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Pull-in Voltage of Electrostatically-Actuated Microbeams in Terms of Lumped Model Pull-in Voltage Using Novel Design Corrective Coefficients

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Abstract

In this paper, we present a study of the static and dynamic responses of a fixed–fixed and cantilever microbeam (using both the lumped and the distributed models) to a DC and a step DC voltage. A Galerkin-based step by step linearization method and a Galerkin-based reduced order model have been used to solve the governing static and dynamic equations, respectively. The calculated static and dynamic pull-in voltages have been validated by previous experimental and theoretical results and a good agreement has been achieved. The introduction of novel design corrective coefficients, independent of the beam’s material and geometric properties, results in a closed form relationship between static pull-in voltage of the lumped model and static & dynamic pull-in voltages of the distributed models, and takes into account the residual stresses, axial force and damping effects. Multiplying these design coefficients with the static pull-in voltage of the lumped model, the static and dynamic pull-in voltage of a given microbeam can be obtained without the need to solve the nonlinear governing equations.

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Authors and Affiliations

  1. Mechanical Engineering Department, Urmia University, Urmia, Iran

    Ghader Rezazadeh

  2. Mechanical Engineering Department, University of Tabriz, Tabriz, Iran

    Mohammad Fathalilou & Morteza Sadeghi

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  1. Ghader Rezazadeh
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  2. Mohammad Fathalilou
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  3. Morteza Sadeghi
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Correspondence to Ghader Rezazadeh.

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Rezazadeh, G., Fathalilou, M. & Sadeghi, M. Pull-in Voltage of Electrostatically-Actuated Microbeams in Terms of Lumped Model Pull-in Voltage Using Novel Design Corrective Coefficients. Sens Imaging 12, 117–131 (2011). https://doi.org/10.1007/s11220-011-0065-2

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  • DOI: https://doi.org/10.1007/s11220-011-0065-2

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