Closed Form Representations of Some Series in Darling’s Model for Squeeze Film Damping with a Rectangular Plate

Gugat M (2012)


Publication Language: English

Publication Type: Journal article, Original article

Publication year: 2012

Journal

Publisher: MDPI

Book Volume: 2

Pages Range: 479-484

Journal Issue: 2

URI: http://www.mdpi.com/2076-3417/2/2/479

DOI: 10.3390/app2020479

Open Access Link: http://www.mdpi.com/2076-3417/2/2/479/htm

Abstract

Compressible squeeze film damping is a phenomenon of great importance for micromachines. For example, for the optimal design of an electrostatically actuated micro-cantilever mass sensor that operates in air, it is essential to have a model for the system behavior that can be evaluated efficiently. An analytical model that is based upon a solution of the linearized Reynolds equation has been given by R.B. Darling. In this paper we explain how some infinite sums that appear in Darling’s model can be evaluated analytically. As an example of applications of these closed form representations, we compute an approximation for the critical frequency where the spring component of the reaction force on the microplate, due to the motion through the air, is equal to a certain given multiple of the damping component. We also show how some double series that appear in the model can be reduced to a single infinite series that can be approximated efficiently.

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How to cite

APA:

Gugat, M. (2012). Closed Form Representations of Some Series in Darling’s Model for Squeeze Film Damping with a Rectangular Plate. Applied Sciences, 2(2), 479-484. https://dx.doi.org/10.3390/app2020479

MLA:

Gugat, Martin. "Closed Form Representations of Some Series in Darling’s Model for Squeeze Film Damping with a Rectangular Plate." Applied Sciences 2.2 (2012): 479-484.

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