Orientador: Bento Rodrigues de Pontes Junior / Co-orientador: Marcos Silveira / Banca: Marcio Antonio Bazani / Banca: Paulo José Paupitz Gonçalves / Resumo: Este trabalho explora os diferentes tipos de comportamento dinâmicos, encontrados em sistemas eletromecânicos linear e não-linear análogos, sendo o sistema eletromecânico não-linear constituído de rigidez tipo Duffing. A modelagem matemática dos sistemas físicos hipotéticos é realizada através de técnicas Langrangeanas, inclusive para a modelagem que aborda componentes eletromagnéticos de um circuito RLC. O transdutor utilizado no acoplamento dos subsistemas é o de bobina móvel e magnetismo permanente e tem suas equações conhecidas na literatura. Os modelos são baseados em absorvedores utilizados no automobilismo, no entanto são abordados de forma simplificada, comparando-se com o modelo completo de uma suspensão de automóvel. No trabalho é investigada a influência dos parâmetros do circuito RLC, que podem ser responsáveis pelo aumento do amortecimento mecânico. É feita a correlação do amortecimento mecânico com os parâmetros de resistência e capacitância elétrica para o modelo linear. É realizada também a análise dos autovalores do modelo linear e lugar natural das raízes. Para o modelo não-linear é realizada a análise do comportamento dinâmico, levando-se em consideração a variação da capacitância para quatro valores de frequência da força externa ao sistema. Essa análise mostra a diversidade de comportamento dinâmicos encontrados para esse modelo. As variedades de comportamento dinâmicos resultantes do modelo não-linear variam entre dinâmicas caóticas, periódicas, quasi-periódicas e multiperiódica. Indica a possibilidade de utilização do parâmetro da capacitância como parâmetro de controle do sistema e mostra que a resistência elétrica dissipa a energia oirunda do domínio mecânico, fato esse que abre a discussão para as possibilidades de geração de energia / Abstract: This work investigates the different types of dynamic behaviour, found in linear and nonlinear electromechanical system, which are analogue, being the nonlinear electromechanical system constituted of rigidity type Duffing. The mathematical modelling of the hypothetical physical system is realized with Langrangian techniques, including for the modeling of the system is a moving coil and permanent magnet tranducer, which it have their equations deducted in other studies. The models are based in absorbers utilized in automobiles, however in this investigation it is discussed in a simplified way, if it is compared with a complete model of and automobile supension. This work investigates the influence of the RLC circuit parameters, which it may be responsible by the increasing of the mechanical damping. It is realized the correlation of the mechanical damping with resistance and capacitance, for the linear model. It is realized the anlysis of the eigenvalues it is found de root locus of the linear model. For the nonlinear model it is realized the analysis of the dynamic behaviour, considering the variation of the capacitance, for each one of the four values of frequency of the external force. This analysis shows the diversity of dynamic behaviours found for the nonlinear model. The variations of dynamic behaviours resulted of the nonlinear model varies around some types of dynamics, which can be, chaotic, periodic, quasi periodic, quasi periodic and multi periodic. That's indicate the possibility of utilization of the capacitance as control parameter of the system and shows the dissipation of energy by the resistance, this energy is from the mechanical domain, this fact open the discussion for the energy generation possibilities / Mestre

