The vibrations of microcantilevers in Atomic Force Microscopes (AFM) or Radio Frequency (RF) switches strongly couple to the viscous hydrodynamics of the surrounding fluid in the vicinity of a solid wall. While prior efforts have focused on squeeze film damping effects at high Knudsen and squeeze numbers, the regime of low Knudsen and squeeze numbers is also very important for which squeeze film models need to be discarded in favor of unsteady Stokes hydrodynamics. We present convenient semi-analytical expressions for the unsteady viscous hydrodynamic functions of slender microbeams oscillating near solid walls in terms of key non-dimensional numbers. Using these expressions it becomes possible to predict semi-analytically the quality factors of multiple modes of microcantilever beams near solid walls in diverse applications ranging from AFM in liquids to RF microswitches under ambient conditions. The predictions compare favorably with fully three dimensional, transient flow-structure interaction computations as well as with preliminary experiments on cantilevers under ambient conditions.
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ASME 2008 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference
August 3–6, 2008
Brooklyn, New York, USA
Conference Sponsors:
- Design Engineering Division and Computers in Engineering Division
ISBN:
978-0-7918-4328-4
PROCEEDINGS PAPER
Hydrodynamic Damping of Microcantilevers Oscillating Near Solid Walls at Low Knudsen Numbers
Ryan C. Tung,
Ryan C. Tung
Purdue University, West Lafayette, IN
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Anirban Jana,
Anirban Jana
Purdue University, West Lafayette, IN
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Arvind Raman,
Arvind Raman
Purdue University, West Lafayette, IN
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Hartono Sumali
Hartono Sumali
Sandia National Laboratories, Albuquerque, NM
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Ryan C. Tung
Purdue University, West Lafayette, IN
Anirban Jana
Purdue University, West Lafayette, IN
Arvind Raman
Purdue University, West Lafayette, IN
Hartono Sumali
Sandia National Laboratories, Albuquerque, NM
Paper No:
DETC2008-49792, pp. 647-654; 8 pages
Published Online:
July 13, 2009
Citation
Tung, RC, Jana, A, Raman, A, & Sumali, H. "Hydrodynamic Damping of Microcantilevers Oscillating Near Solid Walls at Low Knudsen Numbers." Proceedings of the ASME 2008 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. Volume 4: 20th International Conference on Design Theory and Methodology; Second International Conference on Micro- and Nanosystems. Brooklyn, New York, USA. August 3–6, 2008. pp. 647-654. ASME. https://doi.org/10.1115/DETC2008-49792
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