Size-dependent behavior of a MEMS microbeam under electrostatic actuation

Abstract

The size-dependent behavior of a silicon microbeam with an axial force in MEMS is studied using a nonlinear finite element procedure. Based on a refined third-order shear deformation theory and the modified couple stress theory (MCST), nonlinear differential equations of motion for the beam are derived from Hamilton’s principle, and they are transferred to a discretized form using a two-node beam element. Newton-Raphson based iterative procedure is used in conjunction with Newmark method to obtain the pull-in voltages and deflections of a clamped-clamped microbeam under electrostatic actuation. The influence of the axial force, applied voltage and material length scale parameter on the behavior of the beam is studied in detail and highlighted.

Size dependent pull-in instability of functionally graded microbeams using a finite element formulation

“…The beam deflection and the pull-in voltage were determined using the modified variational iteration method. Le et al [14] presented a MCST based finite element formulation for assessing frequencies and pull-in voltages of microbeams subjected to electrostatic force. Their numerical investigation showed that the deflections are overestimated while the pull-in voltages are underestimated by ignoring the microsize effect.…”

Vibration of electrically actuated MEMS Timoshenko microbeams based on a hierarchical beam element

“…The proposed method agreed with literature values to within 4%. Recently, Le et al [23] studied the size dependent behavior of a MEMS microbeam under electrostatic actuation using the improved third-order shear deformation theory of Shimpi and Patel [24]. The authors concluded that the dynamic deflections of the beam are overestimated when ignore the microsize effect.…”