Nonlinear pull-in instability of microplates with piezoelectric layers using modified couple stress theory

Abstract

In this study, the effects of piezoelectric layers, residual stresses and von Karman nonlinearity on the pull-in instability of a microplate are studied by taking into account the size effect of the system. The strain energy is obtained using the modified couple stress theory and the set of nonlinear equations of motion are derived using Hamilton's principle and finite element method (FEM) based on classical plate theory. Newton–Raphson's procedure is used to solve the nonlinear equations. The proposed model is used to study the pull-in voltage, pull-in displacement, and small amplitude vibration about the equilibrium position of microplates with piezoelectric layers. The results are validated by available experimental and theoretical data. They show that the pull-in voltage is affected by the material length scale parameter, but this effect is quite negligible when the ratio of plate thickness to material length scale parameter is larger than 10. It is found that the results obtained by the nonlinear theory are larger than those by the linear theory and their differences are increased by increasing the ratio of initial gap to the plate thickness. Moreover, it is found that applying a small positive voltage to the piezoelectric layers can decrease the maximum pull-in voltage.