Modal Parameter Tuning of an Axisymmetric Resonator via Mass Perturbation

This paper reports the permanent frequency mismatch reduction of the primary wineglass modes in a planar axisymmetric resonator by strategic mass loading. The resonator consists of a set of concentric rings that are affixed to neighboring rings by a staggered system of spokes. The outer layers of spokes are targets for mass deposition. This paper develops modified ring equations that guide the mass perturbation process, and despite the fact that the deposited mass and deposition locations are quantized, it is possible to systematically reduce the frequency difference of the wineglass modes to effective degeneracy such that two modes cannot be distinguished in a frequency response plot. Results on five resonators are reported with nominal wineglass modes near 14 kHz, quality factors of 50k, and frequency mismatches exceeding 30 Hz in some cases, but with postperturbation mismatches smaller than 80 mHz. Furthermore, it is also shown that the quality factors remain unchanged.