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Identification of Finite-Degree-of-Freedom Models for Ship MotionsSuleiman, Baha M. 15 December 2000 (has links)
Accurate ship-motion prediction is important because it is directly related to the design, control, and economic operation of ships. Many methods are available for studying and predicting ship motions, including time-domain, strip-theory, and system-identification-based predictions. Time-domain and strip-theory predictions suffer from several physical and computational limitations. In this work, we use system-identification techniques to predict ship motions. We establish an identification methodology that can handle general finite-degree-of-freedom (FDOF) models of ship motions.
To establish this methodology, we derive the correct form of the equations of motion. This form contains all relevant linear and nonlinear terms.
Moreover, it explicitly specifies the dependence of the linear and nonlinear parameters on the forward speed. The energy-formulation approach is utilized to obtain full nonlinear ship-motion equations. The advantages of using this formulation are that self-sustained motions are not allowed and the dependence of the parameters on the forward speed is derived explicitly.
The data required for the identification techniques are generated using the Large Amplitude Motions Program (LAMP) developed by the Science Applications International Corporation (SAIC). The ship studied in this work is a Series 60 ship, which is a military cargo ship. LAMP data for different sea states and forward speeds are used to identify and predict the ship motions.
For linear parametric identification, we use the Eigensystem Realization Algorithm (ERA) to determine the coefficients in the linearly coupled equations and the effects of the forward speed on these coefficients.
For linear nonparametric identification, we present a new analysis technique, namely, the circular-hyperbolic decomposition (CHD), which avoids the leakage effects associated with the discrete Fourier transform (DFT). The CHD is then utilized to determine transfer functions and response amplitude operators (RAOs).
For nonlinear parametric identification, we present a methodology that is a combination of perturbation techniques and higher-order spectral moments.
We apply this methodology to identify the nonlinear parameters that cause parametric roll resonance. The level of accuracy of the models and the parameter estimates are determined by validations of the predicted ship motions with the LAMP data. / Ph. D.
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Uma introdução à influência da interação modal nas oscilações não lineares de cascas cilíndricas / An introduction to the influence of modal interactions in non-linear oscillations of cylindrical shellsRodrigues, Lara 14 February 2013 (has links)
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Previous issue date: 2013-02-14 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPES / The aim of this work is to investigate the interaction and modal coupling phenomena on the
nonlinear vibrations of simply supported cylindrical shell subject to both harmonic axial and
lateral loads. The equations of motion of the cylindrical shell are deduced from their energy
functionals and the strain field is based on the nonlinear Donnell shallow shell theory. Finally,
the problem is reduced to a system of nonlinear ordinary differential equations by the
application of the standard Galerkin method. The modal expansion that describes the
transverse displacement of the shell is obtained by applying perturbation techniques, which
identifies the importance of each term in the modal expansion by the power of the
perturbation parameter. The Karhunen-Loève method is applied in order to verify the
importance of each term in the modal expansion, quantifying the contribution of each of these
terms in the total energy of the system. The starting solution used in the perturbation
procedure contains two modes of vibration with the same natural frequency and their
respective companion modes, yielding a modal expansion able to describe the modal
interaction between these two modes. Then, the influence of modal interaction on the
nonlinear behavior of the cylindrical shell, subjected to both lateral and axial harmonic load is
studied. From the analysis of the resonance curves, the parametric instability and escape
boundaries, the bifurcation diagrams, the basins of attraction and phase portraits of the
cylindrical shell is possible to identify situations in which the consideration of modal
interaction is necessary. / Neste trabalho estudam-se as vibrações não lineares de cascas cilíndricas simplesmente
apoiadas sujeitas a um carregamento lateral e a um carregamento axial, ambos harmônicos,
com o objetivo de se analisar fenômenos como o acoplamento e a interação modal. As
equações de movimento da casca cilíndrica são deduzidas a partir de seus funcionais de
energia. O campo de deformações da casca cilíndrica é descrito com base na teoria não linear
de Donnell para cascas esbeltas e o problema é reduzido a um sistema de equações
diferenciais ordinárias não lineares a partir da aplicação do método de Galerkin. As expansões
modais que descrevem o campo de deslocamento transversal da casca são obtidas através da
aplicação do método da perturbação, que identifica a importância de cada termo da expansão
modal a partir da potência do parâmetro de perturbação. O método de Karhunen-Loève é
aplicado a fim de se verificar a importância de cada termo da expansão modal, quantificando
a participação de cada um desses termos na energia total do sistema. Utilizam-se, como
solução inicial do método da perturbação, dois modos de vibração com frequência natural
igual e com seus respectivos companion modes, obtendo-se uma expansão modal capaz de
descrever a interação modal entre esses dois modos. Em seguida, analisa-se a influência da
interação modal no comportamento não linear da casca cilíndrica submetidas a cargas laterais
e axiais harmônicas. A partir da análise das curvas de ressonância, das fronteiras de
instabilidade paramétrica, dos diagramas de bifurcação, das bacias de atração e dos planosfase
da casca cilíndrica é possível identificar em quais situações de carregamento a
consideração da interação modal se faz necessária.
