Appl. Sci. 2012, 2(2), 479-484; doi:10.3390/app2020479
Article

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

email
Received: 25 April 2012; in revised form: 11 May 2012 / Accepted: 14 May 2012 / Published: 21 May 2012
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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.
Keywords: squeeze film; optimal sensor design; resonant mass sensor; double series; efficient approximation of double series; evaluation of infinite series; Darling’s model
PDF Full-text Download PDF Full-Text [259 KB, uploaded 21 May 2012 14:38 CEST]

Export to BibTeX |
EndNote


MDPI and ACS Style

Gugat, M. Closed Form Representations of Some Series in Darling’s Model for Squeeze Film Damping with a Rectangular Plate. Appl. Sci. 2012, 2, 479-484.

AMA Style

Gugat M. Closed Form Representations of Some Series in Darling’s Model for Squeeze Film Damping with a Rectangular Plate. Applied Sciences. 2012; 2(2):479-484.

Chicago/Turabian Style

Gugat, Martin. 2012. "Closed Form Representations of Some Series in Darling’s Model for Squeeze Film Damping with a Rectangular Plate." Appl. Sci. 2, no. 2: 479-484.

Appl. Sci. EISSN 2076-3417 Published by MDPI AG, Basel, Switzerland RSS E-Mail Table of Contents Alert