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.File | Dimensione | Formato | |
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