Aleksei Lukin

In this work, we study the nonlinear dynamics of a mode-localized mass detector. A system of equations is obtained for two weakly coupled beam resonators with an alternating electric current flowing through them and taking into account the point mass on one of the resonators. The onedimensional problem of thermal conductivity is solved, and a steady-state harmonic temperature distribution in the volume of the resonators is obtained. Using the method of multiple scales, a system of equations in slow variables is obtained, on the basis of which instability zones of parametric resonance, amplitude-frequency characteristics, as well as zones of attraction of various branches, are found. It is shown that in a completely symmetrical system (without a deposited particle), the effect of branching of the antiphase branch of the frequency response is observed, which leads to the existence of an oscillation regime with different amplitudes in a certain frequency range. In the presence of a deposited particle, this effect is enhanced, and the branching point and the ratio of the amplitudes of oscillations of the resonators depend on the mass of the deposited particle.

This article presents an analytical study of the dynamics of a micromechanical integrating gyroscope with a disk resonator. A discrete dynamic model of the resonator is obtained, taking into account the axial anisotropy of its mass and stiffness properties, as well as the action of the electrical control system of oscillations. An analysis of the spectral problem of disk vibrations in the plane is carried out. The nonlinear dynamics of the resonator in the regimes of free and parametrically excited vibrations are investigated. In the mode of parametric oscillations, qualitative dependencies of the gyroscopic drift on the operating voltage, angular velocity and parameters of defects are obtained.