Finite element method and analytical analysis of static and dynamic pull-in instability of a functionally graded microplate

Abstract

The static and dynamic pull-in phenomenon of a functionally graded Al/Al2O3 microplate, considering the damping coefficient and fringing field effects, has been analyzed because of its crucial effect in micro-electromechanical systems application, especially in microswitches. The nonlinear equation of motion of functionally graded microplate has been derived using Hamilton’s principle, and solved analytically. Furthermore, a finite element code has been developed to solve the problem. Comparing the theoretical and numerical results for specific boundary conditions demonstrates that the numerical solution predicts the pull-in phenomenon with the least errors; and it can be used for various material power laws, damping coefficients, and initial gaps between the microplate and the substrate. The numerical results for various boundary conditions demonstrate that by increasing the damping coefficient, the dynamic pull-in voltage is also increased, and pull-in time will slow down. Moreover, the effect of power law and applied voltage on the pull-in instability is investigated.