Size-dependent electro-elasto-mechanics of MEMS with initially curved deformable electrodes

• Electro-elasto-mechanics of MEMS with initially curved deformable electrodes is analysed.
• System shows both size-dependent hardening and softening responses for sufficiently large AC voltages.
• AC voltage–amplitude curves display four limit point bifurcations at sufficiently large AC frequencies.

The aim of this paper is to examine the nonlinear size-dependent electro-elasto-statics/dynamics of a MEMS with an initially curved deformable electrode, based on the modified couple stress theory; in particular, the nonlinear motion characteristics of an initially curved deformable electrode actuated by a combination of DC and AC voltages are examined, taking into account small-size effects through use of the modified couple stress theory. The deformable electrode is modelled by means of an initially curved Euler–Bernoulli microbeam theory; the coupling between the electrical field and restoring microbeam force is demonstrated by electrical/displacement nonlinearities in the continuous model of the system, which is obtained by means of Hamilton׳s principle. The Galerkin method is employed to obtain a high-dimensional reduced-order model of the continuous system. The reduced-order model is solved by means of the pseudo-arclength continuation technique in order to analyse pull-in instabilities, snap-through motions, and nonlinear dynamical behaviour. Particularly, the electro-elasto-static deformation of the deformable electrode and pull-in instabilities are analysed when the system is subject to a DC voltage. The electro-elasto-dynamic motions of the deformable electrode are also analysed when the system is subject to both DC and AC voltages; the AC frequency-motion and AC amplitude-motion characteristics of the system are examined in the presence of coupled mechanical and electrical nonlinearities. A stability analysis is conducted via the Floquet theory. The importance of employing the modified couple stress theory, rather than the classical continuum theory, is highlighted by comparing the system response based on each of these theories.