Thesis (M.S.)--Rochester Institute of Technology, 2005. / Typescript. Includes bibliographical references (leaves 144-146).

This dissertation is concerned with the responses of nonlinear systems to both deterministic and stochastic excitations. For a single-degree-of-freedom system, the response of a simply-supported buckled beam to parametric excitations is investigated. Two types of excitations are examined: deterministic and random. For the nonlinear response to a harmonic axial load, the method of multiple scales is used to determine to second order the amplitude-and phase-modulation equations. Floquet theory is used to analyze the stability of periodic responses. The perturbation results are verified by integrating the governing equation using both digital and analog computers. For small excitation amplitudes, the analytical results are in good agreement with the numerical solutions. The large-amplitude responses are investigated by using simulations on a digital computer and are compared with results obtained using an analog computer. For the stochastic response to a wide-band random excitation, the Gaussian and non-Gaussian closure schemes are used to determine the response statistics. The results are compared with those obtained from real-time analysis (analog-computer simulation). The normality assumption is examined. A comparison between the responses to deterministic and random excitations is presented. / Ph. D.

Spatiotemporal properties of classical coupled nonlinear oscillators are investigated in this thesis. Chapter 1 gives an introduction to nonlinear lattices and to the concept of breathers, that are spatially localized and temporally periodic excitation in nonlinear lattices. The concept of anti-continuous limit that provides the basic methodology in probing spatiotemporal breather properties is discussed. In Chapter 2, the general approach for finding exact breather solutions from the anti-continuous limit is examined, and the rotating wave approximation(RWA) is applied to probe the spatial structure of static breathers. Numerical evidence reveals that the RWA relates the spatial structure of stable multi-breathers to a single breather of the same frequency. Chapter 3 presents linear stability analysis of static breathers and gives a systematic way to construct mobile breathers. Formation and collision properties of this moving breathers are also studied. Chapter 4 discusses dynamics of kinks and anti-kinks in hydrogen-bonded chains in the context of two-component soliton model. From molecular dynamics simulations with finite temperature, it is observed that, in a real system (eg. ice), a pair of kink and anti-kink can evolve into a moving-breather-like excitation. Chapter 5 is devoted to the understand of the effects of disorder in the Holstein model. The summary is given in Chapter 6.

Synchronization of an ensemble of oscillators is a phenomenon present in systems of different fields, ranging from social and physical to biological and technological systems. The most successful approach to describe how synchrony emerges in these systems is given by the Kuramoto model. This model as it stands, however, assumes oscillators of fixed natural frequencies and a homogeneous all-to-all coupling strength. The Kuramoto model has been analytically discussed to address the synchronization phenomena of coupled oscillators in the thermodynamic limit (N --> ∞). However, there needs to be a modi cation to address the inevitable in uence of external fields on the pattern of various real life synchronization phenomena which, in general; involves a finite number of oscillators. This research introduces a time dependent coupling strength K(t) which is from the modulation of external elds in the form of, for example, a periodic impulse, in the nite oscillators assembly. A sinusoidal function with some arbitrary values of amplitude and frequency is added to the fixed coupling strength as a perturbation of external elds. Temporal evolution of order parameter r(t) and phase θ(t), both of which measure the degree of synchronization of an assembly of oscillators simultaneously, are compared between uniform and time dependent cases. Graphical comparison are made using a 2 oscillator system, a building block of any finite oscillators case. Also, similar comparisons are performed for a system of 32 oscillators which are chosen randomly as a representative of a nite number of oscillators (2 < N < ∞). A temporal variation of the relative phase angle θ(t) = θ2(t) - θ1(t) in 2 and 32 oscillators systems using uniform and time dependent cases is also a part of this research. This work also introduces a time-dependent coupling strength in the form of a step function. The main objective of using such a function is to keep the synchronized behavior of the oscillators persistently. This behavior can be achieved with the perception that occasional boosting with higher coupling strength K(t) should be enough to sustain synchronous behavior of oscillators which, in general, are tuned with lower K(t). / Includes bibliography. / Dissertation (Ph.D.)--Florida Atlantic University, 2018. / FAU Electronic Theses and Dissertations Collection

