Pull-in and snap-through instabilities in transient deformations of microelectromechanical systems

Abstract

We analyze transient finite electroelastodynamic deformations of a perfect electrically conducting undamped clamped–clamped beam, a clamped–clamped parabolic arch and a clamped–clamped bell-shaped arch suspended over a flat rigid semi-infinite perfect conductor. The pull-in instability in a beam and the pull-in and the snap-through instabilities in the two arches due to time-dependent potential difference between the two electrodes have been studied. The potential difference is applied either suddenly or is increased linearly in time. Since the time scale of the transient electric forces is very small as compared to that of the mechanical forces, inertia effects only in the mechanical deformations are considered. Effects of both material and geometric nonlinearities are incorporated in the problem formulation and solution; however, damping due to the interaction of the structure with the surrounding medium is neglected. The coupled nonlinear partial differential equations for mechanical deformations are solved numerically by the finite element method and those for the electrical problem by the boundary element method. The Coulomb pressure due to the potential difference between the two electrodes is a nonlinear function of the a priori unknown distance between them. The potential difference that induces either the pull-in instability in a beam or the snap-through followed by the pull-in instabilities in an arch has been computed. Wherever possible these results are compared with those available in the literature. With a decrease in the rate of the applied potential difference, the pull-in and the snap-through parameters approach those for a static problem. Also, for large rates of increase in the potential difference between the two electrodes, the snap-through instability in an arch is suppressed and only the pull-in instability occurs.

Theoretical and Experimental Investigation of the Nonlinear Behavior of an Electrostatically Actuated In-Plane MEMS Arch

“…where, (5) is multiplied by the denominator of the electrostatic force term (1-w o -w) 2 in order to reduce the computational cost [31,33]. Then, substituting equation (8) into the resulting equation, multiplying by the mode shape φ j (x), and then integrating the outcome over the normalized domain…”

“…The bistability nature of arches gives them the advantage of exhibiting large motion stroke when moving between the two stable states, which can be advantageous for resonators and other actuation applications because it yields significantly large signal-to-noise ratio. Consequently, the bistability of arches has been thoroughly studied in order to exploit them in useful applications [1][2][3][4][5][6][7][8][9][10]. For example, micro arches are used as microbridges [7], microvalves [11], microelectro switches or relays [12], logic memories [13], micromuscles [14], and micro-optical switches [15].…”

“…Das et al [2] studied the snap-through and pull-in instabilities of parabolic-and bell-shaped clamped-clamped micro arches. Zhang et al [3] derived an analytical expression to predict the snap-through and pull-in instabilities.…”

MEMS Technologies for Energy Harvesting

“…A similar approach is taken in [26] on which pre shaped buckled beams are designed [27]. In general the physics of curved arches requires additional analysis in order to predict the nonlinear effects due to the curvature of the structures and the snap-through instability [28,29].…”

An Electrostatically Actuated MEMS Arch Band-Pass Filter

“…A shallow arch is a beam, which is designed and fabricated to be curved without the need for an axial stress or buckling to form its shape. This kind of structure posses a bi-stable behavior, which has drawn attention for MEMS applications, especially as MEMS switches and actuators [12][13][14][15][16][17][18][19]. Recent works using static and transient models [18,19] have shown that initially curved clamped-clamped beams can undergo several scenarios of escapes via snap-through and pull-in instabilities due to DC electrostatic load.…”