Parametric Excitation in a Two Degree of Freedom MEMS System

Abstract

This contribution investigates the influence of parametric excitation on the dynamic stability of a microelectromechanical system. In systems with just a single degree of freedom, parametric excitation causes the oscillator to exhibit unstable behavior within certain intervals of the parametric excitation frequency. In multi-degree of freedom systems on the other hand, unstable behavior is caused within a wider range of intervals of the parametric excitation frequency. Moreover, such systems show frequency intervals of enhanced stability, an effect known as anti-resonance phenomenon. Both types of phenomena, the parametric resonance and anti-resonance, are modeled and studied for a microelectromechanical system with two degrees of freedom and some novel results are discussed.

Stability of dynamic response of suspension bridges

“…Indeed, near ω � = (ω � ,1 − ω � ,1 ) we get a large stable region even for wind speed level higher than the Flutter one. In fact, as reported also in different papers [48], the so called anti-parametric resonance with respect to the parametric and additive parametric ones has a stabilizing effect on the dynamic response of the system. This is due primary to the fact that this phenomenon is able to increase significantly the damping of the system.…”

“…In many real systems the parameters into the governing equations may vary periodically in time [48]. This is not generally the case when dealing with suspension bridges, since structural parameters are fixed and can vary only in a very long period.…”

Internal Parametric Resonance and Aeroelastic Effects for Long-Span Suspension Bridges

“…An interesting feature is that near the curve of anti-resonance we get always a larger stable region. In fact, as reported also in different papers [41], the so called anti-parametric resonance with respect to the parametric and additive parametric ones has a stabilizing effect on the dynamic response of the system. This is due primary to the fact that this phenomenon is able to increase significantly the damping of the system.…”

“…In many real-life systems, mainly in the electrical field, the parameters which govern the equations of motion may vary periodically in time [41]. When dealing with suspension bridges, this is not the case since structural parameters are fixed and can vary only in a very long period.…”

Jump and pull-in dynamics of an electrically actuated bistable MEMS device

“…Kumar and Rhoads investigate an optically actuated bistable MEMS device [3], Hornstein and Gottlieb multimode dynamics and internal resonances in noncontact atomic force microscopy [4], Cho et al nonlinear hardening and softening response and the switching among them [5], Welte et al parametric resonance and anti-resonance [6], Kacem et al primary and superharmonic resonances [7], Tusset et al chaos control designs [8], Gerson et al pull-in phenomenon in electrically actuated meso scale beams [9], Vyasarayani et al past pull-in behavior [10], Ouakad and Ramini et al response to mechanical shock [11,12] Motivated by the increasing relevance of nonlinear features, the present research study analyzes a theoretical bistable MEMS device, Fig. 1.…”