Pull-in behavior of functionally graded micro/nano-beams for MEMS and NEMS switches

In this paper, pull-in behavior of cantilever micro/nano-beams made of functionally graded materials (FGM) with small-scale effects under electrostatic force is investigated. Consistent couple stress theory is employed to study the influence of small-scale on pull-in behavior. According to this theory, the couple tensor is skew-symmetric by adopting the skew-symmetric part of the rotation gradients. The material properties except Poisson’s ratio obey the power law distribution in the thickness direction. The approximate analytical solutions for the pull-in voltage and pull-in displacement of the microbeams are derived using the Rayleigh–Ritz method. Comparison between the results of the present work with Osterberg and Senturia’s article for pull-in behavior of microbeams made of isotropic material reveals the accuracy of this study. Numerical results explored the effects of material length scale parameter, inhomogeneity constant, gap distance and dimensionless thickness. Presented model has the ability to turn into the classical model if the material length scale parameter is taken to be zero. A comparison between classical and consistent couple stress theories is done which reveals the application of the consistent couple stress theory. As an important result of this study can be stated that a micro/nano-beams model based on the couple stress theory behaves stiffer and has larger pull-in voltages.