Closed-form empirical relations to predict the dynamic pull-in parameters of electrostatically actuated tapered microcantilevers

Abstract

We develop novel closed-form empirical relations to estimate the dynamic pull-in parameters of electrostatically actuated linearly tapered microcantilever beams driven by a step-function voltage. A computationally efficient single degree-of-freedom model is employed in the setting of an energy-based technique to characterize the dynamic pull-in of the distributed electromechanical model that takes into account the effects of fringing field capacitance. The model exploits the fundamental mode shape of the respective nonprismatic geometry obtained using the differential transform technique. A unique surface fitting model is proposed to characterize the variations of both pull-in displacement and pull-in voltage over a realistically wide range of system parameters. Optimum coefficients of the proposed surface fitting model are obtained using nonlinear regression analysis. The empirical estimates of dynamic pull-in parameters are validated against 3D finite element simulations and available data in the literature. Excellent agreement indicates that the proposed relationships are sufficiently accurate to be safely used for the preliminary design of tapered microcantilever beams.

A new approach and model for accurate determination of the dynamic pull-in parameters of microbeams actuated by a step voltage

“…The The The present empirical The present empirical g 0 b model (error) model [20] model (error) model [20] 0 0.653 (−0.45%) 0.656 1.676•γ 1 (−0.65%) 1.687•γ 1 0.1 0.660 (−0.75%) 0.665 1.638•γ 1 (0.43%) 1.631•γ 1 0.2 0.667 (−1.04%) 0.674 1.603•γ 1 (1.52%) 1.579•γ 1…”

“…In this case, the electric load applied to the devices is often composed of a dc bias voltage and an ac component designed to excite harmonic motion. The second group [15][16][17][18][19][20] deals with the dynamic pull-in due to transient excitation (dc excitation). The aim of this paper is to present an easy-to-use model for calculating the dynamic pull-in position and voltage of microbeams actuated by a step voltage.…”

“…Using the method, they obtained an analytical model for the dynamic pull-in parameters of the rigid parallel-plate actuators. There are four papers [15,17,18,20] on analytical modeling of the dynamic pull-in parameters of flexible microbeams. Next, we summarize the analytical models for the dynamic pull-in of flexible microbeam actuated by a step voltage.…”

“…εbL 4 is very close to equation (19). Using the values obtained by the empirical model [20] as the baseline, table 5 shows the percentage differences between the results obtained by the two models in the range from g 0 /b = 0 to 0.2. As shown in table 5, the discrepancy between the present model and the empirical model [20] is very small.…”

Modeling the material structure and couple stress effects of nanocrystalline silicon beams for pull-in and bio-mass sensing applications

“…On the other hand, because the elastic moduli of NcMs are likely to decrease due of the interface effect, the material structure can affect the rigidity through a softening mechanism depending on the grain size. Therefore, the classical mathematical models [17,[55][56][57] lose the accuracy to estimate the pull-in voltage values of actuated beams. Moreover, including only couple stress effect in the mathematical model [32,33,34] results in an overestimation of the pull-in voltage values of actuated beams.…”