Pull-in instability analysis of electrostatically actuated microplate with rectangular shape

As the size of the micro-electro-mechanical systems (MEMS) continues to decrease, the classical elasticity continuum theory may be inefficient to describe their mechanical behaviors. By introducing the strain gradient elasticity into the classical Kirchhoff plate theory, the size-dependent model for electrostatically actuated microplate-based MEMS is developed. The sixth-order partial differential equation (PDE), derived with the help of the principle of minimum potential energy, can be numerically solved by utilizing generalized differential quadrature (GDQ) method and pseudo arc-length algorithm. The model, with three material length scale parameters (MLSPs) included, can predict prominent size-dependent normalized pull-in voltage with the reduction of characteristic structural size, especially when the plate dimension is comparable to the MLSP (on the order of microns). This study may be helpful to characterize the mechanical properties of electrostatically actuated MEMS, or guide the design of microplate-based devices for a wide range of potential applications.