Made available in DSpace on 2015-03-03T11:52:42Z (GMT). No. of bitstreams: 0 Previous issue date: 2014-05-06Bitstream added on 2015-03-03T12:07:10Z : No. of bitstreams: 1 000800685.pdf: 1492848 bytes, checksum: 66d029b83fe3516cc9b217657df61d80 (MD5) / Este trabalho explora os diferentes tipos de comportamento dinâmicos, encontrados em sistemas eletromecânicos linear e não-linear análogos, sendo o sistema eletromecânico não-linear constituído de rigidez tipo Duffing. A modelagem matemática dos sistemas físicos hipotéticos é realizada através de técnicas Langrangeanas, inclusive para a modelagem que aborda componentes eletromagnéticos de um circuito RLC. O transdutor utilizado no acoplamento dos subsistemas é o de bobina móvel e magnetismo permanente e tem suas equações conhecidas na literatura. Os modelos são baseados em absorvedores utilizados no automobilismo, no entanto são abordados de forma simplificada, comparando-se com o modelo completo de uma suspensão de automóvel. No trabalho é investigada a influência dos parâmetros do circuito RLC, que podem ser responsáveis pelo aumento do amortecimento mecânico. É feita a correlação do amortecimento mecânico com os parâmetros de resistência e capacitância elétrica para o modelo linear. É realizada também a análise dos autovalores do modelo linear e lugar natural das raízes. Para o modelo não-linear é realizada a análise do comportamento dinâmico, levando-se em consideração a variação da capacitância para quatro valores de frequência da força externa ao sistema. Essa análise mostra a diversidade de comportamento dinâmicos encontrados para esse modelo. As variedades de comportamento dinâmicos resultantes do modelo não-linear variam entre dinâmicas caóticas, periódicas, quasi-periódicas e multiperiódica. Indica a possibilidade de utilização do parâmetro da capacitância como parâmetro de controle do sistema e mostra que a resistência elétrica dissipa a energia oirunda do domínio mecânico, fato esse que abre a discussão para as possibilidades de geração de energia / This work investigates the different types of dynamic behaviour, found in linear and nonlinear electromechanical system, which are analogue, being the nonlinear electromechanical system constituted of rigidity type Duffing. The mathematical modelling of the hypothetical physical system is realized with Langrangian techniques, including for the modeling of the system is a moving coil and permanent magnet tranducer, which it have their equations deducted in other studies. The models are based in absorbers utilized in automobiles, however in this investigation it is discussed in a simplified way, if it is compared with a complete model of and automobile supension. This work investigates the influence of the RLC circuit parameters, which it may be responsible by the increasing of the mechanical damping. It is realized the correlation of the mechanical damping with resistance and capacitance, for the linear model. It is realized the anlysis of the eigenvalues it is found de root locus of the linear model. For the nonlinear model it is realized the analysis of the dynamic behaviour, considering the variation of the capacitance, for each one of the four values of frequency of the external force. This analysis shows the diversity of dynamic behaviours found for the nonlinear model. The variations of dynamic behaviours resulted of the nonlinear model varies around some types of dynamics, which can be, chaotic, periodic, quasi periodic, quasi periodic and multi periodic. That's indicate the possibility of utilization of the capacitance as control parameter of the system and shows the dissipation of energy by the resistance, this energy is from the mechanical domain, this fact open the discussion for the energy generation possibilities

A study is presented of the instability mechanisms of a damped axisymmetric circular disk of uniform thickness rotating about its axis with constant angular velocity and subjected to various transverse space-fixed loading systems. The natural frequencies of spinning floppy disks are obtained for various nodal diameters and nodal circles with a numerical and an approximate method. Exploiting the fact that in most physical applications the thickness of the disk is small compared with its outer radius, we use their ratio to define a small parameter. Because the nonlinearities appearing in the governing partial-differential equations are cubic, we use the Galerkin procedure to reduce the problem into a finite number of coupled weakly nonlinear second-order equations. The coefficients of the nonlinear terms in the reduced equations are calculated for a wide range of the lowest modes and for different rotational speeds. We have studied the primary resonance of a pair of orthogonal modes under a space-fixed constant loading, the principal parametric resonance of a pair of orthogonal modes when the disk is subject to a massive loading system, and the combination parametric resonance of two pairs of orthogonal modes when the excitation is a linear spring. Considering the case of a spring moving periodically along the radius of the disk, we show how its frequency can be coupled to the rotational speed of the disk and lead to a principal parametric resonance. In each of these cases, we have used the method of multiple scales to determine the equations governing the modulation of the amplitudes and phases of the interacting modes. The equilibrium solutions of the modulation equations are determined and their stability is studied. / Master of Science

