Size-Dependent Pull-In Instability of Hydrostatically and Electrostatically Actuated Circular Microplates

This article is concerned with the development of a distributed model based on the modified strain gradient elasticity theory (MSGT), which enables us to investigate the size-dependent pull-in instability of circular microplates subjected to the uniform hydrostatic and nonuniform electrostatic actuations. The model developed herein accommodates models based on the classical theory (CT) and modified couple stress theory (MCST), when all or two material length scale parameters are set equal to zero, respectively. On the basis of Hamilton's principle, the higher-order nonlinear governing equation and corresponding boundary conditions are obtained. In order to linearize the nonlinear equation, a step-by-step linearization scheme is implemented, and then the linear governing equation is discretized along with different boundary conditions using the generalized differential quadrature (GDQ) method. In the case of CT, it is indicated that the presented results are in good agreement with the existing data in the literature. Effects of the length scale parameters, hydrostatic and electrostatic pressures, and various boundary conditions on the pull-in voltage and pull-in hydrostatic pressure of circular microplates are thoroughly investigated. Moreover, the results generated from the MSGT are compared with those predicted by MCST and CT. It is shown that the difference between the results from the MSGT and those of MCST and CT is considerable when the thickness of the circular microplate is on the order of length scale parameter.