Open AccessTimoshenko beam effects in lateral‐mode microcantilever‐based sensors in liquids
Author(s) -
Schultz Joshua A.,
Heinrich Stephen M.,
Josse Fabien,
Nigro Nicholas J.,
Dufour Isabelle,
Beardslee Luke A.,
Brand Oliver
Publication year - 2013
Publication title -
micro and nano letters
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.25
H-Index - 31
ISSN - 1750-0443
DOI - 10.1049/mnl.2013.0395
Subject(s) - timoshenko beam theory , beam (structure) , materials science , cantilever , mechanics , inertia , buckling , deformation (meteorology) , physics , composite material , optics , classical mechanics
Recent experimental and analytical research has shown that higher in‐fluid quality factors ( Q ) are achieved by actuating microcantilevers in the lateral flexural mode, especially for microcantilevers having larger width‐to‐length ratios. However, experimental results show that for these geometries the resonant characteristics predicted by the existing analytical models differ from the measurements. A recently developed analytical model to more accurately predict the resonant behaviour of these devices in viscous fluids is described. The model incorporates viscous fluid effects via a Stokes‐type fluid resistance assumption and ‘Timoshenko beam’ effects (shear deformation and rotatory inertia). Unlike predictions based on Euler‐Bernoulli beam theory, the new theoretical results for both resonant frequency and Q exhibit the same trends as seen in the experimental data for in‐water measurements as the beam slenderness decreases. An analytical formula for Q is also presented to explicitly illustrate how Q depends on beam geometry and on beam and fluid properties. Beam thickness effects are also examined and indicate that the analytical results yields good numerical estimates of Q for the thinner (5 μm) specimens tested, but overestimate Q for the thicker (20 μm) specimens, thus suggesting that a more accurate fluid resistance model should be introduced in the future for the latter case.