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Dissertation Submitted in Partial Satisfaction of the Requirements for the Degree Of UNIVERSITY OF CALIFORNIA Santa Barbara Development of Nonlinear and Coupled Microelectromechanical Oscillators for Sensing Applications A Dissertation submitted in partial satisfaction of the requirements for the degree of Doctor of Philosophy in Mechanical Engineering by Barry Ernest DeMartini Committee in Charge: Professor Kimberly L. Turner, Chair Professor Jeff Moehlis Professor Karl J. Astr¨om˚ Professor Noel C. MacDonald Professor Steven W. Shaw September 2008 The Dissertation of Barry Ernest DeMartini is approved: Professor Jeff Moehlis Professor Karl J. Astr¨om˚ Professor Noel C. MacDonald Professor Steven W. Shaw Professor Kimberly L. Turner, Committee Chairperson August 2008 Development of Nonlinear and Coupled Microelectromechanical Oscillators for Sensing Applications Copyright © 2008 by Barry Ernest DeMartini iii Acknowledgements First of all, I would like to dedicate this dissertation to my parents, Sharon and Ernie, my brothers, Kevin and Joel, and my girlfriend Michele for their un- conditional love and support over the past years. I would like to give special thanks to my advisors, Kimberly Turner and Jeff Moehlis, for giving me the opportunity to work in their research groups, for their guidance, and for all that they have taught me over the past five years. I would also like to thank Steve Shaw, Karl Astr¨om,˚ and Noel MacDonald for being on my committee and for their vital input on the various projects that I have worked on in graduate school. I would like to thank Jeff Rhoads and Nick Miller for the valuable collabora- tions and for being such great people to work with. I would also like to thank past and present members of Kimberly Turner’s group, Raji Baskaran, Wenhua Zhang, Weibin Zhang, Laura Oropeza, Abhishek Srivastava, Mike Requa, Mike Northen, Matt Garten, Kyle Owen, Holly Butterfield, Mark Zielke, Benedikt Zeyen, Kari Moran, John Tamelier, Sathya Chary, Chris Burgner, Zi Yie, and Ashfaque Ud- din, and the Jeff Moehlis’ group Lina Kim, Allison Kolpas, Per Danzl, and Margot Kimura, who have all helped me through this endeavor in their own way. Finally, I would like to thank Dave Bothman for all of his help with lab equipment and the cleanroom staff for all of their advise on fabrication. iv The content and figures in Chapter 2 and 3 is reprinted with permission from “B.E. DeMartini, J.F. Rhoads, K.L. Turner, S.W. Shaw, and J. Moehlis, Linear and Nonlinear Tuning of Parametrically Excited MEMS Oscillators. Journal of Microelectromechanical Systems, 16(2): p. 310-318, 2007. (©2007 IEEE)” and “B.E. DeMartini, H.E. Butterfield, J. Moehlis, and K.L. Turner, Chaos for a Microelectromechanical Oscillator Governed by the Nonlinear Mathieu Equation, Journal of Microelectromechanical Systems, 16(6): p. 1314-1323, 2007. (©2007 IEEE)”, respectively. Figures 6.1, 6.4, 6.5, 6.7, 6.8, and 6.9 are reprinted with permission from “Barry E. DeMartini, Jeffrey F. Rhoads, Steven W. Shaw, Kimberly L. Turner, A single input-single output mass sensor based on a coupled array of microres- onators, Sensors and Actuators A Physical, 137(1): p. 147-156, 2007. (©2007 Elsevier)”, “Jeff F. Rhoads, Barry E. DeMartini, Steve W. Shaw, and Kimberly L. Turner. A SISO Multi-Analyte Sensor Based on a Coupled Microresonator Array, 2006 ASME Mechanical Engineering Congress and Exposition, Chicago, Il 2006. (©2006 ASME)”, and “Barry E. DeMartini, Jeff F. Rhoads, Steve W. Shaw, and Kimberly Turner, A Resonant SISO Sensor Based on a Coupled Array of Microelectromechanical Oscillators, Hilton Head 2006: A Solid-State Sensor, Ac- tuator, and Microsystems Workshop, Hilton Head, SC 2006. (©2006 Transducer Research Foundation)”. v Finally, Figures 7.1, 7.7, 7.10, and 7.11 are reprinted with permission from: “Barry E. DeMartini, Jeffrey F. Rhoads, Mark A. Zielke, Kyle G. Owen, Steven W. Shaw, and Kimberly L. Turner, A single input-single output coupled microres- onator array for the detection and identification of multiple analytes, Applied Physics Letters, 93(5): 054102, 2008. (©2008 American Institute of Physics).” vi Curriculum Vitæ Barry Ernest DeMartini Education September 2008 Doctor of Philosophy, Mechanical Engineering, University of California, Santa Barbara. 2003 Bachelor of Science, Mechanical Engineering, University of California, Santa Barbara. Experience Summer 2000 Intern, Bovis Lend Lease, San Francisco, CA. Summer 2001 Intern, Agilent Technologies, Rohnert Park, CA. Summer 2003 Intern, Friedman Research Corp., Santa Barbara, CA. Fall/Winter 2003 Teaching Assistant, University of California, Santa Barbara. Summer 2006 Mentor, Summer Institute in Mathematics and Science (SIMS), University of California, Santa Barbara. 2007 – 2008 Mentor, Expanding Pathways to Science, Engineering, and Math- ematics (EPSEM), University of California, Santa Barbara. 