Thesis (Ph.D.)--Massachusetts Institute of Technology, Dept. of Ocean Engineering, 1980. / MICROFICHE COPY AVAILABLE IN ARCHIVES AND ENGINEERING. / Includes bibliographical references. / by Robert Bradlee Campbell. / Ph.D.

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.

The concern of this thesis was to investigate the nonlinear dynamics inherent in oscillating waterfalls.

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.

Thesis (M. Eng.(Mechanical Engineering))--University of Pretoria, 2004. / Includes bibliographical references.

Laplacian differential operator -- Vibrations of plucked strings and Hollow cylinders.

[Truncated abstract] This thesis is split into two parts. In part one; A 50 K dual mode oscillator, the aim of the project was to build a 50 K precision oscillator with frequency stability on the order of 1014 from 1 to 100 seconds. A dual-mode temperature compensation technique was used that relied on a turning point in the frequency-temperature relationship of the difference frequency between two orthogonal whispering gallery modes in a single sapphire crystal. A cylindrical sapphire loaded copper cavity resonator was designed, modelled and built with a turning point in the difference frequency between an E-mode and H-mode pair at approximately 52.5 K . . . The frequencies and Q-factors of whispering spherical modes in the 3-12 GHz range in the fused silica resonator are measured at 6, 77 and 300 K and the Q-factor is used to determine the loss tangent at these temperatures. The frequency and Q-factor temperature dependence of the TM2,1,2 whispering gallery mode at 5.18 GHZ is used to characterise the loss tangent and relative permittivity of the fused silica from 4-300 K. Below 22 K the frequency-temperature dependence of the resonator was found to be consistent with the combined effects of the thermal properties of the dielectric and the influence of an unknown paramagnetic impurity, with a spin resonance frequency at about 138 ± 31 GHz. Below 8 K the loss tangent exhibited a 9th order power law temperature dependence, which may be explained by Raman scattering of Phonons from the paramagnetic impurity ions. A spherical Bragg reflector resonator made from multiple concentric dielectric layers loaded in a spherical cavity that enables confinement of field in the centre of the resonator is described. A set of simultaneous equations is derived that allow the calculation of the required dimensions and resonance frequency for such a resonator and the solution is confirmed using finite element analysis. A spherical Bragg reflector resonator is constructed using Teflon and free-space as the dielectric materials. A Q-factor of 22,000 at 13.87 GHz was measured and found to compare well with the design values.

Piezoelectricity crystal is used in different area in industry, such as downhole oil, gas industry, and ballistics. The piezoelectricity crystals are able to create electric fields due to mechanical deformation called the direct piezoelectric effect, or create mechanical deformation due to the effect of electric field called the indirect piezoelectric effect. In this thesis, piezoelectricity effect is the core part. There are 4 parts in the frequency output pressure transducer: two crystal oscillators, phase-locked loop (PLL), mixer, frequency counter. Crystal oscillator is used to activate the piezoelectricity crystal which is made from quartz. The resonance frequency of the piezoelectricity crystal will be increased with the higher pressure applied. The signal of the resonance frequency will be transmitted to the PLL. The function of the PLL is detect the frequency change in the input signal and makes the output of the PLL has the same frequency and same phase with the input signal. The output of the PLL will be transmitted to a Mixer. The mixer has two inputs and one output. One input signal is from the pressure crystal oscillator and another one is from the reference crystal oscillator. The frequency difference of the two signal will transmitted to the frequency counter from the output of the mixer. Thus, the frequency output pressure transducer with a frequency counter is a portable device which is able to measure the pressure without oscilloscope or computer.

