Inherent non-linear damping in resonators with inertia amplification

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