Alguns métodos aproximados são sugeridos na literatura relacionada para encontrar a resposta de sistemas com amortecimento não-proporcional. Muitas vezes procura-se estabelecer um critério para aproximar o amortecimento não-proporcional por um modelo de amortecimento proporcional. Neste trabalho foram utilizadas simulações de modelos dinâmicos com três graus de liberdade, com amortecimento não proporcional, a fim de analisar os valores obtidos para as freqüências naturais, estimados a partir dos autovalores resultantes desses modelos. Os cálculos das freqüências naturais e dos amortecimentos modais foram feitos admitindo-se a validade das relações entre estes parâmetros e os autovalores do problema como são bem conhecidas no caso do amortecimento proporcional. Observa-se que, para o caso de amortecimento não-proporcional, este procedimento pode levar a erros significativos na avaliação destes parâmetros. Nos problemas simulados é possível quantificar os erros nas avaliações das freqüências naturais, sendo significativos para fatores de amortecimentos altos. Observa-se que para os fatores de amortecimento não é possível quantificar estes erros, sendo que seus valores são apenas aproximações baseadas na teoria de amortecimento proporcional. Este trabalho apresenta dados que possibilitam uma discussão sobre as diferenças encontradas entre os valores das freqüências naturais e os valores estimados pelas expressões clássicas do amortecimento proporcional. / Some approximate methods are suggested in the related literature to find the output of mechanical systems with non-proportional damping. Often they try to establish a criterion that approximates the non-proportional damping to proportional damping model. In this work, stimulations of dynamics models of three degree of freedom with non-proportional damping were used to examine the values of natural frequencies, estimated from the eigenvalues obtained by these models. The calculations of natural frequencies and modal damping ratio were performed assuming the validity of the relationship between these parameters and the well known eigenvalues of the problem in the proportional damping case. In the simulated problems is possible to quantify the errors in the evaluations of the natural frequencies and this errors are significant for the case where the damping factors are high. It is observed that for the damping factors it is not possible to quantify these errors, and their magnitudes are only approximations based on the theory of proportional damping. This work presents data which enables a discussion about the differences between the magnitude of natural frequencies and the magnitude estimated by the classic equations of proportional damping.

Concepção, desenvolvimento de projeto e fabricação de um mini-moinho vibratório para cerâmica avançada. Diversas áreas de engenharia são hoje dependentes de componentes de cerâmica avançada. A conformação da cerâmica, baseada na compactação de pós, seguida de sinterização, tem encontrado diversas aplicações em processos de manufatura dos produtos cerâmicos avançados. Tamanhos de partículas pequenas (abaixo de 1 \'mü\'m) e controle da distribuição granulométrica são desejáveis, porque aumentam a reatividade das partículas cerâmicas. O presente projeto busca pela concepção de um moinho que processe pequena quantidade de material em múltipla moagem no atendimento das necessidades de ambientes de trabalho de desenvolvimento e fabricação de peças especiais tais como os laboratórios e indústrias de pequeno porte. Normalmente os moinhos encontrados no mercado são para escalas maiores e moagem simples. Dessa forma, baseado em técnicas de metodologia de projeto, principalmente na busca de soluções para a concepção e desenvolvimento, tanto do sistema \"moinho vibratório\", quanto dos jarros, procurou-se desenvolver um procedimento para um projeto adaptativo de moinho vibratório. Foi projetado e construído um moinho para moagem simultânea de seis jarros com volume útil de moagem de 20 a 300 mL em cada jarro. Foram realizadas moagens de alumina de tamanho médio inicial de 5,2 \'mü\'m as quais foram analisadas em sedígrafo. Foram obtidos pós com 0,7 \'mü\'m de diâmetro médio equivalente e pós com 18% abaixo de 0,2 \'mü\'m. / Conception, project development and manufacture of a vibratory mini-mill for advanced ceramics. Diverse areas of engineering today are dependent on advanced ceramic components. The ceramic conformation, based on powder compaction, and followed by sintering, has been found to have many different applications in manufacturing process in advanced ceramic products. Small size particles (below 1 \'mü\'m) and the control of particle size distribution are desirable, as they increase the reactivity of ceramic particles. The present project involves a search for the conception of a mill that process small amounts of material in multiple milling to meet the requirements of research laboratories and small industries. Normally the mills available on the market are for larger scale and simple, milling. Therefore based on techniques of project methodology, mainly in brainstorming for conception and development, not only on the \"vibratory mill system\" but also on the jars, it was developed a procedure for an adaptable project for a vibratory mill. A mill for the simultaneous milling of six jars with milling volume from 20 to 300 mL on each jar was projected and built. Alumina with medium particle size of 5.2 \'mü\'m, were milled using the \"vibratory mill system\" and analyzed by sedigraph. After milling the particles had an average diameter of 0.7 \'mü\'m with 18% of the particles below 0.2 \'mü\'m.

