Bifurcation Topology Tuning of 2:1 Internal Resonance in Electrostatically Coupled Resonators

Abstract The 2:1 internal resonance of electrostatically coupled resonators is theoretically investigated. A general dynamical model of the coupled resonators is established, and a reduced-order model incorporating the quadratic and cubic coupling terms is derived by the Galerkin method. The safe operating range of the system is determined by static analysis, and the operating voltage satisfying the frequency commensurable relation is determined by eigenvalue analysis. Finally, the dynamic response of the system is solved by a second-order method of multiple scales, and the results are verified by asymptotic numerical method coupled with harmonic balance method. For the case of response symmetry detuning due to cubic nonlinearity, we use non-resonant quadratic terms to adjust the bifurcation topology of this behavior, thus correcting the symmetry of the system and restoring the amplitude saturation at the antiresonance point.