Hemispherical Resonator of a Rate-integrating Gyroscope: A ‎Novel Method for Determination of Eigenfrequencies and ‎Eigenforms in Presence of Imperfections‎

This paper investigates the problem of free vibrations of a hemispherical shell resonator of a rate-integrating gyroscope. A new realization of the approximate Ritz method for determining the frequencies and forms of free vibrations of an elastic hemisphere is proposed. Based on comparison with the results of direct finite-element modeling, it is shown that the proposed approach provides significantly greater accuracy in solving the spectral problem as compared to the solution based on analytical Rayleigh expressions for the forms of pure bending of the hemispherical surface. The importance of considering the potential energy of stretching of the mid-shell surface for the exact determination of frequencies and resonators waveforms for typical geometric parameters is noted. The degree of influence of the introduced refinements into the resonator’s mathematical model on the values of frequency splitting associated with gyroscopic forces and mass imperfections is investigated.