Investigating the size effect on the pull-in displacement of geometric non-linear micro-bridges

The main object of the present paper is to investigate the effect of couple stress components on the pull-in displacement of geometric non-linear micro-beams. To this end, a size-dependent and geometric non-linear Euler-Bernoulli beam model with fully clamped boundary conditions is employed. The governing integro-differential equation of equilibrium is reduced to a non-linear algebraic equation in terms of the micro-beam mid-point deflection using the Galerkin projection method. Utilizing the stability analysis of the micro-beam, pull-in displacement and pull-in voltage of the system are simultaneously obtained. The results reveal that despite of linear micro-bridges, pull-in displacement in geometric non-linear micro-beams is size-dependent. For the purpose of validation, the present findings are compared and successfully verified by those published in the literature.