Nonlinear dynamics of mode-localized MEMS accelerometer with two electrostatically coupled microbeam sensing elements

In the presented work, a model of a microelectromechanical accelerometer with two movable beam elements located between two fixed electrodes is proposed. The action of the transfer forces of inertia in the longitudinal direction leads to a change in the spectral properties of the system, which is a useful output signal of the sensor. The dynamics of the system in the presence of a weak electrostatic coupling between the sensitive elements is characterized by the phenomenon of modal localization - a significant change in the amplitude ratios for the forms of inphase and antiphase oscillations with small changes in the measured component of the acceleration vector of the moving object. Diagrams of equilibrium positions are plotted for varying the potential difference between a fixed electrode and a movable element and between two movable elements. The dependences of the frequencies and the ratio of the components of the eigenvectors on the magnitude of the inertial action are investigated. It is shown that the sensitivity of a sensor based on modal localization can be orders of magnitude higher than the sensitivity of known systems based on measuring the shift of natural frequencies. A nonlinear dynamic model of an accelerometer with external harmonic electrostatic excitation of oscillations is constructed. Resonance characteristics are obtained, a comparison is made between the model describing the modal characteristics of the system and the model describing the real dynamic mode of operation taking into account nonlinear factors.