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Numerical singular perturbation approaches based on spline approximation methods for solving problems in computational financeKhabir, Mohmed Hassan Mohmed January 2011 (has links)
Options are a special type of derivative securities because their values are derived from the value of some underlying security. Most options can be grouped into either of the two categories: European options which can be exercised only on the expiration date, and American options which can be exercised on or before the expiration date. American options are much harder to deal with than European ones. The reason being the optimal exercise policy of these options which led to free boundary problems. Ever since the seminal work of Black and Scholes [J. Pol. Econ. 81(3) (1973), 637-659], the differential equation approach in pricing options has attracted many researchers. Recently, numerical singular perturbation techniques have been used extensively for solving many differential equation models of sciences and engineering. In this thesis, we explore some of those methods which are based on spline approximations to solve the option pricing problems. We show a systematic construction and analysis of these methods to solve some European option problems and then extend the approach to solve problems of pricing American options as well as some exotic options. Proposed methods are analyzed for stability and convergence. Thorough numerical results are presented and compared with those seen in the literature.
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Numerical singular perturbation approaches based on spline approximation methods for solving problems in computational financeKhabir, Mohmed Hassan Mohmed January 2011 (has links)
Options are a special type of derivative securities because their values are derived from the value of some underlying security. Most options can be grouped into either of the two categories: European options which can be exercised only on the expiration date, and American options which can be exercised on or before the expiration date. American options are much harder to deal with than European ones. The reason being the optimal exercise policy of these options which led to free boundary problems. Ever since the seminal work of Black and Scholes [J. Pol. Econ. 81(3) (1973), 637-659], the differential equation approach in pricing options has attracted many researchers. Recently, numerical singular perturbation techniques have been used extensively for solving many differential equation models of sciences and engineering. In this thesis, we explore some of those methods which are based on spline approximations to solve the option pricing problems. We show a systematic construction and analysis of these methods to solve some European option problems and then extend the approach to solve problems of pricing American options as well as some exotic options. Proposed methods are analyzed for stability and convergence. Thorough numerical results are presented and compared with those seen in the literature.
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Numerical singular perturbation approaches based on spline approximation methods for solving problems in computational financeKhabir, Mohmed Hassan Mohmed January 2011 (has links)
Philosophiae Doctor - PhD / Options are a special type of derivative securities because their values are derived from the value of some underlying security. Most options can be grouped into either of the two categories: European options which can be exercised only on the expiration date, and American options which can be exercised on or before the expiration date. American options are much harder to deal with than European ones. The reason being the optimal exercise policy of these options which led to free boundary problems. Ever since the seminal work of Black and Scholes [J. Pol. Econ. 81(3) (1973), 637-659], the differential equation approach in pricing options has attracted many researchers. Recently, numerical singular perturbation techniques have been used extensively for solving many differential equation models of sciences and engineering. In this thesis, we explore some of those methods which are based on spline approximations to solve the option pricing problems. We show a systematic construction and analysis of these methods to solve some European option problems and then extend the approach to solve problems of pricing American options as well as some exotic options. Proposed methods are analyzed for stability and convergence. Thorough numerical results are presented and compared with those seen in the literature. / South Africa
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Numerical singular perturbation approaches based on spline approximation methods for solving problems in computational financeKabir, Mohmed Hassan Mohmed January 2011 (has links)
Philosophiae Doctor - PhD / Options are a special type of derivative securities because their values are derived from
the value of some underlying security. Most options can be grouped into either of
the two categories: European options which can be exercised only on the expiration
date, and American options which can be exercised on or before the expiration date.
American options are much harder to deal with than European ones. The reason being
the optimal exercise policy of these options which led to free boundary problems. Ever
since the seminal work of Black and Scholes [J. Pol. Bean. 81(3) (1973), 637-659],
the differential equation approach in pricing options has attracted many researchers.
Recently, numerical singular perturbation techniques have been used extensively for
solving many differential equation models of sciences and engineering. In this thesis,
we explore some of those methods which are based on spline approximations to solve
the option pricing problems. We show a systematic construction and analysis of these
methods to solve some European option problems and then extend the approach to
solve problems of pricing American options as well as some exotic options. Proposed
methods are analyzed for stability and convergence. Thorough numerical results are
presented and compared with those seen in the literature.
