Determination of Principal Axes of a Wineglass Using Acoustic Testing

Abstract

A general methodology to determine the principal axes of an arbitrary quasi-axi-symmetric resonator oscillating at its low-frequency flexural modal pair has been proposed. For an ideal axi-symmetric case, 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. This paper describes a simple mathematical method to determine the principal axes using acoustic signals of the structure’s free oscillations in air. An ordinary wineglass was chosen to verify the methodology. An impulse was applied to the wineglass in an arbitrary direction that generates a beating, and the oscillatory data were acquired by a pair of microphones located in a vicinity of the shell rim to estimate its principal axes using the proposed method. The accuracy of this approach was verified by additional tests, in which impacts were applied along the calculated principal axes to show that there is no beating. This method can be applied for initial tuning of an imperfect shell resonator and can be generalized for a fine tuning of a gyroscopic resonator.