Application of the Energy Method for Calculating the Ring Resonators Natural Oscillations Frequency Splitting With Spatial Defects
Published: 11.02.2026
Authors: Kiselev R.M., Sorokin F.D.
Published in issue: #2(170)/2026
Category: Mechanics | Chapter: Theoretical Mchanics, Machine Dynamics
The energy-based method developed by the authors calculating the ring resonators natural oscillations frequency splitting in micromechanical gyroscopes is extended to resonators with spatial defects. Since splitting of natural frequencies has a significant impact on the accuracy of navigation instruments with ring resonators, effective methods are required to study the dynamics of such resonators. In previous publications the authors demonstrated that the energy method exhibits high convergence, accuracy, and simplicity in calculating the vibrations of resonators in their own plane, therefore, this method was chosen to study the dynamics of ring resonators with spatial defects. The energy method was applied to calculate the resonator natural frequencies splitting caused by a screw defect. The calculation results were confirmed using an alternative approach based on numerical integration of the differential equations of flexible elastic rods.
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