[pt] O presente trabalho tem por objetivo desenvolver uma formulação e certas estratégias que permitam a análise da perda de estabilidade de colunas esbeltas submetidas a carregamento axial periódico, fenômeno este conhecido como ressonância paramétrica. Uma excitação é dita paramétrica quando aparece nas equações de movimento do sistema na forma de coeficientes variáveis com o tempo - geralmente periódicos - e não como uma não homogeneidade. A coluna é descrita pela formulação clássica de Navier. O presente trabalho trata a coluna considerando-se um e três graus de liberdade com ou sem não-linearidades. As equações de movimento são obtidas utilizando-se o princípio de Hamilton através do método de Ritz. A equação linear (equação de Mathieu) e a equação de Duffing com pequeno amortecimento, são resolvidas de forma aproximada pelo método das múltiplas escalas, revelando a possibilidade de instabilização da posição de equilíbrio em diversas regiões do espaço definido pelos parâmetros de controle. A mesma conclusão é mostrada utilizando-se procedimentos computacionais para a resolução dos sistemas de equações lineares e nãolineares, com ou sem imperfeição geométrica inicial, podendo-se obter assim, a resposta do sistema, planos fase, seções de Poincaré e diagramas de bifurcação. Mostra-se a partir dos resultados numéricos, que a coluna submetida a cargas axiais harmônicas, pode tanto apresentar soluções com o mesmo período da força excitadora, quanto oscilações subarmônicas e superarmônicas de diversas ordens, além de movimentos caóticos. / [en] The main aim of the present work is to develop a formulation and some strategies for the instability analysis of slender columns under an axial harmonic force this phenomenon is known as parametric ressonance. An excitation is said to be parametric if it appears as timedependent - often periodic - coefficients in the equations governing the motion of the system,and not as an inhomogeneous term.The column is described by Navier classical formulation. The present work consider the column with one or three degrees of freedom with or without nonlinearities. The equations governing the motion are obtained by the Ritz method.The linear equation (Mathieu equation) and the Duffing equation with small damping are solved in an approximate way using multiple scales techniques, revealing the possibility of destabilizing the static equilibrium position in certain regions of the control space. A similar conclusion is obtained by employing numerical methods for the solution of linear and nonlinear equation systems with or without initial geometrical imperfections.This enables one to obtain time response, phase space, projections Poincaré sections and bifurcation diagrams. These numerical results show that the column with nonlinearities and loaded by a periodic longitudinal force can present various solutions with the same period as the forcing and subharmonic e superharmonic oscillations, as well as chaotic motions.

[Truncated abstract] Advanced laser interferometer gravitational wave detectors require an extremely high optical power in order to improve the coupling between the gravitational wave signal and the optical field. This high power requirement leads to new physical phenomena arising from nonlinear interactions associated with radiation pressure. In particular, detectors with multi-kilometer-long arm cavities containing high density optical fields suffer the possibility of 3-mode opto-acoustic interactions. This involves the process where ultrasonic vibrations of the test mass cause the steady state optical modes to scatter. These 3-mode interactions induce transverse optical modes in the arm cavities, which then can provide positive feedback to the acoustic vibrations in the test masses. This may result in the exponential growth of many acoustic mode amplitudes, known as Parametric Instability (PI). This thesis describes research on 3-mode opto-acoustic interactions in advanced interferometric gravitational wave detectors through numerical investigations of these interactions for various interferometer configurations. Detailed analysis reveals the properties of opto-acoustic interactions, and their dependence on the interferometer configuration. This thesis is designed to provide a pathway towards a tool for the analysis of the parametric instabilities in the next generation interferometers. Possible techniques which could be helpful in the design of control schemes to mitigate this undesirable phenomenon are also discussed. The first predictions of parametric instability considered only single interactions involving one transverse mode and one acoustic mode in a simple optical cavity. ... In Chapter 6, I was able to make use of a new analytical model due to Strigin et al., which describes parametric instability in dual recycling interferometers. To make the solution tractable, it was necessary to consider two extreme cases. In the worst case, recycling cavities are assumed to be resonant for all transverse modes, whereas in the best cases, both recycling cavities are anti-resonant for the transverse modes. Results show that, for the worst case, parametric gain values as high as ~1000 can be expected, while in the best case the gain can be as low as ~ 3. The gain is shown to be very sensitive to the precise conditions of the interferometer, emphasising the importance of understanding the behaviour of the detectors when the cavity locking deviates from ideal conditions. Chapter 7 of this thesis contains work on the observation of 3-mode interactions in an optical cavity at Gingin, which confirms the analysis presented here, and also a paper which shows how the problem of 3-mode interactions can be harnessed to create new devices called opto-acoustic parametric amplifiers. In the conclusions in Chapter 8, I discuss the next important steps in understanding parametric interactions in real interferometers – including the need for more automated codes relevant to the design requirements for recycling cavities. In particular, it is pointed out how the modal structure of power and signal recycling cavities must be understood in detail, including the Gouy phase for each transverse mode, to be able to obtain precise predictions of parametric gain. This thesis is organised as a series of papers which are published or have been submitted for publication. Such writing style fills the condition for Ph.D. thesis at the University of Western Australia.