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[pt] MÉTODOS SEMIANALÍTICOS PARA A ANÁLISE DA PROPAGAÇÃO ELETROMAGNÉTICA EM GUIAS DE ONDA ANISOTRÓPICOS E NÃO HOMOGÊNEOS COM SEÇÃO TRANSVERSAL ARBITRÁRIA USANDO HARMÔNICOS CILÍNDRICOS / [en] SEMI-ANALYTICAL METHODS FOR THE ELECTROMAGNETIC PROPAGATION ANALYSIS OF INHOMOGENEOUS ANISOTROPIC WAVEGUIDES OF ARBITRARY CROSS-SECTION BY USING CYLINDRICAL HARMONICSJOHNES RICARDO GONCALVES 28 October 2022 (has links)
[pt] Esta tese apresenta um estudo sobre métodos semianalíticos para
modelagem de guias de ondas com contornos complexos. Os campos
eletromagnéticos dentro de meios não homogêneos e anisotrópicos são
resolvidos por meio de harmônicos cilíndricos como base para outras
abordagens numéricas, como o método de perturbação regular (RPM), o
método de perturbação de material em cavidade (CMPM) e o método de
casamento de pontos (PMM). As novas soluções semianalíticas que exploramos
aqui podem ser empregadas para a análise de comunicação sem fio ao longo
de túneis, bem como para a modelagem de sensores realistas de perfilagem
durante a perfuração em problemas geofísicos de baixa frequência. Estudamos
o potencial do RPM ao combiná-lo com os princípios da transformação óptica
(TO) para analisar um guia de onda coaxial excêntrico preenchido com
materiais anisotrópicos. Além disso, estendemos o CMPM clássico proposto
por Harrington para lidar com meios anisotrópicos para resolver os números
de onda de corte dos campos modais no mesmo guia de onda de maneira
aproximada, mas numericamente eficiente. Outra solução de perturbação é
proposta combinando as correções de baixa ordem do RPM no CMPM para
fornecer correções de alta ordem para os números de onda de corte dos
modos suportados pelo guia. Uma formulação matemática de um método
semianalítico baseado em PMM para resolver guias de onda preenchidos com
meios anisotrópicos e com camadas arbitrárias também é apresentada. Uma
versão melhorada deste método é introduzida para modelar estruturas guiadas
cilíndricas de múltiplas camadas não circulares. Essas soluções baseadas em
casamento de pontos representam boas alternativas para abordagens de força
bruta, como métodos de elementos finitos e de diferenças finitas. / [en] This thesis presents a study on semi-analytic methods for modeling
waveguides with complex-shaped boundaries. The electromagnetic fields inside
inhomogeneous and anisotropic media are solved via cylindrical harmonics as
a basis for other numerical approaches, including the regular perturbation
method (RPM), the cavity-material perturbation method (CMPM), and the
point-matching method (PMM). The novel semi-analytic solutions we have
explored here can be employed for the analysis of wireless communication along
tunnels and boreholes as well as for the modeling of realistic logging-whiledrilling
(LWD) sensors and their environments at low-frequency geophysical
problems. We studied the potential of the RPM when combining it with
the transformation optics (TO) principles to analyze an eccentric coaxial
waveguide filled with anisotropic materials. Furthermore, we have extended
the classical CMPM proposed by Harrington to handling anisotropic media
for solving the cutoff wavenumbers of the modal fields in the same eccentric
coaxial waveguide in an approximated but numerically efficient manner.
Another perturbation solution is proposed here and combines the low-order
corrections from RPM into the CMPM for providing high-order corrections to
the cutoff wavenumbers of the modes supported in this guide. A mathematical
formulation of a semi-analytic point-matching method for solving more
complex anisotropic-filled waveguides with an arbitrary number of layers is also
presented. An improved version of this method is introduced for modeling noncircular
multi-layered cylindrical guided structures. Such point-matching-based
solutions represent good alternatives to brute-force approaches such as finiteelement
and finite-difference methods and motivate further investigations. We
present a series of validation results showing the accuracy, efficiency, and
potential limitations of the explored methods.
