Three-dimensional elastohydrodynamics of a thin plate oscillating above a wall

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dc.contributor.author Clarke, Richard en
dc.contributor.author Jensen, OE en
dc.contributor.author Billingham, J en
dc.date.accessioned 2012-03-09T01:19:11Z en
dc.date.issued 2008 en
dc.identifier.citation Phys Rev E Stat Nonlin Soft Matter Phys 78(5 Pt 2):056310 Nov 2008 en
dc.identifier.issn 1539-3755 en
dc.identifier.uri http://hdl.handle.net/2292/13594 en
dc.description.abstract We consider deflections of a thin rectangular elastic plate that is submerged within a Newtonian fluid. The plate is clamped along one edge and supported horizontally over a plane horizontal wall. We consider both external driving, where the clamped edge is vibrated vertically at high frequencies, and thermal driving, where the plate fluctuates under Brownian motion. In both cases, the amplitude of oscillation is assumed sufficiently small that the resulting flow has little convective inertia, although the oscillation frequency is sufficiently high to generate substantial unsteady inertia in the flow, a common scenario in many nano- and microdevices. We exploit the plate’s thinness to develop an integral-equation representation for the three-dimensional flow a so-called thin-plate theory which offers considerable computational savings over a full boundary-integral formulation. Limiting cases of high oscillation frequencies and small wall-plate separation distances are studied separately, leading to further simplified descriptions for the hydrodynamics. We validate these reduced integral representations against full boundary-integral computations, and identify the parameter ranges over which these simplified formulations are valid. Addressing the full flow-structure interaction, we also examine the limits of simpler two-dimensional hydrodynamic models. We compare the responses of a narrow plate under two- and three-dimensional hydrodynamic loading, and report differences in the frequency response curves that occur when the plate operates in water, in contrast to the excellent agreement observed in air. en
dc.publisher The American Physical Society en
dc.relation.ispartofseries Physical Review E - Statistical, Nonlinear, and Soft Matter Physics en
dc.rights Items in ResearchSpace are protected by copyright, with all rights reserved, unless otherwise indicated. Previously published items are made available in accordance with the copyright policy of the publisher. Details obtained from http://www.sherpa.ac.uk/romeo/issn/1539-3755/ en
dc.rights.uri https://researchspace.auckland.ac.nz/docs/uoa-docs/rights.htm en
dc.title Three-dimensional elastohydrodynamics of a thin plate oscillating above a wall en
dc.type Journal Article en
dc.identifier.doi 10.1103/PhysRevE.78.056310 en
pubs.issue 056310 en
pubs.begin-page 1 en
pubs.volume 78 en
dc.rights.holder Copyright: The American Physical Society en
dc.identifier.pmid 19113219 en
pubs.end-page 17 en
dc.rights.accessrights http://purl.org/eprint/accessRights/RestrictedAccess en
pubs.subtype Article en
pubs.elements-id 96063 en
pubs.org-id Engineering en
pubs.org-id Engineering Admin en
pubs.record-created-at-source-date 2010-09-01 en
pubs.dimensions-id 19113219 en


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