Analytical Modeling of Microcantilever-Based Resonant Sensors in Lateral Flexural Mode

Microcantilever-based resonant sensors are currently being utilized in chemical and biological sensor technology. The primary mode of excitation results in resonant vibrations of the beam in transverse bending. This introduces a high level of damping and added inertia caused by the presence of any surrounding fluid and causes sensor performance to be drastically reduced. Recent studies as well as intuition suggest that lateral excitation may produce more efficient displacement of the microcantilever through the surrounding gas or liquid and consequently reduce the amount of damping/drag imposed on the beam by the environment. However, in order to fully understand the beam-fluid interaction problem associated with lateral excitation and response, a complete derivation of the beam mechanics in vacuum is first necessary. Therefore, the focus of this thesis is to develop and validate a model for the steady-state displacement response of a two-layer (elastic/viscoelastic) beam subjected to lateral, sinusoidal loading in a vacuum and to compare the dynamic characteristics of the lateral and transverse modes of vibration. The results obtained will then provide a benchmark solution for further research which may include the effects of various fluid environments. After formulating the boundary value problem, the analytical solution is obtained using two methods: (l) the mode superposition method and (2) the correspondence principle for viscoelastic beams. The response equations are made dimensionless and are then utilized to generate results for different materials, load functions, and geometries. In order for the solution of the lateral vibration case to be compared to that of transverse vibration, a recent transverse solution from the literature is summarized. The final results presented are for the tip response generated by a point load applied at the beam tip. These numerical results are presented and discussed for a general frequency-dependent coating, a Standard Linear Solids (SLS) coating (theoretical), and a Polyisobutylene (PIB) coating (experimental). The results for each coating type include parametric studies relating the complex flexural rigidity, resonant frequencies/amplitudes, and quality factors to the various system parameters. Upon comparison of the results of the lateral case to its transverse counterpart, it is shown that the lateral case exhibits many advantages in characteristics important to sensor sensitivity and other performance characteristics. For most physically practical beam configurations considered, the lateral vibration direction results in higher first resonant frequencies and quality factors. As a result, sensor sensitivity and detection limits may potentially be improved and a broader range of coating materials (e.g., those with higher losses) may be considered than might otherwise be possible when using the transverse vibration mode