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Frequency response of cantilever beams immersed in viscous fluids with applications to the atomic force microscope: Arbitrary mode order

J. Appl. Phys. 101, 044908 (2007); doi:10.1063/1.2654274

Published 27 February 2007

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Cornelis A. Van Eysden and John E. Sader
Department of Mathematics and Statistics, University of Melbourne, Victoria 3010, Australia
The frequency response of a cantilever beam is well known to depend strongly on the fluid in which it is immersed. In this article, we present a theoretical model for the frequency response of a rectangular cantilever beam immersed in a viscous fluid that enables the flexural and torsional modes of arbitrary order to be calculated. This extends the previous models of Sader and Green [J. Appl. Phys. 84, 64 (1998); 92, 6262 (2002)], which were formulated primarily for the fundamental mode and the next few harmonics, to the general case of arbitrary mode order by accounting for the three-dimensional nature of the flow field around the cantilever beam. Due to its importance in atomic force microscope applications, results for the thermal noise spectrum are presented and the influence of mode order on the frequency response investigated. ©2007 American Institute of Physics
History: Received 21 December 2006; accepted 2 January 2007; published 27 February 2007
Permalink: http://link.aip.org/link/?JAPIAU/101/044908/1
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KEYWORDS and PACS

Keywords
PACS
  • 46.70.De
    Beams, plates, and shells (continuum mechanics)
  • 07.10.Cm
    Micromechanical devices and systems
  • YEAR: 2007

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ISSN:
0021-8979 (print)   1089-7550 (online)
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REFERENCES (25)
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