Nonlinear Oscillations in a Microelectromechanical System

The dynamics of an electret-based, capacitive micro- converter is described by a nonlinear set of ODEs, where the equation of a damped, driven oscillator is coupled, through a non linear term, to two first-order, non-linear differential equations. The system, which can admit pe- riodic, steady-state solutions, exhibits behaviors typical of non-linear, Duffing-like oscillators, as jump phenom- ena and hysteretic frequency response curves. In fact, for particular combinations of the physical parameters of the system, multiple steady-state solutions appear. The fre- quency response curves and the stability properties of the solutions are analyzed with a semianalytic approach. It is also proved, through perturbative analysis, that the system always acts as a linear oscillator under appropriate combi- nations of parameters: in this case the non-linear coupling term reduces to a viscouslike term, physically interpretable as electromechanical damping.