Submitted by Maria Medeiros (maria.dilva1@ufcg.edu.br) on 2018-08-29T14:12:32Z No. of bitstreams: 1 DESIANE MAIARA GOMES DOS SANTOS - DISSERTAÇÃO (PPGF) 2015.pdf: 6011160 bytes, checksum: a5021549766593cfe2eb8fe5314ea39b (MD5) / Made available in DSpace on 2018-08-29T14:12:32Z (GMT). No. of bitstreams: 1 DESIANE MAIARA GOMES DOS SANTOS - DISSERTAÇÃO (PPGF) 2015.pdf: 6011160 bytes, checksum: a5021549766593cfe2eb8fe5314ea39b (MD5) Previous issue date: 2015-04-10 / Capes / Nesta dissertação, analisamos a dinâmica de osciladores parametricamente forçados, com enfoque na amplificação de pequenos sinais. Iniciamos por uma revisão da ressonância paramétrica e da amplificação paramétrica em um oscilador linear parametricamente excitado. Em seguida, estudamos dois tipos de osciladores não-lineares parametricamente forçados e concluímos a dissertação com a análise de um dímero parametricamente excitado. Basicamente, analisamos os fenômenos de ressonância paramétrica e de amplificação paramétrica, comparando os resultados obtidos analiticamente (via métodos da média ou do balanço harmônico) com os obtidos via integração numérica das equações do movimento. Em todos os casos, obtivemos a linha de transição para a instabilidade paramétrica do oscilador paramétrico. Nós excitamos os amplificador paramétrico com e sem dessintonia entre entre o bombeamento e o sinal externo ac. Verificamos que o ganho da amplificação paramétrica depende da sensitivamente na fase do sinal externo ac e na amplitude do bombeamento. Mostramos que tais sistemas podem ser facilmente utilizados para recepção e decodificação de sinais com modulação de fase. Além disso, obtivemos séries temporais, envelopes e transformadas de Fourier para a resposta da amplificação paramétrica de pequenos sinais ac. Especificamente nos casos dos osciladores de Duffing parametricamente forçados, obtivemos e analisamos linhas de bifurcação e a amplitude dos ciclos limites como função da frequência e da amplitude de bombeamento. Adicionalmente, conseguimos obter uma relação analítica para os ganhos do sinal e do idler dos osciladores não-lineares parametricamente forçados pelo método do balanço harmônico. Os resultados obtidos implicam que os amplificadores paramétricos não-lineares podem ser excelentes detectores, especialmente em pontos próximos a bifurcações para instabilidade, em que apresentam altos ganhos e largura de banda bem estreitas. Por último, investigamos também o comportamento de dois osciladores lineares acoplados e parametricamente estimulados, com e sem força externa ac. Tais sistemas são muito sensíveis à fase do sinal a ser amplificado e podem ser utilizados para criar amplificadores sintonizáveis em função do parâmetro de acoplamento. / In this dissertation, we studied the dynamics of parametrically-driven oscillators, with a focus on the amplification of small signals. We begin with a revision of parametric resonance and parametric amplification in a linear oscillator parametrically excited. Next, we studied two types of nonlinear parametrically-driven oscillators and finished the dissertation with an analysis of a parametric dimer. Basically, we analyzed the phenomena of parametric resonance and parametric amplification by comparing the results obtained analytically (via the averaging or harmonic balance methods) with those of numerical integration of the equations of motion. In all cases, we obtained the transition line to parametric instability of the parametric oscillator. We excited the parametric amplifier with and without detuning between the pump and the external signal. We found that the parametric amplification depends sensitively on the phase of the external ac signal and on the internal pump amplitude. We showed that such amplifiers can be easily used for the reception and decoding of signals with phase modulation. Furthermore, we obtained time series, envelopes, and Fourier transforms of the response of the parametric amplifier to small external ac signals. Specifically in the cases of the parametrically-driven Duffing oscillators, we obtained and analysed the bifurcation lines and the amplitude of limit cycles as function of the pump amplitude and frequency. In addition, we derived an expression for the signal and idler gains of the nonlinear parametrically-driven oscillators with the harmonic balance method. The results imply that the nonlinear parametric amplifiers can be excellent detectors, specially near bifurcations to instability, due to their high gains and narrow bandwidths. Finally, we studied the dynamics of two linear oscillators coupled and parametrically excited, with and without external ac driving. We found that such systems have a wealth of dynamical responses. They present parametric amplification that is dependent on the coupling parameter and on the phases of the external ac signals. Such systems may be used as tunable amplifiers.