[Truncated abstract] The research described in this thesis investigated optical spring interactions and instabilities in a macroscopic opto-mechanical resonator. The thesis describes an experiment designed to model an optical spring `tranquiliser’ cavity which has been proposed to suppress the predicted parametric instabilities in the next generation of interferometric gravitational wave detectors. In a series of experiments, the optical spring effect was observed in macroscopic optical cavities through measured changes in mechanical stiffness, and measured changes in mechanical loss. The optical spring effect was further characterised through investigation of its dependent parameters. Two pairs of identical, low optical loss mirrors were bonded to a mechanical structure using a novel low mechanical loss technique, forming an opto-mechanical composite resonator. The technique uses the naturally occurring resin Yacca gum as a bonding agent. This resulted in the formation of two optical cavities with a length of l = 0.100±0.001m, only one of which was used in experiments. Using finite element modelling, the resonator?s two lowest modes, with frequencies of fm1 = 722.8Hz and fm2 = 747.9Hz, and an effective mass 0.0323±0.0001kg, were found to be subject to the optical spring effect. ... The instabilities are expected to have a parametric gain factor of up to 100 in the frequency range of 15-120kHz. Therefore, if optical spring damping can be made large enough to reduce the Q-factor of the Advanced LIGO test-masses by a factor of 100, all parametric instabilities should be eliminated. For a simple servo loop and an optical cavity with the practically achievable finesse of F = 30,000, a tranquiliser cavity length of 1.3cm was found to produce optimum enhanced damping. This configuration only requires 1.47W of input power, resulting in an intra-cavity power of 5.72kW. The cavity mirrors were assumed to have optical coatings with a damage threshold of 1MW/cm2, which limited the spot size to a minimum area of 0.572mm2, or a radial beam waist of w = 0.427mm. This nearly flat-flat cavity has a stability g-factor of 0.9997. Even given these technical challenges, suppression of the parametric instabilities predicted to occur in the next generation of interferometric detectors is possible to achieve practically using enhanced optical spring damping. A possible design for such a tranquiliser cavity is also suggested.

[pt] Com base nas equações de Donnell para cascas abatidas, estudam-se as vibrações não-lineares e a instabilidade dinâmica de cascas cilíndricas carregadas axialmente, considerando o efeito simultâneo de cargas estáticas e harmônicas. Para isto, o problema é primeiro reduzido a um sistema finito de graus de liberdade usando o método de Galerkin. O sistema de equações diferenciais de movimento não-lineares é resolvido através do método de Runge-Kutta. Na análise do fenômeno de acoplamento modal foi usado um modelo com dois graus de liberdade, que reflete de maneira consistente o comportamento pós-crítico inicial da casca. Os resultados obtidos com esse modelo simplificado foram comparados com diversas modelagens encontradas na literatura, permitindo assim aferir o modelo utilizado. Para o estudo da interação modal, escolheram-se três modelos distintos com freqüências e cargas críticas próximas ou semelhantes. Para estudar o comportamento não- linear da casca, diversas estratégias numéricas foram usadas para se obter os mapas de Poincaré, expoentes de Lyapunov, pontos fixos estáveis e instáveis, diagramas de bifurcação e bacias de atração. Particular atenção foi dada a dois fenômenos de instabilidade dinâmica que podem ocorrer sob estas condições de carregamento, a saber: excitação paramétrica dos modos de flexão e escape da bacia de atração pré-flambagem. Os cálculos foram realizados nas regiões principal e secundária de instabilidade paramétrica associadas com a menor freqüência natural da casca. Mostra-se de forma detalhada a determinação dos limites de instabilidade no espaço de controle e a identificação dos mecanismos de escape relacionados com estes limites. Os resultados mostram a importância do acoplamento e da interação modal na solução pós-crítica e no comportamento dinâmico não-linear de cascas cilíndricas. / [en] Based on Donnell shallow shell equations, the nonlinear vibrations and dynamic instability of axially loaded circular cylindrical shells under both static and harmonic forces are analyzed. For this, the problem is first reduced to that of a finite degree-of-freedom system by the Galerkin method. The resulting set of coupled non-linear ordinary differential equations of motion is, in turn, solved by the Runge-Kutta method. For the study of modal coupling, a 2 DOF model was used that describes consistently the initial post-buckling behavior of the shell. This model was compared favorably with others found in literature. For the analysis of modal interaction three different models were used considering shells with close or equal frequencies and critical loads. To study the non-linear behavior of the shell several numerical strategies were used to obtain Poincaré maps, Lyapunov exponents, stable and unstable fixed points, bifurcation diagrams and basins of attraction. Particular attention is paid to two dynamic instability phenomena that may arise under these loading conditions:parametric excitation of flexural modes and escape from the pre-buckling potential well.Calculations are carried out for the principal and secondary instability regions associated with the lowest natural frequency of the shell. Special attention is given to the determination of the instability boundaries in control space and the identification of the bifurcational events connected with these boundaries. The results also clarify the importance of modal coupling and modal interaction to the post-buckling solution and non-linear dynamic behavior of cylindrical shells.

