Frequency Tuning of a Wineglass Resonator Based on Acoustic Testing

A methodology to make a frequency tuning of an arbitrary quasi-axi-symmetric gyroscopic resonator oscillating at its low-frequency flexural modal pair has been proposed. For an ideal axi-symmetric resonator, such a structure has two degenerated modes with identical eigen frequencies and similar modal shapes distinguished by their angular orientation only. However, in reality, due to a small non-uniformity of the structure, the structure has two specific directions corresponding to slightly-different modal properties. Assuming only a mass imbalance, a mathematical formulation has been derived for the tuning by attaching point masses at specific locations. An ordinary wineglass has been chosen to verify this methodology. The principal axes and frequency mismatches were determined using acoustic signals of the free oscillations in air. Then, the magnitude of the point mass calculated by the proposed method has been applied for initial tuning of the imperfect shell resonator. The experimental result shows that the frequency mismatch has been reduced significantly, so, the validity of the proposed method has been verified. The proposed method can be generalized for a fine tuning of a gyroscopic resonator.