Les microsystèmes sont des systèmes dynamiques multi-physiques. Leurs caractéristiques spécifiques, liées à leur petite dimension et aux phénomènes associés, nécessitent des études approfondies. Les méthodologies de l'automatique peuvent apporter des solutions nouvelles pour l'optimisation de ces systèmes. Dans ce contexte, ce travail de recherche s'intéresse plus particulièrement aux nonlinéarités dans les microsystèmes capteurs. La première partie de cette thèse est consacrée à la conception d'un micro-accéléromètre asservi à sortie numérique. L'objectif principal de l'asservissement est l'amélioration de la linéarité de la mesure. L'étude s'attache à la modélisation du comportement dynamique du capteur en prenant en compte l'effet des non-linéarités (lecture capacitive et actionnement électrostatique) et à l'analyse des performances globales de la mesure (aspect dynamique, transfert de bruit et non-linéarité). Le circuit réalisant l'asservissement est conçu de manière à permettre l'utilisation d'outils de l'automatique avancée : l'identification pour la commande et la synthèse robuste de correcteur. L'architecture présentée est validée en simulation et sur un d´emonstrateur. Dans une deuxième partie, ce travail de recherche propose d'exploiter la non-linéarité dite de Duffing afin de réaliser un principe de détection original. Cette non-linéarité d'origine mécanique est fréquemment rencontrée dans les microsystèmes. Les résultats présentés ouvrent des perspectives nouvelles pour l'utilisation de structures mécaniques de dimensions nanométriques.

The diploma thesis is focused on the use of heuristic and metaheuristic methods to stabilization and controlling the selected systems distinguished by the deterministic chaos behavior. There are discussed parameterization of chosen optimization methods, which are the genetic algorithm, simulated annealing and pattern search. The thesis also introduced the suitable controlling methods and the definition of the objective function. In the theoretical part of the thesis there is a brief introduction to the deterministic chaos theory. The next chapters describes the most common and deployed methods in~the~control theory, especially OGY and Pyragas methods. The practical part of the thesis is divided into two chapters. The first one describes the~stabilization of the artifical chaotic systems with the time delayed Pyragas method - TDAS and its modification ETDAS. The second chapter shows the real chaotic system control. The Duffing oscillator system was chosen to serve this purpose.

Accurately predicting graft failure following kidney transplantation is essential for identifying high-risk patients and tailoring treatment strategies. This thesis aims to forecast kidney graft failure by estimating and predicting the glomerular filtration rate (GFR) using real data related to pre-transplant and post-operative patients status, provided to us by Hannover Medical School. To achieve this, we implement three Bayesian filtering techniques: the Extended Kalman Filter (EKF), the Unscented Kalman Filter (UKF), and the Particle Filter (PF), on a discrete-time state-space stochastic Duffing oscillator model. We also conduct regression analysis between available GFR measurements and the filters' estimated and predicted values, followed by an error analysis using root mean square error. Our results demonstrate that Particle Filter, utilizing 10,000 particles, consistently produced accurate estimates compared to other filters in most patients. Furthermore, we observe that data interpolation yields more accurate results.

