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

Fang, Yuming; Li, Pu

doi:10.1088/0960-1317/23/4/045010

Cited by 25 publications

(12 citation statements)

References 25 publications

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“…6(b), shows a banded chaotic attractor. This chaotic attractor was found to extend over the frequency [10][11][12][13][14][15][16][17][18] kHz during a forward sweep.…”

Section: Resultsmentioning

confidence: 91%

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Quasi-Static Pull-in: an Instability in Electrostatic Actuators

Al‐Ghamdi

Khater

Abdel‐Rahman

et al. 2020

Sci Rep

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We identify a new instability in electrostatic actuators dubbed quasi-static pull-in. We report experimental evidence of the instability and study its characteristics in two types of micro actuators operating in ambient air. We found that the underlying mechanism is a fast-slow dynamic interaction between slowly-varying electrostatic excitation and fast resonator response that instigate large nonresonant oscillatory orbits and eventually disappears in a global Shilnikov bifurcation. Based on these findings, we formulate and present a new taxonomy of pull-in instabilities in electrostatic actuators.Nonlinearities in electrostatic Micro-Electro-Mechanical Systems (MEMS) are a rich source of interesting dynamic phenomena. Sources of nonlinearity in electrostatic MEMS include the dependence of the electrostatic force on displacement, geometric and inertial nonlinearities, nonlinear damping mechanisms, and interactions with the substrate 1 . They result in static and dynamic bifurcations, multivaluedness, and chaos. These phenomena have been exploited to design high sensitivity sensors, large amplitude actuators, mechanical memory bits, and encryption keys 2-6 .One of the most important nonlinear phenomena in electrostatic MEMS is the pull-in instability 7 where the moving structure snaps to the actuation electrode. While significant efforts have been devoted to study this phenomenon, a consistent taxonomy of its different types and underlying mechanisms is yet to emerge. We posit that a classification system based on the ratio of frequency f of the excitation to the actuator's fundamental natural frequency f n can achieve that.Static pull-in is measured using quasi-static ramp waveforms, (f/f n → 0), which minimize inertial and damping effects. As the voltage between the actuator and an electrode increases monotonically, the stable equilibrium (node) and unstable equilibrium (saddle) coincide at a saddle-node bifurcation. Beyond this point, the actuator snaps to the electrode. Krylov and Maimon 8 and Khater et al. 3 utilized ramp waveforms with frequencies of f = 1 kHz and f = 1.8 Hz, respectively, to measure static pull-in. While a step or other waveforms may also be used, the common characteristic of static pull-in is transient (non-repeatable) dynamics.A margin of stability exists around the saddle-node bifurcation. The size of this margin is proportional to the waveform rise time and the actuator quality factor 9 . A slow rise allows for accurate determination of the bifurcation point corresponding to static pull-in voltage. A fast rise instigates transients, thereby decreasing the effective static pull-in voltage. Many researchers have investigated the boundaries of this margin 8,10,11 .Dynamic pull-in is instigated by resonant waveforms where the excitation frequency and one of the natural frequencies are integer multiples or submultiples of each other (f/f n ≈ p∕q), such as the case for primary, superharmonic, and subharmonic resonances 12,13 . Dynamic pull-in occurs at lower RMS voltage than static pull-in be...

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“…6(b), shows a banded chaotic attractor. This chaotic attractor was found to extend over the frequency [10][11][12][13][14][15][16][17][18] kHz during a forward sweep.…”

Section: Resultsmentioning

confidence: 91%

“…A fast rise instigates transients, thereby decreasing the effective static pull-in voltage. Many researchers have investigated the boundaries of this margin 8,10,11 .…”

mentioning

confidence: 99%

Quasi-Static Pull-in: an Instability in Electrostatic Actuators

Al‐Ghamdi

Khater

Abdel‐Rahman

et al. 2020

Sci Rep

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“…Many studies have been done on this type of microresonators, providing lots of valuable references on the static pull-in position, pull-in voltage, and fundamental frequency. From the application perspective, some studies focus on nondimensional analysis [5], while some focus on dimensional analysis through using detailed physical parameters [34]. Few works focus on comparative analyses between 1-DOF model and the continuous model from a qualitative and physical viewpoint.…”

