A size-dependent model for beam-like MEMS driven by electrostatic and piezoelectric forces: A variational approach

• A size-dependent model for beam-like MEMS is derived by a variational approach.
• Size effect is found in the micro-beam, which is ignored in classical model.
• Small voltage on piezoelectric layers can reduce the DC pull-in voltage.
• Size effect should be considered for precisely modeling MEMS.

A size-dependent model of a micro-electromechanical system (MEMS) actuated by both electrostatic and piezoelectric forces is proposed based on the modified couple stress. The governing equation and boundary conditions are derived with the help of the Hamilton principle and solved numerically by employing the Galerkin method and Newton downhill method. A material length scale parameter (MLSP) is incorporated in the model to capture the size effect in microstructures. An excellent agreement is found between the results of the present model and the experimental data, providing the validity of this model. The results reveal that the introduction of the MLSP stiffens the system and increases the pull-in voltage. The size-effect is significant when the dimension of the beam is comparable to the MLSP but it becomes smaller as the beam size increases. Besides, the static characteristic of the micro-switch is studied. It is found that the piezoelectric material attached on the beam can reduce the pull-in voltage remarkably, which may guide the design of the micro-structure when the system is on the order of micron or submicron.