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arXiv · 1409.2812

A variational approach to a stationary free boundary problem modeling MEMS

Philippe Laurencot·Christoph Walker
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Abstract

A variational approach is employed to find stationary solutions to a free boundary problem modeling an idealized electrostatically actuated MEMS device made of an elastic plate coated with a thin dielectric film and suspended above a rigid ground plate. The model couples a non-local fourth-order equation for the elastic plate deflection to the harmonic electrostatic potential in the free domain between the elastic and the ground plate. The corresponding energy is non-coercive reflecting an inherent singularity related to a possible touchdown of the elastic plate. Stationary solutions are constructed using a constrained minimization problem. A by-product is the existence of at least two stationary solutions for some values of the applied voltage.

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Philippe Laurencot, Christoph Walker. 2014-09-09. A variational approach to a stationary free boundary problem modeling MEMS. https://arxiv.org/abs/1409.2812

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