Differential resonant MEMS accelerometer: synchronization characteristics of weakly coupled microbeam sensing elements

This work is devoted to studying the conditions and scenarios for synchronizing oscillations of weakly coupled microbeam elements of a differential resonant MEMS accelerometer operating in the dual-loop self-oscillator mode. The model of a system of two Van der Pol self-oscillators with a nonlinear elastic coupling between moving elements, obtained using the Galerkin method, was studied using the multiscale method. The modes of beats and synchronization of oscillations of two resonators are found analytically and numerically, and the boundary between these modes in the space of system parameters is determined. Along with a local bifurcation analysis of the considered stationary regimes, a global analysis of the evolution and branching of limit cycles in the space of slow variables was also carried out, which made it possible to detect zones of coexistence of stable synchronization and beat regimes with their basins of attraction. The influence of the factor of the designed or technologically determined non-identity of the design of two resonators on the location of the parametric zones of synchronization and beats is studied.