Pull-in voltage analysis of electrostatically actuated MEMS with piezoelectric layers: A size-dependent model

• Modified couple stress theory is introduced into the current model to capture size effect.
• By using Hamilton's principle, governing equation and boundary conditions are derived.
• The pull-in voltage significantly decreases by applying very small voltage on piezoelectric layers.
• Size effect is found in MEMS, which is ignored in classical model.
• The present model is a more precisely one than existing models.

A size-dependent model for electrostatically actuated microbeam-based MEMS (micro-electro-mechanical systems) with piezoelectric layers attached is developed based on a modified couple stress theory. By using Hamilton's principle, the nonlinear differential governing equation and boundary conditions of the MEM structure are derived. In the newly developed model, the residual stresses, fringing-field and axial stress effects are considered for the fixed–fixed microbeam with piezoelectric layers. The results of the present model are compared with those from the classical model. The results show the size effect becomes prominent if the beam dimension is comparable to the material length scale parameter (MLSP). The effects of MLSP, the residual stresses and axial stress on the pull-in voltage are also studied. The study may be helpful to characterize the mechanical and electrostatic properties of small size MEMS, or guide the design of microbeam-based devices for a wide range of potential applications.