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

This paper investigates the randomness of the pull-involtage of functionally graded material micro-beams due torandomness in constituent material properties. Theboundary condition is clamped-clamped and materialproperties vary smoothly based on the power lawdistribution in thickness, are under the influence ofelectrostatic and intermolecular forces. The governingequations are derived based on Euler-Bernoulli beam theoryand nonlinear von Karman strain based on modified couplestress theory. The effects of volume fraction, the materiallength scale parameter, geometric parameters and theCasimir on mean value and relative standard deviation ofthe pull-in voltage are studied. The effect of individualconstituent materials and volume fraction index, whilerelative standard deviation changes are also investigated.