Session: MNS-01-02: Dynamics of MEMS/NEMS 2nd Session

Paper Number: 97497

97497 - Necessary and Sufficient Criteria for Bistability in Electrostatically Actuated Initially Curved Pre-Stressed Micro-Plates 

The study brings forth extended criteria for electrostatically actuated micro-plates, which take into account the presence of prestress. Following previous studies that analysed the veracity of a reduced order (RO) model, based on Berger's plate approximation, we present here an analysis of a single-degree-of-freedom (DOF) model. The resulting simplified model has enabled a semi-analytical derivation of criteria, for which the plate must adhere in order to gain bistability in the presence of electrostatic load. The study entails a precursor analysis of a ``mechanically'' loaded plate, so as to inspect the reliability of Berger's RO (BRO) model, whilst laying the analytical-numerical foundation for the subsequent electrostatic analysis. The end result is a set of criteria in the space of the plate elevation, thickness-to-gap ratio, and membrane load, splitting it into mono- and bistable domains. Numerical fits, obtained for various cases are also presented. In the process of the study, an upper bound for the condition was also disclosed, representing a necessary condition for bistability. The resulting criteria were compared to numerically obtained ones, extracted from the validated F\"{o}ppl-von-K\'{a}rm\'{a}n's RO (vKRO) model, as well as from direct finite differences (FD) based solutions (vKFD). The result has shown a remarkable qualitative resemblance, especially in low enough thickness-to-gap ratios, providing a much needed tool in the design of such structures.

Presenting Author: Lior Medina Tel-Aviv University

Presenting Author Biography: Received both B.Sc. (2010) and M.Sc. (2012) Magna Cum Laude in mechanical engineering from Tel Aviv University. My M.Sc. thesis was on "Symmetry breaking in electrostatically loaded curved bistable microbeams", conducted under the combined supervision of Prof. Slava Krylov & Prof. Rivka Gilat. In December 2012 I began my Ph.D. studies at the same institution, expanding my studies to the investigation of stability properties in electrostatically operated bistable microdevices. The research was supported by one of the best fellowships in Israel, granted by the Israel Ministry of Science. Further support came from Broadcom and the Israel Science Foundation following successful proposal applications. Upon obtaining a Ph.D. and a successful application to the Tel-Aviv Uni. – Northwestern Uni. joint postdoctoral fellowship, I relocated to Northwestern University in October 2018 as a postdoctoral fellow, conducting research on Kirigami structures under the guidance of Prof. Espinoza. In October 2019 I have relocated to the University of Cambridge, following a successful application to the Blavatnik postdoctoral fellowship and worked on electrostatically multistable structures under the guidance of Prof. Seshia. In October 2021 I relocated back to Tel Aviv University as a Senior Lecturer.

Authors:

Lior Medina Tel-Aviv University
Rivka Gilat Ariel University
Slava Krylov Tel-Aviv University