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Nonlinear Effects in Contactless Ultrasound Energy Transfer SystemsMeesala, Vamsi Chandra 05 January 2021 (has links)
Ultrasound acoustic energy transfer (UAET) is an emerging contactless technology that offers the capability to safely and efficiently power sensors and devices while eliminating the need to replace batteries, which is of interest in many applications. It has been proposed to recharge and communicate with implanted medical devices, thereby eliminating the need for invasive and expensive surgery and also to charge sensors inside enclosed metal containers typically found in automobiles, nuclear power plants, space stations, and aircraft engines. In UAET, energy is transferred through the reception of acoustic waves by a piezoelectric receiver that converts the energy of acoustic waves to electrical voltage. It has been shown that UAET outperforms the conventional CET technologies that use electromagnetic waves to transfer energy, including inductive coupling and capacitative coupling. To date, the majority of research on UAET systems has been limited to modeling and proof-of-concept experiments, mostly in the linear regime, i.e., under small levels of acoustic pressure that result in small amplitude longitudinal vibrations and linearized piezoelectricity. Moreover, existing models are based on the "piston-like" deformation assumption of the transmitter and receiver, which is only accurate for thin disks and does not accurately account for radiation effects. The linear models neglect nonlinear effects associated with the nonlinear acoustic wave propagation as well as the receiver's electroelastic nonlinearities on the energy transfer characteristics, which become significant at high source strengths.
In this dissertation, we present experimentally-validated analytical and numerical multiphysics modeling approaches aimed at filling a knowledge gap in terms of considering resonant acoustic-piezoelectric structure interactions and nonlinear effects associated with high excitation levels in UAET systems. In particular, we develop a reduced-order model that can accurately account for the radiation effects and validate it by performing experiments on four piezoelectric disks with different aspect ratios. Next, we study the role of individual sources of nonlinearity on the output power characteristics. First, we consider the effects of electroelastic nonlinearities. We show that these nonlinearities can shift the optimum load resistance when the acoustic medium is fluid. Next, we consider the nonlinear wave propagation and note that the shock formation is associated with the dissipation of energy, and as such, shock formation distance is an essential design parameter for high-intensity UAET systems. We then present an analytical approach capable of predicting the shock formation distance and validate it by comparing its prediction with finite element simulations and experimental results published in the literature. Finally, we experimentally investigate the effects of both the nonlinearity sources on the output power characteristics of the UAET system by considering a high intensity focused ultrasound source and a piezoelectric disk receiver. We determine that the system's efficiency decreases, and the maximum voltage output position drifts towards the source as the source strength is increased. / Doctor of Philosophy / Advancements in electronics that underpinned the development of low power sensors and devices have transformed many fields. For instance, it has led to the innovation of implanted medical devices (IMDs) such as pacemakers and neurostimulators that perform life-saving functions. They also find applications in condition monitoring and wireless sensing in nuclear power plants, space stations, automobiles and aircraft engines, where the sensors are enclosed within sealed metal containers, vacuum/pressure vessels or located in a position isolated from the operator by metal walls. In all these applications, it is desired to communicate with and recharge the sensors wirelessly. Such a mechanism can eliminate the need for invasive and expensive surgeries to replace batteries of IMDs and preserve the structural integrity of metal containers by eliminating the need for feed through wires. It has been shown that ultrasound acoustic energy transfer (UAET) outperforms conventional wireless power transfer techniques. However, existing models are based on several assumptions that limit their potential and do not account for effects that become dominant when a higher output power is desired. In this dissertation, we present experimentally validated numerical and theoretical investigations to fill those knowledge gaps. We also provide crucial design recommendations based on our findings for the efficient implementation of UAET technology.