京都大学 / 0048 / 新制・課程博士 / 博士(理学) / 甲第20173号 / 理博第4258号 / 新制||理||1612(附属図書館) / 京都大学大学院理学研究科物理学・宇宙物理学専攻 / (主査)教授 大西 明, 教授 國廣 悌二, 教授 川合 光 / 学位規則第4条第1項該当 / Doctor of Science / Kyoto University / DGAM

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Submitted by Biblioteca do Instituto de Física (bif@ndc.uff.br) on 2017-05-26T19:15:31Z No. of bitstreams: 1 tese-mestrado.pdf: 17362957 bytes, checksum: 024ecd9a310935efc222a31e2a31dca0 (MD5) / Made available in DSpace on 2017-05-26T19:15:31Z (GMT). No. of bitstreams: 1 tese-mestrado.pdf: 17362957 bytes, checksum: 024ecd9a310935efc222a31e2a31dca0 (MD5) / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / Nesta Dissertação são estudadas as condições em que um pulso eletromagnético (semente) é amplificado e comprimido através da interação não linear de três ondas de um plasma. Para isto, foi empregada uma abordagem analítica em que os três modos, fonte-plasma-semente, variam lentamente no tempo e no espaço. Durante a interação dos três modos, a amplitude da fonte é completamente depletada, enquanto que a onda de plasma e o pulso semente se amplificam. Durante este processo, o pulso semente se dividirá num pulso principal, o qual diminui sua largura proporcionalmente com o tempo de interação, e em vários outros pulsos secundários e de largura constante. Observa-se que a saturação do pulso semente ocorre antes que as instabilidades dos tipos lamentação, quebra de onda e espalhamento Raman para frente ocorram. Fazendo uso do código computacional XOOPIC e de acordo com as condições iniciais impostas ao sistema, obtem-se a potência final do pulso semente e a e ciência do processo. / The conditions under which an electromagnetic (seed) pulse is amplified and compressed by nonlinear three wave interaction in a plasma are studied. An analytical approach is used considering the slowly varying, in space and time, envelope amplitudes of the three wave modos (pump-plasma-seed). It is noted that the amplitude of the pump wave is completely depleted during the interaction while the plasma wave and the seed pulse are amplified. During the interaction, the seed pulse is divided into a main pulse, which decreases its width during the interaction, and in many other secondary pulses with constant width. The process of the saturation of the ampli ed seed pulse occurs before the filamentation, plasma wavebreaking and Raman forward scattering instabilities take place. Using the particle simulation code XOOPIC and according to the prescribed initial conditions of the system, the nal power of the seed pulse and the e ficiency of the process are obtained.

