Investigating of size-dependent buckling and instability caused by support forces and electrostatic field in porous annular microplates

Document Type : Article

Authors

1 Mechanical and Energy Engineering, Shahid Beheshti University

2 Distinguished Professor of Mechanical Engineering, Iran University of Science and Technology

3 Master's student, School of Mechanical Engineering, Iran University of Science and Technology

Abstract

In this paper, the static behavior, instability and buckling in porous micro/nano plates under electrostatic field are investigated based on the modified couple stress theory and with regard to modeling, determining equations and solution methods. The plate is considered to be porous and the porosity distribution is considered to be non-uniform. The equations are obtained considering the distributed support load. By using the definition of dimensionless parameters such as load, voltage and length scale, the equations of motion become dimensionless. It can be seen that in the special case, by removing the dimensionless non-classical parameters, the equation of the classical plate under the electrostatic field is obtained. Galerkin mode summation and finite element methods are utilized to solve the static deformation equation and assess the pull-in instability voltages and buckling loads. Convergence analysis is done and the number of approximation functions and elements required for both methods are calculated and the compatibility of the results obtained from the two methods is examined. In the results section, the difference between classical and non-classical theories is examined and the effect of dimensionless parameters of length scale and porosity ratio on maximum displacement, pull-in instability voltages and buckling load is studied. The results show that the use of modified stress couple theory leads to a very large stiffness prediction compared to modified couple stress theory. This result highlights the necessity of using the modified couple stress couple theory for the micro-scale. It is observed that the length scale parameter plays the role of stiffening. The change of porosity ratios also shows that as this ratio increases, the displacement increases and the stable areas decrease. Variations in this ratio lead to uniform changes in buckling load and pull-in instability voltage, and linear relationships are obtained to calculate buckling load and pull-in instability voltage versus porosity ratio. Also, in small values of support load, it is shown that the relationship between the instability voltage and the compressive load of the support is linear, but in the buckling range, this relationship is not linear.

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Sharif Journal of Mechanical Engineering

Articles in Press, Accepted Manuscript
Available Online from 20 June 2024

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