Magnetostrictive mechanical frequency combs

Magnetostriction plays a pivotal role in magneto-mechanical systems. Here, we propose and experimentally demonstrate a mechanical frequency comb solely requiring the fundamental mode f₀ of a magnetostrictive mm-scale macroresonator. Both integer-harmonic combs and half-integer-harmonic combs are observed in kHz regime with Hz resolution by near-resonant pumping f_p ≈ f₀ and parametrical stiffness modulation f_s ≪ f₀. The tooth spacing of both combs is determined by f_s, which can be continuously tuned by changing f_s from Hz to kHz. Moreover, the half-integer-harmonic combs can be purposely switched with frequency shifting half a tooth spacing via suppressing period-doubling bifurcation. The experimentally observed formation, evolution, and switching of combs can be well understood by introducing the bias magnetical force and the parametrically modulated stiffness into the Duffing equation. Our findings could provide a magneto-mechanical platform with tunability for potential applications in the acoustic frequency range such as non-invasive/contactless sensor and wireless antenna.