Andrew B. Sabater

On the Dynamics of Two Mutually-Coupled, Electromagnetically-Actuated Microbeam Oscillators

This work describes the modeling, analysis, predictive design, and control of self-excited oscillators, and associated arrays, founded upon electromagnetically-actuated microbeams. The study specifically focuses on the characterization of nonlinear behaviors arising in isolated oscillators and small arrays of nearly-identical, mutually-coupled oscillators. The work provides a framework for the exploration of larger oscillator arrays with different forms of coupling and feedback, which can be exploited in practical applications ranging from signal processing to micromechanical neurocomputing.© 2011 ASME

Design and Implementation of a Tunable, Duffing-Like Electronic Resonator via Nonlinear Feedback

To date, many vibration-based sensing modalities have relied upon monitoring small shifts in the natural frequency of a system to detect structural changes (e.g., in mass or stiffness), which are attributable to the chemical or biological species, or other phenomena, that are being measured. Often, this approach carries significant signal processing expense due to the presence of electronics, such as precision phase-locked loops, when high sensitivities are required. Bifurcation-based sensing modalities, in contrast, can produce large easy to detect changes in response amplitude with high sensitivity to structural change if applied appropriately. This paper demonstrates the design and implementation of a tunable, Duffing-like electronic resonator realized via nonlinear feedback electronics, which uses a quartz crystal tuning fork as the device platform. The system in this manifestation uses collocated sensing and actuation, along with readily available electronic components, to realize the desired behavior. The sensitivity of the device is tunable via the control of feedback gain and the type of Duffing-like response (hardening or softening) is also selectable, thus creating a versatile bifurcation-based sensing platform.

Towards a comprehensive model for a resonant nanoelectromechanical system

The mass production and very large scale integration (VLSI) of micro/nanoelectromechanical systems (M/NEMS) requires the development and use of accurate models and simulations, which are capable of rapidly evaluating potential designs. Because of the large range of applications that have been proposed for M/NEMS, the most useful models are those that can accurately capture a system’s response under widely varying input and operating conditions. This allows the M/NEMS devices to be treated as well understood circuit components in simulation contexts. It is towards this end that a first-principles based model is proposed for a resonant nanosystem inclusive of an electrostatically-actuated fixed-fixed beam resonator, test equipment and system parasitics. By encoding the algebraic and differential equations which describe the system into circuit components using Verilog-A, an experimental test setup was simulated using Spectre and subsequently compared to experimental results for qualitative validation of the model. The simulation was then used to investigate the behavior of a representative device for a basic input configuration that more closely represents a final-use scenario for the nanoresonator. Discrepancies between the commonly-employed experimental methodology and the practical final-use scenario are discussed and used as a platform to encourage the development of improved experimental methodologies, while also emphasizing the need for robust and accurate system-level models.

A single-input, single-output electromagnetically-transduced microresonator array

Resonant microsystems have found broad applicability in environmental and inertial sensing, signal filtering and timing applications. Despite this breadth in utility, a common constraint on these devices is throughput, or the total amount of information that they can process. In recent years, elastically-coupled arrays of microresonators have been used to increase the throughput in sensing contexts, but these arrays are often more complicated to design than their isolated counterparts, due to the potential for collective behaviors (such as vibration localization) to arise. An alternative solution to the throughput constraint is to use arrays of electromagnetically-transduced microresonators. These arrays can be designed such that the mechanical resonances are spaced far apart and the mechanical coupling between the microresonators is insignificant. Thus, when the entire array is actuated and sensed, a resonance in the electrical response can be directly correlated to a specific microresonator vibrating, as collective behaviors have been avoided. This work details the design, analysis and experimental characterization of an electromagnetically-transduced microresonator array in both low- and atmospheric-pressure environments, and demonstrates that the system could be used as a sensor in ambient conditions. While this device has direct application as a resonant-based sensor that requires only a single source and measurement system to track multiple resonances, with simple modification, this array could find uses in tunable oscillator and frequency multiplexing contexts.

On the Nonlinear Dynamics of Electromagnetically-Transduced Microresonators

This work investigates the dynamics of electromagnetically-actuated and sensed microresonators. These resonators consist of a silicon microcantilever and a current-carrying metallic wire loop. When placed in a permanent magnetic field, the devices vibrate due to Lorentz interactions. These vibrations, in turn, induce an electromotive force, which can be correlated to the dynamic response of the device. The nature of this transduction process results in an intrinsic coupling between the system’s input and output, which must be analytically and experimentally characterized to fully understand the dynamics of the devices of interest. This paper seeks to address this need through the modeling, analysis, and experimental characterization of the nonlinear response of electromagnetically-transduced microcantilevers in the presence of inductive and resistive coupling between the devices’ input and output ports. A complete understanding of this behavior should enable the application of electromagnetically-transduced microsystems in practical contexts ranging from resonant mass sensing to micromechanical signal processing.Copyright

Dynamics of Globally-, Dissipatively-Coupled Resonators

Examples of coupled resonator and oscillator arrays in engineering, scientific and mathematical contexts are diverse and abundant. However, when the technical scope is limited to mechanical systems, research typically focuses on arrays of resonators in which the coupling between the sub-units is conservative and nearest-neighbor in nature. In these arrays, if the sub-units are nominally identical, and the coupling is weak, collective behaviors such as localization, the spatial confinement of energy in distinct or limited regions, can be observed. In contrast, if the coupling is global and dissipative, very different collective dynamics are observed, namely, group resonance, confined attenuation, and group attenuation, the latter two of which are associated with the local absence of energy. This paper investigates these dynamic phenomena within the context of a generic, globally-, dissipatively-coupled system, which is motivated by recent work related to electromagnetically-coupled microresonator arrays. The results of this work have direct applicability in new single-input, single-output resonant mass sensors, and, with extension, a variety of other sensing and signal processing applications.© 2013 ASME