O Método do Lagrangeano aumentado em problemas de otimização estrutural com restrições dinâmicas, bem como os conceitos matemáticos e numéricos necessários à sua compreensão são descritos. Este método resolve uma seqüência de problemas de minimização sem restrições definidos utilizando a função objetivo e as funções restrições. Um programa de computador é desenvolvido e aplicado em diversos exemplos. Alem disto, foi efetuada uma análise de sensibilidade com relação aos parâmetros utilizados no método. O método mostrou-se eficiente nas aplicações em problemas com restrições dinâmicas. / We present the method of the augmented Lagrangian in problems of scructural optimization with dynamic restrictions, as well as its mathemathical and numerical concepts. This method solves a series of unconstrained minimization problems using the objective function and the restriction functions. A computational program is implemented and applied in several examples. The augmented Lagrangian parameters senbility is analysed. The method is quite efficient in applications in optimization problems with dynamic restrictions.

In mining engineering, blast-induced ground vibration has become one of the major concerns when production blasts are conducted, especially when the mining areas and the blast sites are near inhabited areas or infrastructure of interest. To comply with regulations, a vibration monitoring program should be developed for each mining operation. The vibration level, which is usually indicated by the peak particle velocity (PPV) of the vibration waveform, should fall below the maximum allowable values. Ideally, when blasting is near structures of interest (power towers, dams, houses, etc.), the vibration level (PPV) should be predicted prior to the actual production blasts. There are different techniques to predict the PPV, one in particular is the signature hole technique. This technique is based on signals and systems theory and uses a mathematical operation called convolution to assess the waveform of the production blast. This technique uses both the vibration waveform of an isolated hole and the timing function given by the timing used in the blast. The signature hole technique requires an isolated single-hole waveform to create a prediction. Sometimes this information is difficult to acquire, as it requires the synthesis of a single-hole vibration waveform from a production blast vibration signal. The topic of ground vibrations from mining blasts, and more specifically the synthesis of a single-hole vibration waveform, has been studied by researchers in past decades, but without any concrete success. This lack of success may be partially due to the complexity and difficulty of modelling and calculation. However, this inverse methodology can be very meaningful if successfully applied in blasting engineering. It provides a convenient and economical way to obtain the single-hole vibration waveform and make the prediction of a production blast waveform easier. This dissertation research involves the theories of deconvolution, linear superposition, and Fourier phases to recover single-hole vibration waveforms from a production waveform. Preliminary studies of deconvolution included spectral division deconvolution and Wiener filtering deconvolution. In addition to the adaptation of such methodologies to the blast vibrations problems, the effectiveness of the two deconvolution methods by the influence of delay interval and number of holes is also discussed. Additionally, a new statistical waveform synthesis method based on the theories of linear superposition, properties of Fourier phase, and group delays was developed. The validation of the proposed methodology was also conducted through several field blasting tests. Instead of synthesizing one normalized single-hole vibration waveform by deconvolution, the proposed statistical waveform synthesis methodology generates a different single-hole vibration waveform for each blast hole. This method is more effective and adaptable when synthesizing single-hole vibration waveforms. Recommendations for future work is also provided to improve the methodology and to study other inverse problems of blast vibrations.

This dissertation focuses on the design, modeling, characterization and experimental verification of a class of nonlinear energy sink, based on a cantilever beam vibrating laterally between two specially shaped surfaces that limit the vibration amplitude, thus providing a variable beam length throughout its deflection, therefore producing a smooth nonlinear restoring force. First, a methodology to evaluate and visualize the energy interactions between the nonlinear energy sink and its host structure is developed. Then, an semi-analytical dynamic model for simulating the device under actual working conditions is proposed, and finally, an experimental verification step is conducted where the numerical results are compared and correlated to the experimental results.<br>

