Lateral-Mode Vibration of Microcantilever-Based Sensors in Viscous Fluids Using Timoshenko Beam Theory

To more accurately model microcantilever resonant behavior in liquids and to improve lateral-mode sensor performance, a new model is developed to incorporate viscous fluid effects and Timoshenko beam effects (shear deformation, rotatory inertia). The model is motivated by studies showing that the mo...

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Bibliographic Details
Published inJournal of microelectromechanical systems Vol. 24; no. 4; pp. 848 - 860
Main Authors Schultz, Joshua A., Heinrich, Stephen M., Josse, Fabien, Dufour, Isabelle, Nigro, Nicholas J., Beardslee, Luke A., Brand, Oliver
Format Journal Article
LanguageEnglish
Published IEEE 01.08.2015
Institute of Electrical and Electronics Engineers
Subjects
Educational institutions
Engineering Sciences
Force
Harmonic analysis
Laser beams
lateral mode
liquid-phase sensing
Micro and nanotechnologies
Microcantilevers
Microelectronics
quality factor
Resonant frequency
Sensors
Vibrations
lateral mode
Microcantilevers
resonant frequency
liquid-phase sensing
quality factor
vibrations
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Summary:To more accurately model microcantilever resonant behavior in liquids and to improve lateral-mode sensor performance, a new model is developed to incorporate viscous fluid effects and Timoshenko beam effects (shear deformation, rotatory inertia). The model is motivated by studies showing that the most promising geometries for lateral-mode sensing are those for which Timoshenko effects are most pronounced. Analytical solutions for beam response due to harmonic tip force and electrothermal loadings are expressed in terms of total and bending displacements, which correspond to laser and piezoresistive readouts, respectively. The influence of shear deformation, rotatory inertia, fluid properties, and actuation/detection schemes on resonant frequencies (f res ) and quality factors (Q) are examined, showing that Timoshenko beam effects may reduce f res and Q by up to 40% and 23%, respectively, but are negligible for width-tolength ratios of 1/10 and lower. Comparisons with measurements (in water) indicate that the model predicts the qualitative data trends, but underestimates the softening that occurs in stiffer specimens, indicating that support deformation becomes a factor. For thinner specimens, the model estimates Q quite well, but exceeds the observed values for thicker specimens, showing that the Stokes resistance model employed should be extended to include pressure effects for these geometries.
ISSN:1057-7157
1941-0158
DOI:10.1109/JMEMS.2014.2354596