The Method of Accurate Determination of Frequencies and Modes of Vibration of the Resonator of the Vibration Frequency Sensor

The article is devoted to the development of an accurate method for determining the frequencies and vibration modes of a resonator of a vibration-frequency sensor by applying an exact simplification of the basic equations of resonant oscillations of a resonator taking into account the rigidity (compliance) of the supports and their location. The deviation of the parameters of the geometry of the resonator from the ideal and the heterogeneity of the material of the resonator affect the metrological characteristics of the vibration frequency sensor. However, existing technologies do not provide the possibility of manufacturing resonators with nominal parameters. The existing numerous algorithms for calculating the frequencies and waveforms of resonators are used to estimate the fundamental frequency of an oscillating system that do not take into account the dynamic characteristics. The accuracy of the oscillation frequency of the resonator depends on the choice of the mode of oscillations, which is sometimes difficult to predict in advance. Practical tasks require performing design work with the required accuracy. The lack of an accurate method for determining the frequencies and modes of vibration of the resonator of the vibration-frequency sensor, which would take into account the type of mounting and location of resistance, designers have to adapt existing approaches and calculation models to specific measurement conditions. Therefore, in practice, simplified and approximate methods of calculation are used. In the presence of concentrated masses and in the case of taking into account energy dissipation in the places where the resonator is fixed, the calculation methods become more laborious. In some cases, the possibility of a mathematical interpretation of a task becomes feasible only if some simplifications are introduced into the calculation.