On the uniqueness of the solution for a semi-linear elliptic boundary value problem of the membrane MEMS device for reconstructing the membrane profile in absence of ghost solutions

In this paper, the authors present a new condition of the uniqueness of the solution for a previous 1D semi-linear elliptic boundary value problem of membrane MEMS devices, where the amplitude of the electric field is considered proportional to the curvature of the membrane. The existence of the sol...

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Bibliographic Details
Published in:International journal of non-linear mechanics 2019-03, Vol.109, p.24-31
Main Authors: Versaci, Mario, Angiulli, Giovanni, Fattorusso, Luisa, Jannelli, Alessandra
Format: Article
Language:English
Subjects:
Boundary semi-linear elliptic equations
Boundary value problems
Curvature
Electric fields
Existence and uniqueness of the solution
Mathematical models
MEMS/NEMS devices
Microelectromechanical systems
Numerical methods
Shooting method
Uniqueness
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Summary:In this paper, the authors present a new condition of the uniqueness of the solution for a previous 1D semi-linear elliptic boundary value problem of membrane MEMS devices, where the amplitude of the electric field is considered proportional to the curvature of the membrane. The existence of the solution (membrane deflection) depends on the material of the membrane, which is obtained by Schauder–Tychonoff’s fixed point approach. Thus, in this paper, the result of uniqueness has been completely reformulated to obtain a condition depending on the material of the membrane achieving a new result of existence and uniqueness, depending on both the material of the membrane and the geometrical characteristics of the device. Then, by shooting numerical method, more realistic conditions for detecting eventual ghost solutions and new ranges of both operational parameters and mechanical tension of the membrane ensuring convergence have been achieved confirming the useful information on the industrial applicability of the model under study.
ISSN:0020-7462
1878-5638
DOI:10.1016/j.ijnonlinmec.2018.10.014