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Aplicação do polinômio de Hermite-Caos para a determinação da carga de instabilidade paramétrica de cascas cilíndricas com incerteza nos parâmetros físicos e geométricos / Application of Chaos-Hermite polynomial for determining the load of parametric instability of cylindrical shells witn uncertainty in physical and geometrical parametersBrazão, A. F. 04 April 2014 (has links)
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Previous issue date: 2014-04-04 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPES / The present study aims to investigate the influence of uncertainties in physical and geometric parameters to obtain the load parametric instability of cylindrical shell, using the Galerkin method with the stochastic polynomial Hermite-Caos. The nonlinear equations of motion of the cylindrical shell are deduced from their functional power considering the strain field proposed by Donnell´s nonlinear shallow shell theory. The uncertainties are considered as random parameters with probability density function known in the partial differential equation of motion of the cylindrical shell, which it becomes a stochastic partial differential equation due to the presence of randomness. First, the discretization of the stochastic problem is performed using the stochastic Galerkin method together with polynomial Hermite-Chaos, to transform the stochastic partial differential equation into a set of equivalent deterministic partial differential equations, which take into account the randomness of the system. Then, the discretization of the lateral field displacement is made by a perturbation procedure, indicating the nonlinear vibration modes which couple to the linear vibration mode. The set of partial differential equations is transformed into a deterministic system of equations deterministic ordinary second order in time. Uncertainty is considered in one of its parameters: the Young modulus, thickness and amplitude of initial geometric imperfection. Then we analyze the influence of randomness in two parameters simultaneously: the thickness and the Young modulus. Once obtained the system of ordinary differential equations deterministic containing the randomness of the parameters, the integration over discrete time system is made from the Runge- Kutta fourth order to obtain results as the time response, bifurcation diagrams and
boundaries of instability which are compared with deterministic analysis, indicating that
polynomial Hermite-Chaos is a good numerical tool for predicting the load parametric
instability without the need to perform a process of sampling. / O presente trabalho tem como objetivo investigar a influência de incertezas nos parâmetros
físicos e geométricos para a determinação da carga de instabilidade paramétrica da casca
cilíndrica, utilizando o método de Galerkin Estocástico juntamente com o polinômio de
Hermite-Caos. As equações não-lineares de movimento da casca cilíndrica são deduzidas a
partir de seus funcionais de energia considerando o campo de deformações proposto pela
teoria não linear de Donnell para cascas esbeltas. As incertezas são consideradas como
parâmetros aleatórios com função de densidade de probabilidade conhecida na equação
diferencial parcial de movimento da casca cilíndrica, que passa a ser uma equação diferencial
parcial estocástica devido à presença da aleatoriedade. Primeiramente, faz-se a discretização
do problema estocástico utilizando o método de Galerkin Estocástico juntamente com o
polinômio de Hermite-Caos, para transformar a equação diferencial parcial estocástica em um
conjunto de equações diferenciais parciais determinísticas equivalentes, que levem em
consideração a aleatoriedade do sistema. Em seguida, apresenta-se a discretização do campo
de deslocamentos laterais através do Método da Perturbação, indicando os modos não-lineares
de vibração que se acoplam ao modo linear de vibração, para que o conjunto de equações
diferenciais parciais determinísticas seja transformado em um sistema de equações ordinárias
determinísticas de segunda ordem no tempo. A incerteza é considerada inicialmente em
apenas um de seus parâmetros: no módulo de elasticidade, na espessura e na amplitude da
imperfeição geométrica inicial. Em seguida, analisa-se a influência de aleatoriedades em dois
parâmetros simultaneamente, sendo eles: a espessura e o módulo de elasticidade. Uma vez
obtido o sistema de equações diferenciais ordinárias determinísticas que contêm as aleatoriedades dos parâmetros, a integração ao longo do tempo do sistema discretizado é feita a partir do método de Runge-Kutta de quarta ordem, obtendo-se resultados como resposta no tempo, diagramas de bifurcação e fronteiras de instabilidade, que são comparados com análises determinísticas, indicando que o polinômio de Hermite-Caos é uma boa ferramenta numérica para prever a carga de instabilidade paramétrica sem a necessidade de se realizar um processo de amostragens.
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Mathematical modelling of primary alkaline batteriesJohansen, Jonathan Frederick January 2007 (has links)
Three mathematical models, two of primary alkaline battery cathode discharge, and one of primary alkaline battery discharge, are developed, presented, solved and investigated in this thesis. The primary aim of this work is to improve our understanding of the complex, interrelated and nonlinear processes that occur within primary alkaline batteries during discharge. We use perturbation techniques and Laplace transforms to analyse and simplify an existing model of primary alkaline battery cathode under galvanostatic discharge. The process highlights key phenomena, and removes those phenomena that have very little effect on discharge from the model. We find that electrolyte variation within Electrolytic Manganese Dioxide (EMD) particles is negligible, but proton diffusion within EMD crystals is important. The simplification process results in a significant reduction in the number of model equations, and greatly decreases the computational overhead of the numerical simulation software. In addition, the model results based on this simplified framework compare well with available experimental data. The second model of the primary alkaline battery cathode discharge simulates step potential electrochemical spectroscopy discharges, and is used to improve our understanding of the multi-reaction nature of the reduction of EMD. We find that a single-reaction framework is able to simulate multi-reaction behaviour through the use of a nonlinear ion-ion interaction term. The third model simulates the full primary alkaline battery system, and accounts for the precipitation of zinc oxide within the separator (and other regions), and subsequent internal short circuit through this phase. It was found that an internal short circuit is created at the beginning of discharge, and this self-discharge may be exacerbated by discharging the cell intermittently. We find that using a thicker separator paper is a very effective way of minimising self-discharge behaviour. The equations describing the three models are solved numerically in MATLABR, using three pieces of numerical simulation software. They provide a flexible and powerful set of primary alkaline battery discharge prediction tools, that leverage the simplified model framework, allowing them to be easily run on a desktop PC.
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