Hysteresis Suppression in Coupled Resonators Under Simultaneous Primary and Superharmonic Excitations

A general model of two resonators subjected to electrostatic coupling and simultaneous primary and superharmonic excitations is developped. A reduced-order model including quadratic and cubic nonlinear terms is generated and the multi-scale method is used to solve the dynamic characteristics and analyze the contribution of the different frequency components. In addition, an overall nonlinear coefficient is defined, which can be adjusted to make the system exhibit different dynamic characteristics including softening, hardening, and linear behaviors. Finally, the conditions for restoring the linear behavior at the highest possible amplitude and suppressing its hysteresis are given.