Details
| Original language | English |
|---|---|
| Pages (from-to) | 393-411 |
| Number of pages | 19 |
| Journal | Interfaces and free boundaries |
| Volume | 18 |
| Issue number | 3 |
| Publication status | Published - 2016 |
Abstract
We consider the dynamics of an electrostatically actuated thin elastic plate being clamped at its boundary above a rigid plate. While the existing literature focuses so far on a two-dimensional geometry, the present model considers a three-dimensional device where the harmonic electrostatic potential varies in the three-dimensional time-dependent region between the plates. The elastic plate deflection evolves according to a fourth-order semilinear parabolic equation which is coupled to the square of the gradient trace of the electrostatic potential on this plate. The strength of the coupling is tuned by a parameter λ proportional to the square of the applied voltage. We prove that this free boundary problem is locally well-posed in time and that for small values of λ solutions exist globally in time. We also derive the existence of a branch of asymptotically stable stationary solutions for small values of λ and non-existence of stationary solutions for large values thereof, the latter being restricted to a disc-shaped plate.
Keywords
- Free boundary problem, MEMS, Stationary solutions
ASJC Scopus subject areas
- Physics and Astronomy(all)
- Surfaces and Interfaces
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In: Interfaces and free boundaries, Vol. 18, No. 3, 2016, p. 393-411.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - On a three-dimensional free boundary problem modeling electrostatic MEMS
AU - Laurençot, Philippe
AU - Walker, Christoph
N1 - Publisher Copyright: © European Mathematical Society 2016. Copyright: Copyright 2016 Elsevier B.V., All rights reserved.
PY - 2016
Y1 - 2016
N2 - We consider the dynamics of an electrostatically actuated thin elastic plate being clamped at its boundary above a rigid plate. While the existing literature focuses so far on a two-dimensional geometry, the present model considers a three-dimensional device where the harmonic electrostatic potential varies in the three-dimensional time-dependent region between the plates. The elastic plate deflection evolves according to a fourth-order semilinear parabolic equation which is coupled to the square of the gradient trace of the electrostatic potential on this plate. The strength of the coupling is tuned by a parameter λ proportional to the square of the applied voltage. We prove that this free boundary problem is locally well-posed in time and that for small values of λ solutions exist globally in time. We also derive the existence of a branch of asymptotically stable stationary solutions for small values of λ and non-existence of stationary solutions for large values thereof, the latter being restricted to a disc-shaped plate.
AB - We consider the dynamics of an electrostatically actuated thin elastic plate being clamped at its boundary above a rigid plate. While the existing literature focuses so far on a two-dimensional geometry, the present model considers a three-dimensional device where the harmonic electrostatic potential varies in the three-dimensional time-dependent region between the plates. The elastic plate deflection evolves according to a fourth-order semilinear parabolic equation which is coupled to the square of the gradient trace of the electrostatic potential on this plate. The strength of the coupling is tuned by a parameter λ proportional to the square of the applied voltage. We prove that this free boundary problem is locally well-posed in time and that for small values of λ solutions exist globally in time. We also derive the existence of a branch of asymptotically stable stationary solutions for small values of λ and non-existence of stationary solutions for large values thereof, the latter being restricted to a disc-shaped plate.
KW - Free boundary problem
KW - MEMS
KW - Stationary solutions
UR - http://www.scopus.com/inward/record.url?scp=84992052829&partnerID=8YFLogxK
U2 - 10.4171/IFB/368
DO - 10.4171/IFB/368
M3 - Article
AN - SCOPUS:84992052829
VL - 18
SP - 393
EP - 411
JO - Interfaces and free boundaries
JF - Interfaces and free boundaries
SN - 1463-9963
IS - 3
ER -