Investigation of Nonlinear High-Intensity Dynamic Processes in a Non-ideal Solid-State Wave Gyroscope Resonator

A numerical-analytical method for solving the dynamic equation of an elastic ring resonator mounted on an arbitrarily rotating base is proposed. The method is based on the combined use of the generalized Bubnov-Galerkin (Kantorovich) method in angle and the direct method (Rothe) in time variable. In contrast to the previously presented results, the initial model takes into account terms proportional to the square of the angular velocity of the base and angular acceleration; it is also assumed that the resonator parameters are not uniform in angle. The given example allows us to conclude that the method is suitable for the case of high-intensity dynamic processes (large square of angular velocity and angular acceleration), in particular, the effect of reducing the influence of the defect of the resonator parameters by the 4th harmonic on its dynamics is shown.