Dynamics Of Polysilicon Parallel-plate Electrostatic Actuators

Chu, Patrick; Nelson, Phyllis R.; Tachiki, Mark L.; Pister, Kristofer S. J.

doi:10.1109/sensor.1995.721820

Cited by 18 publications

(16 citation statements)

References 3 publications

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“…These models do not account for the spatial distribution and nonlinearities of inherent electrostatic actuation and structural deformation [2,3] of these sensors. Linear distributedparameter models [5] lead to a better approximation of the device performance provided that the deformations remain small.…”

Section: Introductionmentioning

confidence: 99%

Nonlinear dynamics of a resonant gas sensor

et al. 2009

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We develop a mathematical model for a resonant gas sensor made up of an microplate electrostatically actuated and attached to the end of a cantilever microbeam. The model considers the microbeam as a continuous medium, the plate as a rigid body, and the electrostatic force as a nonlinear function of the displacement and the voltage applied underneath the microplate. We derive closed-form solutions to the static and eigenvalue problems associated with the microsystem. The Galerkin method is used to discretize the distributed-parameter model and, thus, approximate it by a set of nonlinear ordinarydifferential equations that describe the microsystem dynamics. By comparing the exact solution to that associated with the reduced-order model, we show that using the first mode shape alone is sufficient to approximate the static behavior. We employ the Finite Difference Method (FDM) to discretize the orbits of motion and solve the resulting nonlinear algebraic equations for the limit cycles. The stability of these cycles is determined by combining the FDM discretization with Floquet theory. We investigate the basin of attraction of bounded motion for two cases: unforced and damped, and forced and damped systems. In order to detect the lower limit of the forcing at which homoclinic points appear, we conduct a Melnikov analysis. We show the presence of a homoclinic point for a loading case and hence entanglement of the stable and unstable manifolds and non-smoothness of the boundary of the basin of attraction of bounded motion.

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Section: Introductionmentioning

confidence: 99%

Nonlinear dynamics of a resonant gas sensor

et al. 2009

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“…Electrostatically actuated microelectromechanical systems (MEMS) are being used as transistors, switches, micro-mirrors, pressure sensors, micro-pumps, moving valves, and micro-grippers, see for example Nguyen et al (1998), Hung and Senturia (1999), Gupta et al (1997), Chu et al (1996). An electrostatically actuated MEMS is comprised of a conductive deformable body suspended above a rigid grounded body (Pelesko 0020-7683/$ -see front matter Ó 2008 Elsevier Ltd. All rights reserved.…”

Section: Introductionmentioning

confidence: 99%

Reduced-order models for microelectromechanical rectangular and circular plates incorporating the Casimir force

Batra

Porfiri²,

Spinello

2008

International Journal of Solids and Structures

150

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We consider the von Kármán nonlinearity and the Casimir force to develop reduced-order models for prestressed clamped rectangular and circular electrostatically actuated microplates. Reduced-order models are derived by taking flexural vibration mode shapes as basis functions for the transverse displacement. The in-plane displacement vector is decomposed as the sum of displacements for irrotational and isochoric waves in a two-dimensional medium. Each of these two displacement vector fields satisfies an eigenvalue problem analogous to that of transverse vibrations of a linear elastic membrane. Basis functions for the transverse and the in-plane displacements are related by using the nonlinear equation governing the plate in-plane motion. The reduced-order model is derived from the equation yielding the transverse deflection of a point. For static deformations of a plate, the pull-in parameters are found by using the displacement iteration pull-in extraction method. Reduced-order models are also used to study linear vibrations about a predeformed configuration. It is found that 9 basis functions for a rectangular plate give a converged solution, while 3 basis functions give pull-in parameters with an error of at most 4%. For a circular plate, 3 basis functions give a converged solution while the pull-in parameters computed with 2 basis functions have an error of at most 3%. The value of the Casimir force at the onset of pull-in instability is used to compute device size that can be safely fabricated.

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“…At a few microns in size, squeeze film damping should be used to represent the gas-film damping experienced by the moving plates [32,33]. For a rectangular plate, the squeeze film damping force F s (x,ẋ) can be given by Taylor series, i.e.…”

Section: Dynamic Modelmentioning

confidence: 99%

Dynamics of Nonlinear Coupled Electrostatic Micromechanical Resonators under Two-Frequency Parametric and External Excitations

Zhang

Meng

Wei

2010

Shock and Vibration

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Abstract. In this paper, nonlinear dynamics and chaos of electrostatically actuated MEMS resonators under two-frequency parametric and external excitations are investigated analytically and numerically. A nonlinear mass-spring-damping model is used to accounting for squeeze film damping and the parallel plate electrostatic force. The micro-structure is excited by a dc bias electrostatic force and a harmonic force with a frequency tuned closely to their fundamental natural frequencies (combination oscillation). The quality factor is calculated for the microcantilever beam of the resonator considering squeeze film damping. The effect of nonlinear squeeze film damping on the frequency response, quality factor, resonant frequency and nonlinear dynamic characteristics of the dynamic system are provided with numerical simulations using the bifurcation diagram, Poicare maps, largest Lyapunov exponent and phase portrait. The results show that the dynamic system goes through a complex nonlinear vibration as the system parameters change. It is indicated that the effect of nonlinear squeeze film damping should be considered due to its decreasing the quality factor and changing the nonlinear phenomena of the MEMS resonators.

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Dynamics Of Polysilicon Parallel-plate Electrostatic Actuators

Cited by 18 publications

References 3 publications

Nonlinear dynamics of a resonant gas sensor

Nonlinear dynamics of a resonant gas sensor

Reduced-order models for microelectromechanical rectangular and circular plates incorporating the Casimir force

Dynamics of Nonlinear Coupled Electrostatic Micromechanical Resonators under Two-Frequency Parametric and External Excitations

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