A. James Clark School of Engineering
Permanent URI for this communityhttp://hdl.handle.net/1903/1654
The collections in this community comprise faculty research works, as well as graduate theses and dissertations.
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Item Nonlinear and Stochastic Analysis of Miniature Optoelectronic Oscillators based on Whispering-Gallery Mode Modulators(2021) Nguewou-Hyousse, Helene; Chembo, Yanne K.; Electrical Engineering; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)Optoelectronic oscillators are nonlinear closed-loop systems that convert optical energy into electrical energy. We investigate the nonlinear dynamics of miniature optoelectronic oscillators (OEOs) based on whispering-gallery mode resonators. In these systems, the whispering-gallery mode resonator features a quadratic nonlinearity and operates as an electrooptical modulator, thereby eliminating the need for an integrated Mach-Zehnder modulator. The narrow optical resonances eliminate as well the need for both an optical fiber delay line and an electric bandpass filter in the optoelectronic feedback loop. The architecture of miniature OEOs therefore appears as significantly simpler than the one of their traditional counterparts, and permits to achieve competitive metrics in terms of size, weight, and power (SWAP). Our theoretical approach is based on the closed-loop coupling between the optical intracavity modes and the microwave signal generated via the photodetection of the output electrooptical comb. In the first part of our investigation, we use a slowly-varying envelope approach to propose a time-domain model to analyze the dynamical behavior of miniature OEOs. This model takes into account the interactions among the intracavity modes, as well as the coupled interactions with the radiofrequency (RF) microstrip. The stability analysis allows us to determine analytically and optimize the critical value of the feedback gain needed to trigger self-sustained oscillations. It also allows us to understand how key parameters of the system such as cavity detuning or coupling efficiency influence the onset of the radiofrequency oscillation. Furthermore, we determine the threshold laser power needed to trigger oscillations in amplifierless miniature OEOs based on WGM modulators. This latter architecture, while also improving on the size, weight, performance and cost (SWAP-C) constraints, is intended to reduce noise in the system. In the second part of our investigation, we use a Langevin approach to perform a stochastic analysis of our miniature OEO. We propose a stochastic mathematical model to describe the system dynamics and analyze the stochastic behavior below threshold. We also propose a normal form approach for the noise power density and the phase noise spectrum. Our study is complemented by time-domain simulations for the microwave and optical signals, which are in excellent agreement with the analytical predictions. In the third part of our study, we discuss our preliminary results in the analysis of the effects of dispersion in a microcomb oscillator with optical feedback. For this purpose, we propose a closed-loop miniature optical oscillator. The output signal is optically amplified before being coupled back into the cavity using a prism coupling. Using a Lugiato-Lefever approach, we propose a spatiotemporal nonlinear partial differential equation to describe the dynamics of the total intracavity field. We perform temporal and spatial analysis and derive the bifurcation maps in anomalous and normal dispersion regimes.Item DATA-DRIVEN STUDIES OF TRANSIENT EVENTS AND APERIODIC MOTIONS(2019) Wang, Rui; Balachandran, Balakumar; Mechanical Engineering; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)The era of big data, high-performance computing, and machine learning has witnessed a paradigm shift from physics-based modeling to data-driven modeling across many scientific fields. In this dissertation work, transient events and aperiodic motions of complex nonlinear dynamical system are studied with the aid of a data- driven modeling approach. The goal of the work has been to further the ability for future behavior prediction, state estimation, and control of related behaviors. It is shown that data on extreme waves can be used to carry out stability analysis and ascertain the nature of the transient phenomenon. In addition, it is demonstrated that a low number of soliton elements can be used to realize a rogue wave on the basis of nonlinear interactions amongst the basic elements. The pro- posed nonlinear phase interference model provides an appealing explanation for the formation of ocean extreme wave and related statistics, and a superior reconstruction of the Draupner wave event than that obtained on the basis of linear superposition. Chaotic data, another manifestation of aperiodic motions, which are obtained from prototypical ordinary differential and partial differential systems are considered and a neural machine is realized to predict the corresponding responses based on a limited training set as well to forecast the system behavior. A specific neural architecture, called