Constructive utilization of intentional nonlinearity in systems of coupled micro/nanomechanical resonators

Micro/nanomechanical resonators have been actively studied in the last decade in designs of highly sensitive detection, high frequency signal-processing, and high speed switching. These designs benefit from the exceptional dynamic characteristics of these systems, i.e., high frequency resonance and high Q-factor, arising from their small length scales. Most of previous studies in micro/nanomechanical resonators, however, remain in the framework of the linear dynamics while the inherent nonlinearity of these systems is either neglected or considered as unwanted. In some works nonlinear effects are taken into account, but these are considered as perturbations of linear effects, and mostly explored in the regime of weakly nonlinear effects. Some additional recent works have focused on intentionally exploiting the rich dynamics arising from the intrinsic nonlinearities in micro/nanomechanical resonators, and showing that these nonlinear dynamics can be beneficial in satisfying design objectives that could not be met with in linear settings. In this dissertation, we further exploit the constructive utilization of intentional strong nonlinearities in the design of micro/nanomechanical resonators. We present three different studies incorporating intentional strong nonlinear dynamics in diverse applications, with the aim to perform fundamental studies of these systems, but also with significant practical applications. In these systems the intentional utilization of nonlinearity was enabled by introducing ‘mechanical coupling’ through the integration of nanoscale components onto readily realized microcantilever systems. For a system of a microcantilever with an attached nanotube and harmonic base excitation we report expansion of its resonance bandwidth through by the geometric nonlinearity generated by the flexibility of the nanotube, as well as strong nonlinear damping effects. These nonlinearities have significant influence of the resonance bandwidth and the effective Q-factor of the system. In addition, we develop a methodology for identifying and quantifying the nonlinear damping effects originating from the oscillations of flexible nanocomponents to the dynamics of microresonators to which they are attached. For a system of two microcantilever resonators coupled by a nanomembrane and under harmonic base excitation, we study the effect of varying the coupling strength on the nonlinear dynamics and show that in the limit of weak coupling nonlinear localization occurs in this system. Moreover, we report strongly nonlinear resonance phenomena, such as sudden transitions in the resonance amplitude for small increase or decrease of the frequency of base excitation, multiple co-existing resonance solutions and nonlinear hysteresis phenomena. In addition, we report interesting frequency shifts to resonance peaks of the response at different sensing positions of the coupled microcantilevers, and attribute these shifts to nonpropertional damping effects. These same damping effects generate ‘splitting’ of resonance modes with decreasing coupling. In both applications our theoretical findings are validated by experimental tests. Finally, we present a new concept for high-frequency AFM design, whereby an intentional 1:n nonlinear resonance is introduced into a traditional AFM microcantilever with an attached nanomembrane for the purpose of significantly amplifying the nth harmonic component of its steady state response. This is achieved by nonlinear energy transfers from low to high frequencies that are activated by the internal resonance; these energy transfers not only magnify the high frequency components in the detection signal, but, perhaps even more importantly, affect the phase of this signal, which in turn can be used to enhance the sensitivity and performance of the nonlinear AFM design, compared to current traditional linear designs. The capability of the proposed AFM system for discretely imaging the compositional differences of inhomogeneous specimen is assessed experimentally. The findings reported in this dissertation extend the state-of-the-art in the design of nonlinear micro/nanomechanical resonators. Furthermore, our concepts and results can contribute towards a new paradigm of exploiting intentional strong nonlinearities in these systems, with diverse practical applications and with benefits that would not otherwise obtainable with current linear designs.

Name thesis:degree_name

Ph.D.

Level thesis:degree_level

Dissertation

Discipline thesis:degree_discipline

Mechanical Engineering

Grantor

University of Illinois at Urbana-Champaign

Year dc:date

2015

Author dc:creator

• Jeong, Bong Won

Contributors dc:contributor

• Vakakis, Alexander F.
• Bergman, Lawrence A.
• King, William P.
• McFarland, Donald M.
• Yu, Min-Feng

• Micro/Nanomechanical Resonators
• Nonlinear Dynamics
• Intentional Nonlinearity
• Geometric Nonlinearity
• Nanotube
• Micro-electromechanical Systems (MEMS)
• Nano-electromechanical Systems (NEMS)

Statement dc:rights

• Copyright 2014 Bongwon Jeong

Language dc:language

en

Handle dc:identifier

http://hdl.handle.net/2142/72938

OAI identifier oai:identifier

oai:www.ideals.illinois.edu:2142/72938