Date of Award


Document Type


Degree Name

Master of Science (MS)

Legacy Department


Committee Chair/Advisor

Rao, Apparao

Committee Member

Skove , Malcolm

Committee Member

Sosolik , Chad


Micro- and nano-cantilevers have the potential to revolutionize physical, chemical, and biological sensing; however, an accurate and scalable detection method is required. In this work, a fully electrical actuation and detection method is presented, known as the Harmonic Detection of Resonance (HDR). In HDR, harmonic components of the current are measured to determine the cantilever's resonance frequency. These harmonics exist as a result of nonlinearities in the system, principally in the electrostatic actuation force. In order to better understand this rich harmonic structure, a theoretical investigation of the micro-cantilever is undertaken. Both a lumped parameter model and a more accurate continuum model are used to derive the governing nonlinear modal equations of motion (EOM) of the cantilever. Various approximate solution methods applicable to nonlinear equations are then discussed including numerical integration, perturbation, and averaging. An averaging method known as the method of harmonic balance is then used to obtain steady state solutions to the micro-cantilever EOM. Low-order closed-form harmonic balance solutions are derived which explain many of the important features of the HDR results, such as the presence of parasitic capacitance in the first harmonic and super-harmonic resonance peaks in higher harmonics. Finally, higher-order computer generated harmonic balance solutions are presented which show good agreement with the experimental HDR results, validating both the modeling and the solution methods used.

Included in

Physics Commons



To view the content in your browser, please download Adobe Reader or, alternately,
you may Download the file to your hard drive.

NOTE: The latest versions of Adobe Reader do not support viewing PDF files within Firefox on Mac OS and if you are using a modern (Intel) Mac, there is no official plugin for viewing PDF files within the browser window.