Abstract
The objective of the present paper is to represent a novel method to investigate the stable and unstable behaviors of fully clamped rectangular nano/microplates under the effects of electrostatic and Casimir pressures. To this end, the governing partial differential equation of equilibrium is considered and reduced to an algebraic equation using a simple and computationally efficient single degree of freedom (SDOF) model through the Galerkin weighted residual method. The linear and undamped mode-shapes of the plate are used in the Galerkin procedure as the weight function which is obtained by the extended Kantorovich method (EKM). The present findings are compared and validated by available empirical and theoretical results in the literature as well as those obtained by finite element (FE) simulation carried out using COMSOL Multiphysics commercial software and excellent agreements between them are observed.
Highlights
Micron and submicron scale structures are frequently used in different applications such as nano/microelectromechanical systems (N/MEMS) nowadays
Chemical analysis, molecular separation, DNA analysis, and microfluidic systems are some of biological usages of N/MEMS [3, 4]
To find the number of iteration which must be carried out in the extended Kantorovich method (EKM), a convergence study is performed in Table 2 for square microplate first mode-shape parameters as well as its fundamental natural frequency
Summary
Micron and submicron scale structures are frequently used in different applications such as nano/microelectromechanical systems (N/MEMS) nowadays. In this figure, the upper nano/microplate is considered as movable electrode which is modelled as a fully clamped nano/microplate and the other one is stationary electrode. The upper nano/microplate is considered as movable electrode which is modelled as a fully clamped nano/microplate and the other one is stationary electrode Both mechanical and electrical domains play crucial role in N/MEMS. The induced electrostatic force has an upper limit that overcomes the elastic restoring force and causes the sudden collapse conditions in the nano/microstructure This unstable behaviour of electrically actuated nano/microstructures is called pull-in instability and the associated voltage and associated displacement are known as pull-in voltage and pull-in displacement, respectively
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