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 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 fres and Q by up to 40% and 23%, respectively, but are negligible for width-to-length 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.