On the Existence Possibility of Radial Forms of Oscillations of Ring Elements

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Abstract:

Nowadays, Hemispherical Resonator Gyroscope (HRG) are actively developed. HRG resonators have dynamic asymmetry, which leads to specific features in bending vibrations of rings, which in turn can lead to unstable operation of HRG. In the academic literature, the results of theoretical studies do not always match the experimental data. In some of the author’s works, the refinement of the mathematical model led to a number of new results. They show, for example, that some initial imperfections of form and attached masses lead to the appearance of radial modes of oscillations. In this case, the frequencies corresponding to the radial oscillation forms for certain geometric and wave parameters of the ring can be commensurable with the frequencies corresponding to the flexural modes of oscillations. However, it has not been possible to confirm this feature numerically and experimentally up to this day, unfortunately. It is believed that the frequencies of radial oscillations are either present in the frequency spectrum, but always at frequencies of higher oscillations, or absent altogether. In this article, this conclusion is questioned. On the example of oscillations of an isolated ring, the paper shows that the frequencies of radial oscillations can be not only of the same order as the frequencies of bending vibrations (as shown in the author’s previous works), but they can also be in the spectrum of lower frequencies (second, third tone) corresponding to bending modes.

References:

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