In the first part of the dissertation, a novel stochastic averaging technique based on a Hilbert transform definition of the oscillator response displacement amplitude is developed. In comparison to standard stochastic averaging, the requirement of “a priori” determination of an equivalent natural frequency is bypassed, yielding flexibility in the ensuing analysis and potentially higher accuracy. Further, the herein proposed Hilbert transform based stochastic averaging is adapted for determining the time-dependent survival probability and first-passage time probability density function of stochastically excited nonlinear oscillators, even endowed with fractional derivative terms. To this aim, a Galerkin scheme is utilized to solve approximately the backward Kolmogorov partial differential equation governing the survival probability of the oscillator response. Next, the potential of the stochastic averaging technique to be used in conjunction with performance-based engineering design applications is demonstrated by proposing a stochastic version of the widely used incremental dynamic analysis (IDA). Specifically, modeling the excitation as a non-stationary stochastic process possessing an evolutionary power spectrum (EPS), an approximate closed-form expression is derived for the parameterized oscillator response amplitude probability density function (PDF). In this regard, IDA surfaces are determined providing the conditional PDF of the engineering demand parameter (EDP) for a given intensity measure (IM) value. In contrast to the computationally expensive Monte Carlo simulation, the methodology developed herein determines the IDA surfaces at minimal computational cost. In the second part of the dissertation, a novel multiple-input/single-output (MISO) system identification technique is developed for parameter identification of nonlinear and time-variant oscillators with fractional derivative terms subject to incomplete non-stationary data. The technique utilizes a representation of the nonlinear restoring forces as a set of parallel linear sub-systems. Next, a recently developed L1-norm minimization procedure based on compressive sensing theory is applied for determining the wavelet coefficients of the available incomplete non-stationary input-output (excitation-response) data. Several numerical examples are considered for assessing the reliability of the technique, even in the presence of incomplete and corrupted data. These include a 2-DOF time-variant Duffing oscillator endowed with fractional derivative terms, as well as a 2-DOF system subject to flow-induced forces where the non-stationary sea state possesses a recently proposed evolutionary version of the JONSWAP spectrum. In the third part of this dissertation, a joint time-frequency analysis technique based on generalized harmonic wavelets (GHWs) is developed for dynamic cerebral autoregulation (DCA) performance quantification. DCA is the continuous counter-regulation of the cerebral blood flow by the active response of cerebral blood vessels to the spontaneous or induced blood pressure fluctuations. Specifically, various metrics of the phase shift and magnitude of appropriately defined GHW-based transfer functions are determined based on data points over the joint time-frequency domain. The potential of these metrics to be used as a diagnostics tool for indicating healthy versus impaired DCA function is assessed by considering both healthy individuals and patients with unilateral carotid artery stenosis. Next, another application in biomedical engineering is pursued related to the Pulse Wave Imaging (PWI) technique. This relies on ultrasonic signals for capturing the propagation of pressure pulses along the carotid artery, and eventually for prognosis of focal vascular diseases (e.g., atherosclerosis and abdominal aortic aneurysm). However, to obtain a high spatio-temporal resolution the data are acquired at a high rate, in the order of kilohertz, yielding large datasets. To address this challenge, an efficient data compression technique is developed based on the multiresolution wavelet decomposition scheme, which exploits the high correlation of adjacent RF-frames generated by the PWI technique. Further, a sparse matrix decomposition is proposed as an efficient way to identify the boundaries of the arterial wall in the PWI technique.

This work explores the effects of weak nonlinearity on harmonic oscillators.Two particular systems are studied experimentally: A superconductingresonator formed from a coplanar waveguide that oscillates at microwave frequencies,and the cantilever of an atomic force microscope (AFM) vibratingat ultrasonic frequencies. Both of these systems are described in the introduction,followed by a theory chapter giving a general theoretical framework for nonlinear oscillators. Basic properties of nonlinear oscillators, such asbifurcation and intermodulation, are explained using simple models. Experimental methods, including cryogenic and microwave measurement techniques,are described in some detail. The nonlinear superconducting resonator is studied for use as a parametric amplifier. A strong drive tone, called the pump, drives the oscillator nearthe point of bifurcation. A second, much weaker drive signal that is slightlydetuned from the pump, will cause energy to move from the pump to the signal, giving signal amplification. We have measured a signal gain greaterthan 22 dB in a bandwidth of 30 kHz, for a resonator pumped at 7.6 GHz.This type of amplifier is phase-sensitive, meaning that signals in phase withthe pump will be amplified, but signals in quadrature phase of the pump will be deamplified. Phase-sensitivity has important implications on the amplifier’snoise properties. With a parametric amplifier, a signal can be amplified without any additional noise being added by the amplifier, something that is fundamentally impossible for a standard amplifier. The vibrating AFM cantilever becomes a nonlinear oscillator when it is interacting with a surface. When driven with two frequencies, the amplitudeand phase of the cantilever’s response will develop mixing products, or intermodulation products, that are very sensitive to the exact form of the nonlinearity. Very small changes in the surface properties will be detectable when measuring the intermodulation products. Simultaneously measuring many intermodulation products, or acquiring an intermodulation spectrum,allows one to reconstruct the tip-surface interaction. Intermodulation AFM increases the sensitivity of the measurement or the contrast of the acquiredimages, and provides a means of rapidly measuring the nonlinear tip-surface interaction. The method promises to enhance the functionality of the AFM beyond simple topography measurement, towards quantitative analysis of the chemical or material properties of the surface. / <p>QC 20100812</p>