Cette recherche dans le domaine des nano-drones a pour ambition de concevoir un objet volant de taille réduite s’inspirant directement de la nature.Dans ce but, un état de l’art a été fait sur les mécanismes de vol des insectes ainsi que sur l’ensemble des solutions à ailes battantes artificielles développées à ce jour. Il ressort de cette analyse d’une part, que les insectes ont une cinématique des ailes singulière reposant sur un mouvement de battement et de torsion en quadrature de phase et d’autre part, que les nano-drones actuels ne s’appuient pas ou très peu sur le comportement dynamique de leurs ailes artificielles pour générer de la portance. Le concept proposé dans le cadre de ce travail se veut en rupture avec ces approches. Il consiste en un couplage vibratoire en quadrature de phase de modes de battement et de torsion appliqué sur des ailes artificielles flexibles afin de reproduire une cinématique proche de celles des insectes avec un unique actionneur. La méthodologie employée s’est traduite par l’élaboration d’un modèle analytique négligeant les efforts aérodynamiques afin de calculer le comportement dynamique et de dimensionner la structure du nano-drone. Les simulations ont mis en évidence l’existence de modes propres de la structure des ailes dont les déformées correspondent aux mouvements de battement et de torsion recherchés. Fait remarquable, une optimisation a permis de rapprocher les fréquences de ces modes tout en conservant une amplitude suffisante de façon à réaliser leur couplage et donc à reproduire la cinématique souhaitée. La portance produite a été ensuite estimée à l’aide d’un modèle aéroélastique qui a montré que le maximum de portance était obtenu pour deux fréquences coïncidant avec une quadrature de phase entre les deux modes. Ces résultats ont par la suite été confirmés à l’aide de mesures expérimentales effectuées sur un banc de mesure spécifique répondant aux contraintes imposées par les prototypes en termes de sensibilité et de comportement dynamique. Les différentes générations de prototypes testées ont été fabriquées au moyen des procédés de microfabrication, ce qui a permis l’intégration d’une membrane d’aile en parylène d’une épaisseur tout à fait comparable à celle existant chez les insectes. La conclusion de cette étude est que nous disposons dorénavant d’un prototype capable de compenser son poids. / This work in the Nano-Air Vehicle field aims to design a small flying object directly inspired by the nature. For this purpose, a state of the art has been performed on insects flight mecanisms and has reviewed the overall artificial flapping wings solutions developped until today. The result of this analysis is on one hand, that insects use a specific wing kinematics which relies on a flapping motion and a twisting motion coupled in a quadrature phase shift and on the other hand, that the existing Nano-Air Vehicles do not exploit the dynamic behavior of their artificial wings to produce lift. The proposed concept in this research is a departure from those other works. It consists of a vibratory coupling in a quadrature phase shift of a flapping and a twisting mode applied on flexible artificial wings in order to reproduce a kinematics close to the insects ones with a single actuator. The used methodology resulted in the development of an analytic modeling which neglects the aerodynamic forces to calculate the dynamic behavior and dimension the prototype structure. Simulations highlighted the existence of eigen modes of the wings structure whose modal shapes match with the wanted flapping and twisting motion. Noteworthy fact, an optimization allowed to get those modes close in frequency while keeping a non-neglectible amplitude in such a way as to couple them and obtain the expected kinematics. The produced lift force is then estimated with an aeroelastic modeling which has shown that the maximum lift is obtained for two frequencies which provide a quadrature phase shift between the two modes. Those results are then validated by experimental measurements performed on a specific bench made according to the constraints due to the prototype in terms of sensitivity and dynamic behavior. The different generations of prototypes tested are produced with microfabrication process, allowing to integrate a wing membrane in parylene with a thickness comparable to the one existing in insects. The conclusion of this study is that we now have a prototype able to compensate its weight.

Dans la quasi-totalité des missions d'observation de la Terre requérant une grande précision de pointage, les micro-vibrations sont le principal élément dégradant les performances de pointage. Les principales sources de micro-perturbations sont les roues et, lorsqu'il y en a, les refroidisseurs cryogéniques. D’autres sources de perturbations sont les propulseurs chimiques, les moteurs pas à pas de l'antenne solaire, les mécanismes d'entraînement,… L'objectif de cette thèse (NPI) est de concevoir et de valider un système de pointage actif de haute précision à base d’actionneurs piézoélectriques capable de rejeter les micro-vibrations au niveau d’un miroir, avec des pénalités de masse et de puissance contrôlées. Les caractéristiques attendues de ce système sont : • une grande bande passante en boucle fermée : typiquement jusqu'à 100 Hz • une faible erreur résiduelle: typiquement inférieure à 50-100 rad (ordre de grandeur approximatif) • un encombrement et une masse faibles (à quantifier au cours de la thèse) • une puissance requise minimale (à optimiser au cours de la thèse) • la modularité • une possible évolution Ce sujet est fortement pluridisciplinaire (mécanique, automatique, optique et instrumentation). Les défis scientifiques de la thèse sont : • la conception d’un système de pointage actif à bande passante élevée avec impact de masse et de volume faible et une puissance requise à minimiser • la commande robuste du système de pointage actif permettant de rejeter des micro-perturbations dont le spectre varie en fonction des phases de la mission • la tenue des performances en précision • la définition d'une méthodologie générique de conception intégrée applicable à d'autres systèmes de pointage (plusieurs degrés de liberté, ...) / On almost all high accuracy pointing Science and Earth observation missions, micro-vibrations are the major contributor to pointing performances degradations (RPE). The main sources of micro-disturbances being the wheels and, when present, the cry-coolers. Other disturbance sources may originate from chemical thrusters, antenna stepper motors, Solar Array Drive Mechanisms (SADM), antenna trimming mechanisms, or payload mechanisms set either inside the sensitive payload, or inside another payload of the same spacecraft. The objective of this NPI is to investigate and validate a high accuracy active pointing system able to reject micro-vibrations at instrument level: • large control bandwidth : typically up to 100Hz • low residual error : typically lower than 50-100nrad (rough order magnitude to be further defined in the frame of this NPI) • low mass and volume impacts • scalable • modular This subject is strongly multidisciplinary (mechanics, control theory, optics and instrumentation). The scientific challenges of the thesis are: • the design of an active pointing system with high bandwidth, low impact of mass and volume and minimized power • the robust control of the active pointing system allowing to reject micro-disturbances whose spectrum varies according to the phases of the mission • obtaining high accuracy performances • the definition of a generic methodology of integrated design applicable to other pointing systems (several degrees of freedom e.g.)

