The static pull-in instability analysis of electrostatically actuated shear deformable microbeams using single variable refined beam theory variants

The mathematical formulation of higher-order, displacement-based and variationally inconsistent refined beam theory variants is presented. These variants are then utilized for the static pull-in instability analysis of electrostatically actuated narrow shear deformable microbeams. In these variants, the axial and transverse displacements of the beam consist of flexural contributors and shearing contributors. Assumed beam displacement functions are such that flexural contributors do not influence the cross-sectional shearing force and shearing contributors do not influence the cross-sectional flexural moment. These variants do not need the shear correction factor. The governing equation of these variants is derived using beam gross equilibrium equations. These variants involve only one governing equation of fourth order with one unknown variable and have the coherence associated with the Bernoulli–Euler beam theory. Beam end conditions including two distinct and physically meaningful clamped end conditions are described for these variants. These variants and the Galerkin’s weighted residual technique are then used to study the interaction between the linear restoring force of the shear deformable microbeam and the nonlinear electrostatic force acting between the microbeam and the stationary electrode. Effects of the beam thickness-to-length ratio on pull-in instability parameters of electrostatically actuated microbeams with various fixity conditions are presented. In order to validate obtained numerical results, they are compared with corresponding results obtained by the authors using the Timoshenko beam theory-based spectral finite element analysis technique and with three-dimensional finite element simulations carried out using COMSOL Multiphysics[inline-graphic not available: see fulltext].