The present paper studies the influence of nonlinear elastic properties of structural material on the dynamics of wave solid- state gyroscopes. The resonator is manufactured as a thin elastic hemispherical shell, which is mounted on a mobile basis. It is assumed that the elastic properties of the cavity material are nonlinear and obey Hooke's law. We obtained quasi-linear time- dependent system of differential equations, which describe the fluctuations of the sensor by two generalized coordinates. The study of this system is conducted in a quasi-linear formulation of the small-parameter method of Krylov ? Bogolyubov. It is shown that the nonlinear elasticity properties of the resonator leads to the precession of the wave pattern of the resonator and introduces an additional error in the instrument.
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