Complex Oscillations and Chaos in Electrostatic Microelectromechanical Systems under Superharmonic Excitations

Abstract

In this Letter, the formation of complex oscillations of the type 2n 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 2n 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.

Resonant behavior of a membrane of a dielectric elastomer

“…When X % 2x 1 , the membrane oscillates at the frequency x 1 , which is half of the frequency of excitation, indicative of subharmonic resonance. Subharmonic and superharmonic responses are common phenomena in nonlinear oscillations due to parametric excitation (Turner et al, 1998;De and Aluru, 2005).…”

Homoclinic bifurcation and chaos control in MEMS resonators

“…A classical example of a chaotic system is the Lorenz equations [14], which were derived to help understand the dynamics of cellular convection. Chaos due to various mechanisms has also been reported for nonlinear MEM oscillators, including microcantilevers for atomic force microscopy [15][16][17][18][19], in-plane MEM oscillators with separated comb drive actuators for signal encryption applications [20], electrostatically actuated MEM cantilever control systems [21], and MEM oscillators based on variable gap capacitors [22,23]. To the authors' knowledge, the heteroclinic and homoclinic chaos have not been thoroughly investigated for the above oscillators with both complicated potential and time-varying nonlinear stiffness terms.…”

Nonlinear static and dynamic responses of an electrically actuated viscoelastic microbeam

“…For this large surface-to-volume ratio, the integrated circuit (IC) technology in modern industry facilitates the fabrication of thousands of MEMS devices with increased reliability and reduced cost, and thus the research of MEMS has received considerable attentions in recent years [1][2][3][4][5].…”