The thesis is devoted to the study of spontaneous synchronization of coupled nonlinear oscillators. It consists of two major parts. The first describes synchronization of Josephson junctions embedded in a transmission line. I consider in detail a new phenomenon ??eation of inert oscillator pairs ??ich was observed in analytical studies. The second part of the thesis describes synchronization of an array of single mode fiber lasers, with special interest in the phenomenon of synchronization of subsets of fiber lasers in a two dimensional array through a specific arrangement of the under-pumped lasers.

Kyoto University (京都大学) / 0048 / 新制・課程博士 / 博士(工学) / 甲第18946号 / 工博第3988号 / 新制||工||1614 / 31897 / 京都大学大学院工学研究科航空宇宙工学専攻 / (主査)教授 泉田 啓, 教授 藤本 健治, 教授 松野 文俊 / 学位規則第4条第1項該当

Orientador: Nobuo Oki / Banca: Carlos Antonio Alves / Banca: Fabiano Fruett / Resumo: Este trabalho apresenta um Oscilador Controlado por Corrente (CCO) com configuração em anel usando tecnologia CMOS, com melhorias na faixa de operação e ruído de fase. O oscilador proposto tem uma faixa de oscilação de 0,0989 GHz a 1,2 GHz com uma corrente de controle com um intervalo de 0,1 mA a 3 mA com uma potência dissipada de 11,8 mW. A arquitetura apresenta uma melhoria na fase de ruído de -7 dBc / Hz em relação a um oscilador em anel de três estágios (VCO), também apresentado neste trabalho. A estrutura proposta é baseada na mudança da entrada de controle do oscilador e também em modificações nas polarizações dos transistor de carga do estágio de atraso. Estas mudanças, além de aumentar a faixa de operação do oscilador e diminuir o efeito do ruído de fase, também reduzem a variação da amplitude do sinal de saída que acontece a medida que a frequência de operação aumenta ou diminui. Simulações realizadas com ambos os osciladores, confirmam os resultados. / Abstract: This dissertation presents a Current Controlled Oscillator (CCO-Current-Controlled Oscillator) at ring configuration using CMOS (Complementary Metal-Oxide-Semiconductor) technology, with improvements in operating range and phase noise. The proposed oscillator has an oscillation range of 98.959 MHz to 1.2 GHz with a current control with a range of 0.1 mA to 3 mA with a power dissipation of 11.8 mW. The architecture shows an improvement in phase noise of -7 dBc / Hz when compared with a ring oscillator in three stages (VCO-Voltage- Controlled Oscillator), also presented in this paper. The proposed structure is in the change of input control and also in the polarizations of the load transistor stage of delay. These changes, in modifications increase the operations range of the oscillator, reduce the phase noise and minimize the amplitude variation of the output signal when the frequency operation increase or decrease. Simulations with both oscillators and their comparisons confirm these results. / Mestre

京都大学 / 0048 / 新制・課程博士 / 博士(工学) / 甲第18946号 / 工博第3988号 / 新制||工||1614(附属図書館) / 31897 / 京都大学大学院工学研究科航空宇宙工学専攻 / (主査)教授 泉田 啓, 教授 藤本 健治, 教授 松野 文俊 / 学位規則第4条第1項該当 / Doctor of Philosophy (Engineering) / Kyoto University / DFAM