Section: System Descriptionmentioning

confidence: 99%

Qualitative Identification of the Static Pull-In and Fundamental Frequency of One-Electrode MEMS Resonators

Han

Jin

et al. 2018

Micromachines

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This paper attempts to qualitatively identify the static pull-in position, pull-in voltage, and fundamental frequency of one-electrode microresonators from a physical perspective. During theoretical derivation, a generalized one-degree-of-freedom (1-DOF) model in nondimensional form derived using the differential quadrature method (DQM) is first introduced and then transformed for frequency normalization. Based on the deduced formulas, the upper and lower bounds of the static pull-in position and pull-in voltage are both deduced through mathematical proof. To distinguish the monotonic and nonmonotonic behavior of the fundamental frequency versus direct current (DC) voltage, a critical condition decided only by cubic stiffness is then determined. For the first time, two extreme static positions, as well as the corresponding fundamental frequencies and DC voltages to identify different frequency behaviors are derived, and their variations versus cubic stiffness are then discussed and verified. During the simulation process, a high-order DQM and COMSOL 2D model are both applied for numerical analyses. Guided by nondimensional results, typical behaviors with specific physical parameters are examined in detail. Results demonstrate that the curve tendencies between all the qualitative results and quantitative numerical simulations in dimensional form agree well with each other, implying the possibility of using 1-DOF model to qualitatively discuss physical parameters effects on the system statics and dynamics.

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“…Researchers in the past have modeled resonators and obtained pull-in parameters by accounting various effects. [10][11][12][13][14][15][16] However, these models are limited to uniform cantilever beams. At the same time, a few studies performed the computation of frequencies of non uniform cantilever beams as well.…”

Section: Electrostaticallymentioning

confidence: 99%

Pull-in analysis of non-uniform microcantilever beams under large deflection

Singh

Pal

Pandey

2015

Journal of Applied Physics

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Cantilever beams under the influence of electrostatic force form an important subclass of microelectromechanical system (MEMS) and nanoelectromechanical system. Most of the studies concerning these micro-nano resonators are centered around uniform cantilever beams. In this paper, we have investigated another class of micro-resonators consisting of non-uniform cantilever beams. The study is focused around investigating pull-in voltage and resonance frequency of non-uniform cantilever beams when they operate in the linear regime about different static equilibriums. In this paper, we term this frequency as "linear frequency." Calculation of the linear frequency is done at different static equilibriums corresponding to different DC voltages. We have studied two classes of beams, one with increasing cross sectional area from the clamped edge (diverging beam) and other with decreasing cross sectional area from the clamped edge (converging beam). Within each class, we have investigated beams with linear as well as quartic variation in width. We start by obtaining Euler beam equation for non-uniform cantilever beams considering large deflection and their corresponding exact mode shapes from the linear equation. Subsequently, using the Galerkin method based on single mode approximation, we obtain static and dynamic modal equations for finding pull-in voltage and resonance frequency as a function of DC voltage, respectively. We found that the linear frequency of converging beams increases with increase in non-uniform parameter (a) while those of diverging beams decreases with a. A similar trend is observed for pull-in voltage. Within the converging class, beams with quartic variation in width show significant increase in both frequency and pull-in voltage as compared to corresponding linearly tapered beams. In quantitative terms, converging beams with quartic variation in width and a ¼ À0:6 showed an increase in linear frequency by a factor of 2.5 times and pull-in voltage by 2 times as compared to commonly used uniform beams. Our investigation can prove to be a step forward in designing highly sensitive MEMS sensors and actuators. V

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

Cited by 25 publications

References 25 publications

Quasi-Static Pull-in: an Instability in Electrostatic Actuators

Quasi-Static Pull-in: an Instability in Electrostatic Actuators

Qualitative Identification of the Static Pull-In and Fundamental Frequency of One-Electrode MEMS Resonators

Pull-in analysis of non-uniform microcantilever beams under large deflection

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