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Title:Intentional nonlinearity in the small scale with applications to atomic force microscopy (AFM) and mass sensing
Author(s):Potekin, Randi
Director of Research:Vakakis, Alexander F.; Bergman, Lawrence A.
Doctoral Committee Chair(s):Vakakis, Alexander F.
Doctoral Committee Member(s):Kim, Seok; Tawfick, Sameh; McFarland, Michael; Cho, Hanna
Department / Program:Mechanical Sci & Engineering
Discipline:Theoretical & Applied Mechans
Degree Granting Institution:University of Illinois at Urbana-Champaign
Subject(s):Nonlinear AFM
Internal resonance
High-frequency AFM
Broadband nonlinear resonator
Mass sensor
Third harmonic
Nonlinear damping
Abstract:Over the past several decades, the development of ultra-sensitive nano/micromechanical sensor technology has had a transformative effect on the field of nanoscience. These devices are currently used in many different applications including biological, chemical and inertial sensing; atomic force microscopy and infrared spectroscopy; and precise time keeping and synchronization. Traditionally, these systems were studied within the framework of linear dynamics, and incidental nonlinearity was suppressed by design. More recently, researchers have intentionally incorporated nonlinearity in the design of such devices in order to exploit the rich nonlinear behavior. Some of the nonlinear phenomena that researchers aim to utilize include internal resonance, resonant bandwidth expansion, ultra-sensitive bifurcation frequencies associated with sudden jumps in the response, coexistence of multiple solution branches and higher harmonic generation. In this dissertation, I investigate further ways in which intentional nonlinearity can be leveraged to enhance micromechanical resonant sensing techniques. In particular, I focus on applications to AFM and mass sensing. Within the area of AFM, the performance of a new cantilever design during multi-frequency tapping mode AFM is studied. The system consists of a base cantilever with an inner paddle which, under harmonic excitation, vibrates like a system of linearly coupled oscillators engaging simultaneously a lower, in-phase and a higher, out-of phase resonant mode. The cantilever is designed so that the 2nd mode frequency (i.e., the out-of-phase eigenfrequency) coincides with an integer multiple of the fundamental mode frequency, providing the necessary conditions for realization of internal resonance. During tapping mode, the nonlinear tip-sample force activates the internal resonance and thereby amplifies the out-of-phase resonant mode. In contrast to other multi-frequency AFM techniques, the advantage of this approach is that multiple harmonics with strong signal-to-noise ratios (SNR) are excited while maintaining the simplicity of a single excitation frequency. The ability of this inner-paddled cantilever to measure compositional properties of polymers and bacteria was studied, and it was found that the internal resonance-based design results in enhanced sensitivity to Young’s modulus. In another study, a new micromechanical resonant mass sensor design is introduced consisting of a doubly clamped beam having a concentrated mass at its center, subjected to harmonic base excitation. The resonator is specifically designed to exhibit geometric nonlinearity due to midplane stretching. The reduced order model of the system’s fundamental bending mode is that of a Duffing oscillator (i.e., an oscillator having cubic stiffness in addition to linear stiffness) under harmonic base excitation. For positive cubic stiffness, it is well known that the Duffing oscillator exhibits hardening in the frequency response curve resulting in a broadband resonance. The bandwidth of the resonator is determined by the linear resonant frequency (lower bound) and the jump-down bifurcation frequency (upper bound). Under harmonic excitation at a fixed forcing level, the jump down bifurcation frequency is proportional to the forcing level, and at each forcing level there indeed exists a jump down bifurcation. In the proposed system, the forcing level is not fixed; rather, it is proportional to the square of the driving frequency of the base excitation. Interestingly, analytical and computational analyses predict the existence of a critical excitation amplitude above which there is no theoretically predicted jump down bifurcation. It is shown that the effect of the concentrated mass is to lower the threshold of the critical excitation amplitude to a realizable level. In practice, there must inevitably be a jump down bifurcation and this bifurcation may be triggered by the excitation of internal resonances, shrinking domain of attraction of the upper solution branch, variations in the initial state due to noise and/or the presence of nonlinear damping. However, the critical excitation amplitude appears to correspond to sudden and significant bandwidth expansion. Experimental results from a Duffing-like oscillator provide some verification of the powerful theoretical predictions. Ultimately, by operating at an excitation amplitude above the critical level, the ultra-wide resonant bandwidth can be exploited in a mass detection scheme based on amplitude tracking. In comparison to other micromechanical mass sensors, this technique and design offers a wide range of operational frequencies and amplitudes with strong SNR, eliminates the need for frequency sweeping and sophisticated feedback control, and requires relatively simple actuation and microfabrication methods.
Issue Date:2018-07-12
Rights Information:© 2018 Randi Potekin
Date Available in IDEALS:2018-09-27
Date Deposited:2018-08

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