Date of Award
Doctor of Philosophy (PhD)
Heinrich, Stephen M.
Foley, Christopher M.
Dynamic-mode microcantilever-based devices are well suited to biological and chemical sensing applications. However, these applications often necessitate liquid-phase sensing, introducing significant fluid-induced dissipative forces and reducing device quality factors (Q). Recent experimental and analytical research has shown that higher in- fluidQis achieved by exciting microcantilevers in the lateral flexural mode. However, the experimental results show that, for microcantilevers having larger width-to-length (b/L) ratios, the behaviors predicted by current analytical models differ from measurements.
To more accurately model microcantilever resonant behavior in viscous fluids and to improve understanding of lateral-mode sensor performance, a new analytical model is developed, incorporating both viscous fluid effects and "Timoshenko beam" effects (shear deformation and rotatory inertia). Analytical solutions for the frequency response are obtained and verified by reduction to known special cases. Beam response is examined for two harmonic load types that simulate current actuation methods: tip force and support rotation. Results are expressed in terms of total beam displacement and beam displacement due solely to bending deformation, which correspond to current detection methods commonly used with these devices (laser and piezoresistive detection, respectively). Resonant frequencies (fres) and Q are determined from the theoretical beam response. The influences of the shear, rotatory inertia, and fluid parameters, as well as the load/detection scheme, on the resonant characteristics are investigated in detail. Results show that the new model reproduces the experimental trends in fres and Q for lateral- mode microcantilevers at higher b/L ratios (i.e., for the high-Q devices for which Euler- Bernoulli models prove inadequate). Over the practical ranges of system parameters considered, the results indicate that Timoshenko beam effects can account for a reduction in fres and Q of up to 23%, but are negligible (no more than 2% reduction) for length-to- width ratios of 7 and higher. Also derived is a simple analytical expression relating Q to system parameters while incorporating Timoshenko and fluid effects. Finally, to evaluate the influence of lateral-mode chemical sensor design parameters on performance, the results for fres andQ are related to the mass/chemical sensitivities and to the limit of detection (LOD), and illustrative calculations of sensitivity and LOD are presented.