Cette thèse traite de la solution numérique de deux types de problèmes stochastiques. Premièrement, nous nous intéressons aux EDS fortement oscillantes, c'est-à-dire, les systèmes composés de variables ergodiques évoluant rapidement par rapport aux autres. Nous proposons un algorithme basé sur des résultats d'homogénéisation. Il est défini par un schéma d'Euler appliqué aux variables lentes couplé avec un estimateur à pas décroissant pour approcher la limite ergodique des variables rapides. Nous prouvons la convergence forte de l'algorithme et montrons que son erreur normalisée satisfait un résultat du type théorème limite centrale généralisé. Nous proposons également une version extrapolée de l'algorithme ayant une meilleure complexité asymptotique en satisfaisant les mêmes propriétés que la version originale. Ensuite, nous étudions la solution des EDS de type McKean-Vlasov (EDSPR-MKV) associées à la solution de certains problèmes de contrôle sous un environnement formé d'un grand nombre de particules ayant des interactions du type champ-moyen. D'abord, nous présentons un nouvel algorithme, basé sur la méthode de cubature sur l'espace de Wiener, pour approcher faiblement la solution d'une EDS du type McKean-Vlasov. Il est déterministe et peut être paramétré pour atteindre tout ordre de convergence souhaité. Puis, en utilisant ce nouvel algorithme, nous construisons deux schémas pour résoudre les EDSPR-MKV découplées et nous montrons que ces schémas ont des convergences d'ordres un et deux. Enfin, nous considérons le problème de réduction de la complexité de la méthode présentée tout en respectant la vitesse de convergence énoncée. / This Ph.D. thesis deals with the numerical solution of two types of stochastic problems. First, we investigate the numeric solution to strongly oscillating SDEs, i.e. systems in which some ergodic state variables evolve quickly with respect to the remaining ones. We propose an algorithm that uses homogenization results and consists of an Euler scheme for the slow scale variables coupled with a decreasing step estimator for the ergodic averages of the fast variables. We prove the strong convergence of the algorithm as well as a generalized central limit theorem result for the normalized error distribution. In addition, we propose an extrapolated version applicable under stronger regularity assumptions and which satisfies the same properties of the original algorithm with lower asymptotic complexity. Then, we treat the problem of solving decoupled Forward Backward Stochastic Differential equations of McKean-Vlasov type (MKV-FBSDE) which appear in some stochastic control problems in an environment of a large number of particles with mean field interactions. As a first step, we propose a new algorithm, based on the cubature method on Wiener spaces, to weakly approach the solution of a McKean-Vlasov SDE. It is deterministic and can be parametrized to obtain any given order of convergence. Using this first forward approximation algorithm, we construct two procedures to solve the decoupled MKV-FBSDE and show that they converge with orders one and two under appropriate regularity conditions. Finally, we consider the problem of reducing the complexity of the presented method while preserving the presented convergence rates.

L’objectif du présent travail a été de concevoir et de fabriquer des dispositifs sur silicium pour convertir de l’énergie thermique en une énergie électrique en utilisant le changement de phase liquide-gaz dans le but de générer une variation subite de pression suivie d’une conversion d’énergie mécanique vers une énergie électrique à l’aide d’un piézoélectrique. La construction des dispositifs a dû rester simple, avec des matériaux courants et en respectant des limites dimensionnelles. Empreinte inférieure à un diamètre de 20 mm et une épaisseur en dessous des 2 mm.Les prototypes fabriqués sont composés de 3 plaques en silicium, contenant une chambre d’évaporation, une chambre de condensation et un canal réunissant les deux. Un transducteur piézoélectrique a été reporté sur la chambre de condensation et assure l’étanchéité ainsi que la génération d’énergie électrique.Le processus de conception inclut plusieurs étapes, dont la définition de la géométrie et du type de fluide de travail utilisé en tant qu’agent thermique. Le travail effectué a permis de sélectionner le type de piézoélectrique, sa taille ainsi que sa méthode d’intégration. Une étude a également été conduite pour déterminer la méthode optimale d’assemblage des plaques en silicium.La réalisation pratique des dispositifs a été orientée vers la sélection des meilleurs procédés technologiques pour la fabrication des structures. Toutes les expériences ont été conduites en salle blanche avec utilisation de l’oxydation humide, la photolithographie, la gravure KOH, ainsi que d’une technique d’assemblage des plaques silicium avec utilisation de la résine SU-8 comme couche intermédiaire. En plus, quelques outils spécifiques ont été conçus lors du présent travail, pour faciliter la fabrication des dispositifs, dont un système sous vide dédié à l’assemblage des plaques en silicium.Les dispositifs ont été testés afin d’établir leur mécanisme d’oscillation thermique ainsi que leurs propriétés électriques. L’influence tu taux de remplissage et de la température de surface chaude sur le signal en sortie ont également été étudiées. Le calcul de l’énergie générée a aussi été effectué. Dans la dernière partie de l’étude, des étapes d’optimisation pour les dispositifs développés dans le présent travail sont proposées. / The goal of the present work was to design and fabricate a fully silicon oscillating device that converts thermal energy into electricity, applying phenomena of liquid to gas phase-change and piezoelectricity. It should be characterized by simplicity of construction, small size, and ease of manufacture. The diameter should not exceed 2 cm, while the thickness should be within 2 mm.The device was composed of three Si wafers comprising evaporation and condensing chambers, and the channel connecting these two elements. A PZT-based transducer mounted on top of the structure was applied to ensure energy conversion.The design process included the establishment of the device geometry, the type of the working fluid enclosed inside the system, a type, size and assembly technique of a piezoelectric element, as well as a bonding method of several silicon elements of the device.The practical realization of the designed prototypes was aimed at selecting the most suitable technological processes for structure fabrication. All the experiments had been performed in a clean room environment and employed wet oxidation, photolithography, a well-known, easily available wet chemical etching in KOH solution, and a silicon bonding technique with the use of SU-8 photoresist as an intermediate layer. Additionally, during the practical work a few tools have been designed and developed to enhance the device fabrication, amongst which a vacuum pump dedicated to bond the three silicon wafers as structural elements of the prototypesThe fabricated prototypes were tested in terms of oscillation mechanism and electrical properties. The influence of the filling ratio and the hot temperature value on the generated signal was established. Additionally, the power range of the prototypes has been evaluated. In the last part of the study, optimization steps for the devices developed in the present work have been proposed.