Nonlinear size-dependent pull-in instability and stress analysis of thin plate actuator based on enhanced continuum theories including nonlinear effects and surface energy

Abstract

In recent years, size dependent continuum theories have been commonly used to simulate material discontinuities in micro/nano-scales. In the present article, modified strain gradient theory (MSGT) and Gurtin–Murdoch surface elasticity, are used to investigate the size-dependent nonlinear pull-in instability and conduct a stress analysis of thin microplates. This paper modifies the classical equations and surface elasticity theory as a non-classical method which is able to account for the surface effect of nanomaterials with sufficient precision and lower calculation cost in comparison to atomic methods. The effects of van der Waals and Casimir forces are incorporated into the nonlinear governing equation of the system. A finite difference method (FDM) is employed to solve the nonlinear differential equation, and the pull-in parameters of the microplate are extracted. The effect of dispersion attractions and size-dependency on instability as well as the importance of the coupling between them is discussed. The most common types of thin-plates, including fully-clamped, simply-supported, and plates with mixed boundary conditions, are investigated. It is found that the significant difference between the pull-in instability parameters in the MSGT and the classical theory for thin microplates is merely due to the consideration of the size effect parameter in the modified strain gradient theory. The effect of surface/interface is also accounted for in the numerical FDM approach. Then, the stress analysis of the microplate is studied numerically by examining the surface/interface effect on the microplate with a square/rectangular section. The results obtained through this numerical method are plotted graphically.