A typical micro electromechanical system (MEMS) actuator is formed by a micro cantilever beam electrode suspended above a conductive substrate and subject to a voltage difference. Due to electrostatic forces the micro-beam deflects toward to the substrate and pulls-in onto the substrate plane at a critical voltage, named pull-in voltage, thus causing a short circuit. Under the pull-in voltage the micro-beam leaves the principal equilibrium path, which becomes unstable due to the increase of the electrostatic force with the beam deflection, and a kind of snap-through instability occurs. The deflection of an elastic cantilever beam is described by a fourth-order non-linear ODE. Using fixed point Theorem, we prove the local uniqueness of the solution with respect to L2 norm.

Uniqueness condition for the (local) solution of the electrostatic micro-cantilever beam / DI RUVO, Lorenzo; Radi, Enrico. - ELETTRONICO. - (2016), pp. 83-84. (Intervento presentato al convegno The 14th International Conference on Integral Methods in Science and Engineering tenutosi a Padova nel July 25-29, 2016).

Uniqueness condition for the (local) solution of the electrostatic micro-cantilever beam

DI RUVO, LORENZO;RADI, Enrico
2016

Abstract

A typical micro electromechanical system (MEMS) actuator is formed by a micro cantilever beam electrode suspended above a conductive substrate and subject to a voltage difference. Due to electrostatic forces the micro-beam deflects toward to the substrate and pulls-in onto the substrate plane at a critical voltage, named pull-in voltage, thus causing a short circuit. Under the pull-in voltage the micro-beam leaves the principal equilibrium path, which becomes unstable due to the increase of the electrostatic force with the beam deflection, and a kind of snap-through instability occurs. The deflection of an elastic cantilever beam is described by a fourth-order non-linear ODE. Using fixed point Theorem, we prove the local uniqueness of the solution with respect to L2 norm.
2016
The 14th International Conference on Integral Methods in Science and Engineering
Padova
July 25-29, 2016
83
84
DI RUVO, Lorenzo; Radi, Enrico
Uniqueness condition for the (local) solution of the electrostatic micro-cantilever beam / DI RUVO, Lorenzo; Radi, Enrico. - ELETTRONICO. - (2016), pp. 83-84. (Intervento presentato al convegno The 14th International Conference on Integral Methods in Science and Engineering tenutosi a Padova nel July 25-29, 2016).
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