, the importance of amplitude-dependent damping is illustrated when the structure is used as a tuned mass damper for a cantilever beam.