Determine the contribution of parametrically generated components to tip velocity

Determine whether the parametrically generated spectral content in the large-signal LTOI unimorph resonator adds to or subtracts from the whip-mode tip motion, including its base-to-tip amplification ratio and phase relative to the whip mode.

Background

The reported tip velocity is inferred by multiplying the full-bandwidth base-velocity peak by a geometric amplification factor of 3.85, calibrated at low drive. At high drive, however, the base-velocity signal contains parametrically generated components outside the principal whip-mode band.

The authors provide a conservative lower bound by retaining only the whip-band content, yielding 36.2 m/s compared with the reported 58.9 m/s at 192 Vpp. The unresolved issue is how the additional spectral components actually contribute to tip motion, because their spatial amplification and phase relation to the whip mode were not measured.

References

Whether that content adds to or subtracts from the tip motion cannot be determined here, since both its base-to-tip ratio and its phase relative to the whip mode are unknown.

— High-Velocity Whip-Mode Microresonator in LTOI Unimorph: Measurement Methodology and Large-Signal Characterization  (2609.19468 - Hsu et al., 16 Sep 2026) in Section 5, “Discussion and Limitations”