Prediction of pull-in phenomena and structural stability analysis of an electrostatically actuated microswitch

Harsha, C. Sri; Prasanth, C. S.; Pratiher, Barun

doi:10.1007/s00707-016-1633-2

Cited by 7 publications

(10 citation statements)

References 32 publications

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“…Differential equation of motion of a continuous micro-cantilever beam subjected to AC potential difference by stationary electrode has been shown in Figures 1 and 2, while the associated boundary conditions are being expressed in [25,29]. However, the electrostatic force is considered to be uniform across the width, while transverse vx , t ðÞ and axial ux , t ðÞ displacement component holds a constraint equation known as in-extensibility condition…”

Section: Problem Descriptionmentioning

confidence: 99%

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Electrostatically Driven MEMS Resonator: Pull-in Behavior and Non-linear Phenomena

Pratiher¹

2020

Nonlinear Systems -Theoretical Aspects and Recent Applications

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This chapter deals with the investigation on stability and bifurcation analysis of a highly non-linear electrically driven micro-electro-mechanical resonator has been established. A non-linear model of this system will briefly be described considering both transverse and longitudinal displacement of the resonator. A short description to explore the need of incorporating higher-order correction of electrostatic pressure has been highlighted. The pull-in results and consequences of higherorder correction on the pull-in stability will be reported. In addition, consequences of air-gap, electrostatic forcing parameter, and effective damping on non-linear phenomena have been studied to highlight the possible undesirable catastrophic failure at the unstable critical points. Basins of attractions that postulate a unique response in multi-region state for a specific initial condition will also be studied. This chapter can enable a significant adaptation to identify the locus of instability in micro-cantilever-based resonator when subjected to AC voltage polarization with the understanding of theoretical ideas for controlling the systems and optimizing their operation.

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Section: Problem Descriptionmentioning

confidence: 99%

“…(1) equal to zero. Figure 1 shows the tip-deflection with the voltages ranging from zero to forcing level, where the pull-in instability takes place as explained details in [25,29]. Recalling the fact that system leads to a pull-in condition when the system's net stiffness becomes negative.…”

Section: Static Analysismentioning

confidence: 99%

Electrostatically Driven MEMS Resonator: Pull-in Behavior and Non-linear Phenomena

Pratiher¹

2020

Nonlinear Systems -Theoretical Aspects and Recent Applications

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“…Microbeams have been widely employed in micro-electromechanical systems (MEMS) [1][2][3] . There have been many applications of microbeams, such as microscale sensors [4][5][6] , microscale actuators [7][8] , and microswitch [9] .…”

Section: Introductionmentioning

confidence: 99%

“…where u, v and w are the displacement components in directions x, y and z respectively. Substituting (8) into the geometric equation (5), one formulates the nonzero strain component of a Bernoulli-Euler beam as into the rotation tensor expression(7), one has the rotation components of a Bernoulli-Euler beam Substituting (10) into the geometric equation (6), one formulates the nonzero curvature components of a Bernoulli-Euler beam as Using the nonzero strain component(9) and the constitutive equation (1), one expresses the nonzero stress components of a Bernoulli-Euler beam as (…”

mentioning

confidence: 99%

Analytic solution for size-dependent behaviors of micro-beam under forced vibration

Wang¹,

Wang²,

Wang³

et al. 2020

Mech. Eng. Sci.

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This paper focuses on the size-dependently mechanical behaviors of a micro-beam under forced vibration. Governing equations of a micro-beam under forced vibration are established by using the modified couple stress theory, Bernoulli-Euler beam theory and D’Alembert’s principle together. A simply supported micro-beam under forced vibration is solved according to the established governing equations and the method of separation of variables. The dimensionless deflection, amplitude mode and period mode are defined to investigate the size-dependently mechanical behaviors of a micro-beam under forced vibration. Results show that the performance of a micro-beams under forced vibration is distinctly size-dependent when the ratio of micro-beam height to material length-scale parameter is small enough. Both frequency ratio and loading location are the important factors that determine the size-dependent performance of a micro-beams under forced vibration.

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“…53 For the sake of simplicity of the model in terms of the material properties, the authors have considered classical beam theory as that of the similar existing works to calculate the pull-in voltage and its variation upon changing the design variables. Furthermore, authors have considered the nonuniform distribution of electrostatic pressure, geometric nonlinearity, and effect of air-gap thickness, the important aspects to design a small scale device 4,35,41,42,54 into the mathematical model. It is being noted that very few authors have contemplated the uses of nonlinear distribution of electrostatic pressure for pull-in analysis.…”

Section: Introductionmentioning

confidence: 99%

Electrostatic pull-in analysis of a nonuniform micro-resonator undergoing large elastic deflection

Prasanth

Harsha

Pratiher

2017

Proceedings of the Institution of Mechanical Engineers, Part C:

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Pull-in analysis of an electrostatically actuated nonuniform micro-resonator under large elastic deflection has been investigated with a focus on qualitative analysis to understand the essence of nonuniform cross-section on the determination of pull-in voltage. Here, a microcantilever beam with nonuniform cross-section has been adopted to develop a mathematical model considering the important features such as structural nonlinearities, nonlinear electrostatic distribution, and linear viscous effect. The individual effect of each design variables on the diagnosis of the critical voltage and corresponding critical deflection due to pull-in has been graphically depicted. The results in the static condition have been verified with the findings obtained via COMSOL multi-physics software. Present result indicates that a nonuniform microbeam configuration strengthens the structural stability by switching the pull-in voltage up to a higher value. Similarly, stable pull-in deflection within the restriction of pull-in instability has been also augmented. In addition, it has been shown that the nonuniformity within the beam structure is highly sensitive to the nonlinear effects. Hence, outputs provide a useful insight of pull-in behavior and enable an understanding of safe and smooth operating range of microelectromechanical system devices.

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Prediction of pull-in phenomena and structural stability analysis of an electrostatically actuated microswitch

Cited by 7 publications

References 32 publications

Electrostatically Driven MEMS Resonator: Pull-in Behavior and Non-linear Phenomena

Electrostatically Driven MEMS Resonator: Pull-in Behavior and Non-linear Phenomena

Analytic solution for size-dependent behaviors of micro-beam under forced vibration

Electrostatic pull-in analysis of a nonuniform micro-resonator undergoing large elastic deflection

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