Effect of temperature on pull-in voltage and natural frequency of an electrostatically actuated microplate

In this paper a model based on distributed parameters has been presented to study temperature effects on the mechanical behavior of an electrostatically actuated microplate. This work consists of two major parts. First part deals with the effect of temperature, stretching and residual stresses on the static instability of an electrostatically actuated microplate. To do this, the governing nonlinear integro differential equation has been derived using Kirchhoff thin plate theory and linearized using step-by-step linearization method (SSLM). The obtained linearized differential equation has been discretized applying finite difference method (FDM). The results obtained have been compared to other existing experimental results and good agreement is observed. In the second part, in order to study the natural or eigenfrequencies of the system, small vibrations of the electrostatically deflected microplate about the equilibrium position have been studied. Here, the governing linear eigenvalue partial differential equation has been solved using a Galerkin based reduced-order model, and the natural frequencies of the microplate have been determined. The results show that temperature changes and residual stress have considerable effects on the system characteristics such as pull-in voltage and natural frequencies.