the inhibitor mechanism, has been designed to enable chaotic time series forecasting. Without this mechanism, even the short-term predictions would be intractable. Both autonomous and non-autonomous dynamical systems have been studied to demonstrate the long-term forecasting possibilities with the de- veloped neural machine. For each dynamical system considered in this dissertation, a long forecasting horizon is achieved with a short historical data set. Furthermore, with the developed neural machine, one can relax the requirement of continuous historical data measurements, thus, providing for a more pragmatic approach than the previous approaches available in the literature. It is expected that the efforts of this dissertation work will lead to a better understanding of the underlying mechanism of transient and aperiodic events in complex systems and useful techniques for forecasting their future occurrences.Item NOISE-INFLUENCED DYNAMICS OF NONLINEAR OSCILLATORS(2015) Perkins, Edmon; Balachandran, Balakumar; Mechanical Engineering; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)Noise is usually considered detrimental to the performance of a system and the effects of noise are usually mitigated through design and/or control. In this dissertation, noise-influenced phenomena and qualitative changes in responses of nonlinear systems with noise are explored. Here, the author considers a range of nonlinear dynamical systems, including an array of nonlinear, coupled oscillators, a vertically excited pendulum, the Duffing oscillator, and a Rayleigh-Duffing mixed type oscillator. These systems are studied analytically and numerically via stochastic direct numerical integration, and analytically via the Fokker-Planck equation. The array of nonlinear, coupled oscillators is also experimentally studied. The topics covered in this dissertation are as follows: i) the destruction and formation of energy localizations in an array of oscillators, ii) a technique to stabilize an inverted pendulum by using noise, iii) a noise-utilizing control scheme, iv) the effects of noise on the response of a nonlinear system that exhibits chaotic behavior, v) and the effects of phase lag on the information rate of a Duffing oscillator. The understanding gained through this dissertation efforts can be of benefit to a variety of nonlinear systems, including structural systems at the macro-scale, micro-scale, and nano-scale.Item Dynamics of Slender, Flexible Structures(2014) Vlajic, Nicholas A.; Balachandran, Balakumar; Mechanical Engineering; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)Dynamics of slender beam-like structures subjected to rotational motions is studied experimentally, numerically, and analytically within this dissertation. As the aspect ratio of beam-like structures is increased (i.e., as the structures become slender), the structure can undergo large elastic deformations, and in addition, the torsional and lateral motions can be strongly coupled. Two different paradigms of rotor systems are constructed and used to investigate coupled torsional-lateral motions in slender rotating structures. The first rotor model is a modified version of the classical Jeffcott rotor, which accounts for torsional vibrations and stator contact. Analysis and simulations indicate that torsional vibrations are unlikely to exist during forward synchronous whirling, and reveal the presence of phenomena with high-frequency content, such as centrifugal stiffening and smoothening, during backward whirling. The second rotor model is a nonlinear distributed-parameter system that has been derived with the intent of capturing dynamics observed in an experimental apparatus with slender, rotating structures. Nonlinear oscillations observed in the experiments contain response components at frequencies other than the drive speed, a feature that is also captured by predictions obtained from the distributed-parameter model. Further analysis of the governing partial-differential equations yields insights into the origins (e.g., nonlinear gyroscopic coupling and frictional forces) of the nonlinear response components observed in the spectrum of the torsion response. Slender structures are often subject to large deformations with pre-stress and curvature, which can drastically alter the natural frequencies and mode shapes when in operation. Here, a geometrically exact beam formulation based on the Cosserat theory of rods is outlined in order to predict the static configuration, natural frequencies, and mode shapes of slender structures with large pre-stress and curvature. The modeling and analysis are validated with experiments as well as comparisons with a nonlinear finite element formulation. The predictions for the first eight natural frequencies are found to be in excellent agreement with the corresponding experimentally determined values. The findings of this dissertation work have a broad range of applications across different length scales, including drill strings, space tethers, deployable structures, cable supported structures (e.g., bridges and mooring cables), DNA strands, and sutures for non-invasive surgery to name a few.