In support of society's technological evolution, the study of nonlinear systems in engineering and sciences has become a vital research area. Aiming to contribute in this field, this thesis investigates the behaviour of nonlinear systems using the 'Wiener theories'. As a useful example the Duffing oscillator is investigated in this work. In many real-life applications, nonlinear systems are excited randomly so this work examines systems under white-noise excitation using the Wiener series. Equivalent Linearisation (EL) is a well-known and simple method that approximates a nonlinear system by an equivalent linear system. However, it has deficiencies which this thesis attempts to improve. Initially, the performance of EL for different types of nonlinearities will be assessed and an alternative method to enhance it is suggested. This requires the calculation of the first Wiener kernel of various system defined quantities. The first Wiener kernel, as it will be shown, is the foundation of this research and a central element of the Wiener theory. In this thesis, an analytical proof to explain the interesting behaviour of the first Wiener kernel for a system with nonlinear stiffness is included using an energy transfer approach. Furthermore, the method mentioned above to enhance EL known as the Single-Pole Fit method (SPF) is to be tested for different kinds of systems to prove its robustness and validity. Its direct application to systems with nonlinear stiffness and nonlinear damping is shown as well as its ability to perform for systems with two degrees of freedom where an extension of the SPF method is required to achieve the desired solution. Finally, an investigation to understand and replicate the complex behaviour observed by the first Wiener kernel in the early chapters is carried out. The groundwork for this investigation is done by modelling an isolated nonlinear spring with a series of linear filters and certain nonlinear operations. Subsequently, an attempt is made to relate the principles governing the successful spring model presented to the original nonlinear system. An iterative procedure is used to demonstrate the application of this method, which also enables this new modelling approach to be related to the SPF method.

Orientador: Masayoshi Tsuchida / Banca: José Manoel Balthalzar / Banca: Adalberto Spezamiglio / Resumo: Osciladores eletromecânicos podem ser modelados matematicamente através da equação de Duffing ou equação de Van der Pol, mesmo que sejam sistemas de escala nanomética. Nesta dissertação analisamos um oscilador forçado sujeito a um amortecimento não-linear, que é representado pela equação de Duffing - Van der Pol. Em geral, não é fácil obter solução analítica exata para esta equação, então a análise é feita utilizando a teoria de perturbações para obter uma solução analítica aproximada. Para isso consideramos certos parâmetros do problema como sendo pequenos parâmetros, e obtemos a solução na forma de expansão direta. Devido o fato da frequência natural do sistema dinâmico depender do pequeno parâmetro, essa expansão é não uniforme, ou seja, apresenta termos seculares mistos (termos de Poisson), e além disso possui pequenos divisores. Essas inconveniências são eliminadas aplicando o método das múltiplas escalas e o método da média. Inicialmente os pequenos parâmetros são escolhidos de modo que o problema não perturbado se reduz a um oscilador harmônico forçado, e na escolha posterior o problema não perturbado é um oscilador linear amortecido e forçado. / Abstract: Electromechanical oscillators can be mathematically modeled by a Du±ng equation or a Van der Pol equation, even if they are nanometric systems. In this work we studied a forced oscillator having nonlinear damping, that is represented by a Du±ng - Van der Pol equation. In general, it is not easy to get the exact analytical solution for this equation, then the analysis is done using the perturbation theory to get an approximate analytical solution. For this reason we considered that certain parameters of the problem are small parameters and we obtain the solution in the form of straightforward expansion. Due to the fact that natural frequency of the dynamic system depends on the small parameter, this expansion is not uniform, i.e. presents secular terms (Poisson terms) and also small-divisors. These inconveniences are eliminated using the method of multiple scales and the aver- aging method. Initially the small parameters are chosen so that the unperturbed problem is reduced to a forced harmonic oscillator, and in the subsequent choice the unperturbed is a forced oscillator having linear damping. / Mestre

This Thesis is devoted to the investigation of superfluid helium flows due to torsional oscillators. In its first part, flow due to a torsionally oscillating disc suspended on a tungsten filament is studied (building upon the work of A. C. Hollis Hallett from 1952). Measurements of the motion of the torsionally oscillating disc were performed in superfluid helium at temperatures between 1.265 K and 2.157 K at saturated vapour pressure. Time traces of the disc angular deflection were obtained, and critical parameters related to the turbulent flow stability were determined. In laminar flow, scaling of drag forces with the dimensionless Donnelly number was verified. Based on these results, and comparison with the original work, a scenario of the decay of turbulent flow was suggested. The second part of this work is focused on the development and construction of a similar experiment for mK temperatures. A new type of oscillator was designed, a so-called "pillbox", and a series of testing measurements was performed both at room and mK temperatures.