 | | Mechanics of Solids
A Journal of Russian Academy of Sciences | | Founded
in January 1966
Issued 6 times a year
Print ISSN 0025-6544
Online ISSN 1934-7936 |
Archive of Issues
| Total articles in the database: | | 12854 |
| In Russian (Èçâ. ÐÀÍ. ÌÒÒ): | | 8044
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| In English (Mech. Solids): | | 4810 |
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| N.F. Morozov, A.V. Lukin, and I.A. Popov, "Symmetry Breaking and Multistability of Electrostatically Actuated Annular Microplates," Mech. Solids. 59 (1), 32-47 (2024) |
| Year |
2024 |
Volume |
59 |
Number |
1 |
Pages |
32-47 |
| DOI |
10.1134/S0025654423600630 |
| Title |
Symmetry Breaking and Multistability of Electrostatically Actuated Annular Microplates |
| Author(s) |
N.F. Morozov (St. Petersburg State University, St. Petersburg, 199034 Russia; Institute for Problems in Mechanical Engineering, Russian Academy of Sciences, St. Petersburg, 199178 Russia, n.morozov@spbu.ru)
A.V. Lukin (Peter the Great St. Petersburg Polytechnic University, St. Petersburg, 195251 Russia, lukin_av@srbstu.ru)
I.A. Popov (Peter the Great St. Petersburg Polytechnic University, St. Petersburg, 195251 Russia, popov_ia@spbstu.ru) |
| Abstract |
The article investigates the nonlinear problem of statics of a hollow circular microplate in
the electrostatic field of two electrodes. Using the assumptions of the geometrically nonlinear Karman
model, partial differential equilibrium equations for the system are obtained. The branch points of
nontrivial axisymmetric and skew-symmetric forms of equilibrium are analytically rigorously found.
It is noted that at certain ratios between the internal and external radii of the plate, the lowest form of
buckling is the skew-symmetric form with the lowest circumferential variability. Using the Galerkin
projection method and numerical methods of the theory of bifurcations, branching diagrams of both
axisymmetric and skew-symmetric equilibrium positions of the plate in the space of key parameters of
the system are found. It is shown that at certain relationships between the thickness of the plate and
the interelectrode gap, multistability is observed in the system-the existence of two or more non-trivial stable forms of equilibrium that are symmetrical relative to the plane of the plate. A qualitative
(parametric) analysis of the found areas of multistability is performed. The possibility of a plate jumping from one stable equilibrium position to another, controlled by an electrostatic field, is indicated.
The discovered effect can be used to develop high-precision microelectromechanical sensors of limiting values of various physical quantities, the output signal of which is an abrupt change in the amplitude of the static deflection of the sensitive element of the proposed configuration measured by a capacitive sensor. |
| Keywords |
MEMS, elastic stability, asymmetrical forms of equilibrium, symmetry breaking, bifurcation |
| Received |
03 April 2023 | Revised |
03 April 2023 | Accepted |
03 April 2023 |
| Link to Fulltext |
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