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arXiv · 2103.06772

On a Free Boundary Model for Three-Dimensional MEMS with a Hinged Top Plate I: Stationary Case

Katerina Nik
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Abstract

A stationary free boundary problem modeling a three-dimensional electrostatic MEMS device is investigated. The device is made of a rigid ground plate and an elastic top plate which is hinged at its boundary, the plates being held at different voltages. The model couples a nonlocal fourth-order equation for the deformation of the top plate to a Laplace equation for the electrostatic potential in the free domain between the two plates. The strength of the coupling is tuned by a parameter $\lambda$ which is proportional to the square of the applied voltage difference. Existence of a stable stationary solution is established for small values of $\lambda$. Nonexistence of stationary solutions is obtained when $\lambda$ is large enough.

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Katerina Nik. 2021-03-11. On a Free Boundary Model for Three-Dimensional MEMS with a Hinged Top Plate I: Stationary Case. https://arxiv.org/abs/2103.06772

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