### Calculation of eigen frequency splitting of a cylindrical resonator of a solid-state wave gyroscope based on numerical integration of high accuracy

**Published:**23.05.2019

**Authors:** Narajkin O.S., Sorokin F.D., Guskov A.M., Kozubnyak S.A., Vahlyarskiy D.S.

**Published in issue: **#5(89)/2019

**DOI: **10.18698/2308-6033-2019-5-1876

**Category:** Mechanics | **Chapter:** Dynamics, Strength of Machines, Instruments, and Equipment

Solid-state wave gyroscopes are widely used in various fields of technology. The principle of their operation is based on the phenomenon of precession of the elastic wave, which rotates at an angular velocity proportional to the angular velocity of device body rotation. The accuracy of the device is significantly affected by splitting the gyroscope resonator frequency. The article considers splitting caused by the distortion of the cylindrical resonator cross-section shape. Since the splitting is very small, the perturbation method is usually used to determine it. The article proposes a new method for calculating the splitting based on the numerical high accuracy integration of equations of dynamics of a cylindrical shell with a non-circular cross section. To search for two very close frequencies, through the difference of which the splitting was found, a linear boundary eigenvalue problem was solved with retention of a large number of decimal places. Examples of determining the natural frequency splitting are presented for various laws of the distribution of the radial deviation of the cavity cross-section shape along the circumferential coordinate. Verification of the results was performed by the finite element method. When using the method each of the two close frequencies was calculated with high accuracy

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