Complex oscillations and chaos in electrostatic microelectromechanical systems under superharmonic excitations

In this Letter, the formation of complex oscillations of the type 2(n) M oscillations per period at the Mth superharmonic excitation is reported for electrostatic microelectromechanical systems. A dc bias (beyond "dc symmetry breaking") and an ac signal (at the Mth superharmonic frequency) with an amplitude around "ac symmetry breaking" gives rise to M oscillations per period or period M response. On increasing the ac voltage, a cascade of period doubling bifurcations take place giving rise to 2(n) M oscillations per period. An interesting chaotic transition (1-band and 2-band chaos) is observed during the first period doubling bifurcation. The nonlinear nature of the electrostatic force is shown to be responsible for the reported observations.