Stochastic pull-in voltage of nonlinear functionally graded micro-beams with parameter uncertainty based on modified couple stress theory

This paper investigates the randomness of the pull-in voltage of functionally graded material micro-beams due to randomness in constituent material properties. The boundary condition is clamped-clamped and material properties vary smoothly based on the power law distribution in thickness, are under the influence of electrostatic and intermolecular forces. The governing equations are derived based on Euler-Bernoulli beam theory and nonlinear von Karman strain based on modified couple stress theory. The effects of volume fraction, the material length scale parameter, geometric parameters and the Casimir on mean value and relative standard deviation of the pull-in voltage are studied. The effect of individual constituent materials and volume fraction index, while relative standard deviation changes are also investigated. .