Este trabalho contextualiza o problema da análise estrutural bidimensional de risers verticais ou lançados em catenária livre, fazendo uma breve descrição das etapas para a modelagem dessas estruturas. O problema que este trabalho se propõe a resolver é o da análise dinâmica não linear destas estruturas, no domínio do tempo, apresentando uma formulação que seja capaz de representar de forma adequada as etapas de modelagem destes sistemas. A modelagem foi dividida em duas etapas. A primeira delas é referente à fase de lançamento do riser, com o objetivo de determinar a configuração deformada de equilíbrio, assim como os esforços solicitantes internos decorrentes dessa configuração deformada. Ressalta-se que para os casos de risers em catenária livre, considera-se também o contato unilateral da estrutura com o solo marinho. A segunda etapa é a modelagem da fase de operação da estrutura, por meio de um modelo dinâmico bidimensional. Em ambas as etapas, a formulação apresentada considera os efeitos de acoplamento fluidoestrutura. No caso dos risers em catenária, considera-se também o efeito da interação solo-estrutura. Todo o desenvolvimento das equações foi realizado utilizando-se o método dos elementos finitos MEF. A formulação desenvolvida contempla dois elementos finitos, um de treliça e outro de barra, utilizando-se um sistema de coordenadas corrotacionais. A utilização deste sistema de coordenadas possibilitou a adoção de teorias estruturais de pequenas deformações, para a análise de problemas que envolvem grandes deslocamentos e rotações finitas. Além da formulação do problema, também foi apresentado o projeto da ferramenta computacional RiserSys, que é específica para o estudo de risers nas configurações reta (vertical) e em catenária livre. Muito embora não seja o objetivo deste trabalho a implementação computacional do código nesta ferramenta e o estudo de casos referentes a fenômenos de dinâmica não linear nessas estruturas, nas considerações finais, propõe-se, como trabalhos futuros, a utilização desta formulação para o estudo da compressão dinâmica e a instabilidade paramétrica. / This work addresses the problem of the bidimensional analysis of risers, either straight or free hanging, giving a brief description of the modeling steps of these structures. The problem that it is meant to be solved is the nonlinear dynamic analysis in the time domain of these structures, presenting a formulation capable of correctly modeling the steps of the analysis of the system. The modeling was divided into two steps. The first one is referred to the riser installation, in which the objective was to find the deformed configuration of equilibrium and its internal forces. For the free hanging risers, the unilateral contact with the seabed is taken into account. The second step of the modeling is the phase of operation, using a bidimensional dynamic model. Both steps of the modeling consider the fluid-structure coupling phenomenon. For the free hanging risers, the soil-structure interaction is taken into account. All the analyses were performed using the finite element method FEM. Two finite elements were formulated 2D truss and 2D Bernoulli Euler beam both using a co-rotational coordinate system. The co-rotational coordinate system allowed the use of small-strain theory to develop these finite elements to study problems that involve large displacements. Besides the problem formulation, the project of a computational code, named RiserSys, was described. RiserSys is a dedicated computational tool to analyze straight and free hanging risers. Although the objective of this work is not the computational implementation and the analysis of cases studies, in the concluding chapter it is proposed, as future work, the use of the formulation presented herewith to analyze non-linear dynamic phenomena that may take place in these systems, such as dynamic compression and parametric instability.

Electromagnetic waves can be used to transmit information over long distances and are therefore often employed for communication purposes. The electromagnetic waves are reflected off material objects on their paths and interact with the medium through which they propagate. For instance, the plasma in the ionosphere can refract and even reflect radio waves propagating through it. By increasing the power of radio waves injected into the ionosphere, the waves start to modify the plasma, resulting in the generation of a wide range of nonlinear processes, including turbulence, in particular near the reflection region. By systematically varying the injected radio waves in terms of frequency, power, polarisation, duty cycle, inclination, etc. the ionosphere can be used as an outdoor laboratory for investigating fundamental properties of the near-Earth space environment as well as of plasma turbulence. In such ionospheric modification experiments, it has been discovered that the irradiation of the ionosphere by powerful radio waves leads to the formation of plasma density structures and to the emission of secondary electromagnetic radiation, a phenomenon known as stimulated electromagnetic emission. These processes are highly repeatable and have enabled systematic investigations of the nonlinear properties of the ionospheric plasma. In this thesis we investigate features of the plasma density structures and the secondary electromagnetic radiation. In a theoretical study we analyse a certain aspect of the formation of the plasma structures. The transient dynamics of the secondary radiation is investigated experimentally in a series of papers, focussing on the initial stage as well as on the decay. In one of the papers we use the transient dynamics of the secondary radiation to reveal the intimate relation between certain features of the radiation and structures of certain scales. Further, we present measurements of unprecedentedly strong secondary radiation, attributed to stimulated Brillouin scattering, and report measurements of the secondary radiation using a novel technique imposed on the transmitted radio waves.