Date of Award
Spring 2013
Document Type
Dissertation
Degree Name
Doctor of Philosophy (PhD)
Department
Civil, Construction, and Environmental Engineering
First Advisor
Heinrich, Stephen M.
Second Advisor
Dufour, Isabelle
Third Advisor
Foley, Christopher M.
Abstract
Resonant microcantilevers are often considered for use in chemical sensing and biosensing applications. However, when excited in the conventional transverse flexural mode, their performance in liquids is severely compromised. Theoretical and experimental studies have shown that the detrimental effects of the liquid may be mitigated by operating the microcantilever in lateral flexure, especially for microbeams having smaller length-to-width (L/b) ratios. However, for these most promising geometries the predictions of existing models tend to diverge from experimental data for resonant frequency (fres) and quality factor (Q). A likely reason for these discrepancies is support compliance, which has been neglected in existing models. Thus, the derivation of an analytical model for the lateral-mode dynamic response of a microcantilever in a viscous fluid, including the effects of support compliance, is warranted and is the focus of this dissertation.
Analytical solutions for natural frequency and Q are first obtained for the free-vibration case, followed by solutions for the forced-vibration response when the cantilever is excited by an imposed harmonic relative rotation near the support (simulating electrothermal actuation). Values of fres and Q are extracted from the response spectra for the tip deflection and the bending strain near the support. The support compliance (required as model input) is analytically related to device dimensions by employing dimensional analysis and 3-D FEA. The analytical results for the resonant characteristics are also related to sensor performance metrics (sensitivity and limit of detection), thus permitting one to exploit the potential of lateral-mode microcantilever-based liquid-phase sensors. The impact of support compliance, fluid resistance, and beam dimensions on the free- and forced-vibration response are explored, as are the differences associated with the two output signals. Comparisons of results with experimental data show a marked improvement over the previous rigid-support models for smaller L/b values. For the practical ranges of parameters considered the model indicates that, at smaller L/b values, support compliance may reduce Q by up to ~14% and fres and mass sensitivity (Sm) by up to ~21%. Conversely, for L/b>15 the support compliance effects are no more than 2% on Q and 4% on fres and Sm.