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Archive of Applied Mechanics
Published in: Archive of Applied Mechanics 4/2024

06-03-2024 | Original

Size-dependent buckling and instability of a porous microplate under electrostatic fields and Casimir forces

Authors: Mahdi Mojahedi, Mohammad Mojahedi, Majid R. Ayatollahi

Published in: Archive of Applied Mechanics | Issue 4/2024

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Abstract

This paper investigates the instability and buckling characteristics of a porous microplate under the influence of electrostatic fields, taking into account the implications of the intermolecular Casimir forces. Employing the modified couple stress theory, this research formulates equations that encapsulate the interplay between electrostatic and Casimir forces within porous plates. The analysis integrates distributed support loads, employing both Galerkin mode summation and finite element methods to solve static deformation equations and determine pull-in instability voltages and buckling loads. A novel approach is introduced, and equilibrium relationships are derived with respect to displacement to determine both the buckling load and instability voltage. This study effectively compares classical and non-classical theories, scrutinizing the effects of dimensionless length scale parameters and porosity ratios on maximum displacement, pull-in instability voltages, and buckling loads. The results demonstrate that the analytical method converges swiftly and aligns with the findings of the finite element method. The method for deriving equilibrium relationships proves to be accurate in predicting both instability voltage and buckling load. Additionally, the instability voltage exhibits an almost linear relationship with variations in the percentage of porosity, and similarly, the buckling load undergoes linear changes with alterations in porosity percentage. Hence, formulas for the linear relationships are calculated for both of these associations.
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Metadata
Title
Size-dependent buckling and instability of a porous microplate under electrostatic fields and Casimir forces
Authors
Mahdi Mojahedi
Mohammad Mojahedi
Majid R. Ayatollahi
Publication date
06-03-2024
Publisher
Springer Berlin Heidelberg
Published in
Archive of Applied Mechanics / Issue 4/2024
Print ISSN: 0939-1533
Electronic ISSN: 1432-0681
DOI
https://doi.org/10.1007/s00419-024-02567-9

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