A novel relation between pull-in voltage of the lumped and distributed models in electrostatically-actuated microbeams

In this paper static behavior of a fixed-fixed and cantilever microbeam (using both of the lumped and distributed models) to the DC voltage has been studied. By presenting a mathematical modeling Galerkin-based step by step linearization method (SSLM) has been used to solve the governing static equation. The calculated pull-in voltage has been validated by previous experimental and theoretical results and a good agreement has been achieved. Then by introducing novel design corrective coefficients, independent of the beam´s material and geometric, has been given a closed form relationship between pull-in voltage of the lumped and distributed models, with considering the residual stresses and axial force effects. By multiplying these design coefficients with pull-in voltage of the lumped model, the pull-in voltage of a given microbeam can be gained without any need to solve the nonlinear governing equation.