Characterization of the mechanical behavior of an electrically actuated microbeam

Abstract

We present a nonlinear model of electrically actuated microbeams accounting for the electrostatic forcing of the air gap capacitor, the restoring force of the microbeam and the axial load applied to the microbeam. The boundary-value problem describing the static deflection of the microbeam under the electrostatic force due to a dc polarization voltage is solved numerically. The eigenvalue problem describing the vibration of the microbeam around its statically deflected position is solved numerically for the natural frequencies and mode shapes. Comparison of results generated by our model to the experimental results shows excellent agreement, thus verifying the model. Our results show that failure to account for mid-plane stretching in the microbeam restoring force leads to an underestimation of the stability limits. It also shows that the ratio of the width of the air gap to the microbeam thickness can be tuned to extend the domain of the linear relationship between the dc polarization voltage and the fundamental natural frequency. This fact and the ability of the nonlinear model to accurately predict the natural frequencies for any dc polarization voltage allow designers to use a wider range of dc polarization voltages in resonators.

Investigation of the response of microstructures under the combined effect of mechanical shock and electrostatic forces

“…We assume the microbeam to be placed under near-vacuum conditions (no damping), which represents a worst-case scenario. The pull-in voltage of this microbeam based on a static analysis [7,27] is 3.38 V, and accounting for the transient effect, it is 3.11 V. By calculating the natural frequency of this microbeam, we found that its fundamental natural period is close to 0.1 ms. Hence, the microbeam experiences the mechanical shock load of T=1.0 ms as quasi-static load and of T=0.1 ms as dynamic load.…”

“…We assume the microbeam to be placed under nearvacuum conditions (no damping), which represents a worst-case scenario. The pull-in voltage of this microbeam based on a static analysis [7,27] is 0.652 V, and accounting for the transient effect it is 0.6 V. Figure 11(a) shows the time response of the microbeam when actuated by a voltage load V dc = 0.36 V and subjected to a mechanical shock pulse of amplitude 400 g and duration 1.0 ms. Here, W max /d is the maximum deflection of the microbeam at x = L normalized to d, and t is the nondimensional time, as defined in (5).…”

“…Some studies predicted pull-in based on static analysis, which accounts for the dc electrostatic force and the elastic resorting forces of the microstructure [5][6][7]. Others have, in addition, accounted for the transient motion of microstructures, which lead to a dynamic pull-in.…”

Vibrational characteristics of size dependent vibrating ring gyroscope

“…For small vibration of micro-ring around the static deection, the linear natural frequency can be considered as the resonant frequency of the system with negligible error [37]. Using the proposed nite-element formulation and omitting the static deformation results, the linear natural frequency of the system under applied DC voltage can be studied.…”

Modelling of nonlinear circular plates using modal analysis: simulation and model validation

“…In the "large-displacement" regime, the tensile stresses must be taken into account; this results in nonlinear partial differential equations (PDEs), such as the Von Karman equation for plates, and, as a consequence, in nonlinear models. The most common way of handling these nonlinear PDEs consists in linearizing them close to a working point, as in [3][4]. This approach can lead to excellent results, provided the linearization hypothesis holds.…”