2004 – 2008 Graduate Research Assistant, University of California, Santa Bar- bara. vii Publications J.F. Rhoads, S.W. Shaw, K.L. Turner, J. Moehlis, B.E. DeMartini, and W. • Zhang. Generalized parametric resonance in electrostatically-actuated microelec- tromechanical oscillators. Journal of Sound and Vib., 296 (4-5): 797-829, 2006. B.E. DeMartini, J.F. Rhoads, K.L. Turner, S.W. Shaw, and J. Moehlis. Lin- • ear and nonlinear tuning of parametrically excited MEMS oscillators. Journal of Microelectromechanical Systems, 16 (2): 310-318, 2007. G. Schitter, K.J. Astrom, B. DeMartini, P.J. Thurner, K.L. Turner, and P.K. • Hansma. Design and modeling of a high-speed AFM-scanner. IEEE Transactions on Control Systems Technology, 15 (5): 906-915, 2007. B.E. DeMartini, J.F. Rhoads, S.W. Shaw, and K.L. Turner. A single input- • single output mass sensor based on a coupled array of microresonators. Sensors and Actuators A: Physical, 137: 147-156, 2007. B.E. DeMartini, H.E. Butterfield, J. Moehlis, and K.L. Turner. Chaos for a mi- • croelectromechanical oscillator governed by the nonlinear mathieu equation. Jour- nal of Microelectromechanical Systems, 16 (6): 1314-1323, 2007. B.E. DeMartini, J.F. Rhoads, M.A. Zielke, K.G. Owen, S.W. Shaw, and K.L. • Turner. A single input-single output coupled microresonator array for the detection and identification of multiple analytes. Submitted to Applied Physics Letters. 2008. viii Conference Proceedings J.F. Rhoads, S.W. Shaw, K.L. Turner, J. Moehlis, B.E. DeMartini, and W. • Zhang. Nonlinear response of parametrically-excited MEMS. ASME International Design Engineering Technical Conferences, 20th Biennial Conference on Mechan- ical Vibration and Noise, Long Beach, California, 2005. B. DeMartini, J. Moehlis, K. Turner, J. Rhoads, S. Shaw, and W. Zhang. Mod- • eling of parametrically excited microelectromechanical ocillator dynamics with ap- plication to filtering. IEEE Sensors, 4th IEEE Conference on Sensors, Irvine, California, 2005. B.E. DeMartini, J. F. Rhoads, S. W. Shaw, and K. L. Turner. A resonant SISO • sensor based on a coupled array of microelectromechanical oscillators. Hilton Head: A Solid-State Sensor, Actuator, and Microsystems Workshop, Hilton Head, South Carolina, 2006. G. Schitter, K.J. Astrom, B. DeMartini, G.E. Fantner, K. Turner, P.J. Thurner, • and P. K. Hansma. Design and modeling of a high-speed scanner for atomic force microscopy. American Control Conference, Minneapolis, Minnesota, 2006. J.F. Rhoads, B.E. DeMartini, S.W. Shaw, and K.L. Turner. A SISO, multi- • analyte sensor based on a coupled microresonator array. ASME Mechanical Engi- neering Congress and Exposition, Chicago, Illinois, 2006. ix B.E. DeMartini, H.E. Butterfield, J. Moehlis, and K.L. Turner. Prediction and • validation of chaotic behavior in an electrostatically actuated microelectromechan- ical oscillator. Transducers 2007 and Eurosensors XXI, Lyon, France, 2007. Conference Talks J.F. Rhoads, S.W. Shaw, K.L. Turner, B.E. DeMartini, J. Moehlis, and W. • Zhang. Generalized parametric resonance in electrostatically driven MEM oscilla- tors. SIAM Conference on Applications of Dynamical Systems, Snowbird, Utah, 2005. J.F. Rhoads, S.W. Shaw, K.L. Turner, B.E. DeMartini, J. Moehlis, and W. • Zhang. Generalized parametric resonance in electrostatically-actuated microelec- tromechanical systems. ENOC, 5th EUROMECH Nonlinear Dynamics Confer- ence, Eindhoven, The Netherlands, 2005. B.E. DeMartini, H.E. Butterfield, J. Moehlis, and K.L. Turner. Chaotic be- • havior for an electrostatically actuated microelectromechancial oscillator. SIAM Conference on Applications of Dynamical Systems, Snowbird, Utah, 2007. B.E. DeMartini, J.F. Rhoads, M.A. Zielke, K.G. Owen, S.W. Shaw, and K.L. • Turner. Detection and identification of multiple chemicals using a single input- single output coupled microresonator array. International Workshop on Nanome- chanical Cantilever Sensors, Mainz, Germany. 2008. x Abstract Development of Nonlinear and Coupled Microelectromechanical Oscillators for Sensing Applications Barry Ernest DeMartini Microelectromechanical systems (MEMS) have gained a great deal of interest over the years due to their small size, low power consumption, ability to be batch fabricated, and ability to be integrated with on-chip electronics. These bene- fits, coupled with the fact that their minute masses and high frequencies lead to unprecedented sensitivities, make MEMS extremely attractive for sensing applica- tions. To date, the conventional approach to these applications has been to utilize linear, uncoupled microresonators. While this method has proved to be successful, nonlinear and/or coupled MEMS resonators possess rich dynamic behavior that is not obtainable with linear, uncoupled MEMS resonators.
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