Vibrations of a wind turbine have a negative impact on its performance and therefore approaches to effectively control turbine vibrations are sought by wind industry. The body of previous research on wind turbine vibrations has focused on physics-based models. Such models come with limitations as some ideal assumptions do not reflect reality. In this Thesis a data-driven approach to analyze the wind turbine vibrations is introduced. Improvements in the data collection of information system allow collection of large volumes of industrial process data. Although the sufficient information is contained in collected data, they cannot be fully utilized to solve the challenging industrial modeling issues. Data-mining is a novel science offers platform to identify models or recognize patterns from large data set. Various successful applications of data mining proved its capability in extracting models accurately describing the processes of interest. The vibrations of a wind turbine originate at various sources. This Thesis focuses on mitigating vibrations with wind turbine control. Data mining algorithms are utilized to construct vibration models of a wind turbine that are represented by two parameters, drive train acceleration and tower acceleration. An evolutionary strategy algorithm is employed to optimize the wind turbine performance expressed with three objectives, power generation, vibration of wind turbine drive train, and vibration of wind turbine tower. The methodology presented in this Thesis is applicable to industrial processes other than wind industry.

In urban areas, vibrations generated by pile driving often affect the neighboring properties vulnerable to ground shaking. These vibrations may cause damage to surrounding structures either by shaking the ground or by causing settlement of the soil beneath foundations in the proximity of pile driving. It is important to distinguish between the conditions under which the vibrations will cause damage and those under which vibrations are tolerable. The numerical studies on the analysis of pile driving have mostly focused on assessing the driving efficiency and the bearing capacity of dynamically loaded piles. A limited number of studies included the study of ground vibrations due to pile driving and its effects on adjacent structures. However, the factors affecting the ground vibrations in soils such as the nonlinear constitutive behavior of soil, soil-pile interaction and penetration depth of the pile have not been clearly identified. The objective of this research is to implement a numerical method to simulate dynamic loading of a single pile, and study the factors influencing the stress wave propagation in the soil surrounding the pile. The thesis is comprised of two main analyses: (1) the static analysis of a pile in which the phenomenon of static consolidation is studied, and (2) the dynamic analysis of a pile in which pile driving and ground vibrations are studied. In the static analysis, the load capacity of a single pile is investigated. The results from the finite element method are compared with widely recognized theoretical methods. The theoretical methods that are used to estimate the end bearing capacities are: (1) General Formula, (2) Vesic's Method, (3) Janbu's Method, (4) Meyerhof's Method, and (5) Coyle & Castello's Method. The estimation of skin friction resistance (shaft capacity) of single piles is performed using the (1) Alpha method, (2) Beta method, and (3) Lambda method. Two numerical applications are performed to predict the load capacity of single piles in normally consolidated clays. It is observed that the model with no slippage at the interface predicts almost twice as much load capacity as the model with interface. In regards with the end bearing capacities, Coyle & Castello's method is found to be most conservative followed by the finite element method, the Janbu's method, the Meyerhof's method, and finally the Vesic's method. In respect to skin friction resistance, the finite element is found to be the most conservative method, followed by the Beta, the Lambda, and the Alpha method. In the dynamic analysis, the amplitudes of ground vibrations are investigated based on the variation of: (1) the soil type, (2) the pile embedment length and (3) the released hammer energy. In the first analysis, five types of soils - loose and dense sands and, soft, medium stiff, and stiff clays - are modeled. The highest vibration amplitude is calculated for the loose sand with a peak particle velocity (PPV) of 10.0 mm/s followed by the dense sand with a PPV of around 4.0 mm/s. Among the clay types, the vibrations are higher for the stiffer clay in the near field, which is 9 m (half a pile length) or less away from the pile. In the second analysis, three different embedment lengths - full, half, and quarter pile length - are modeled. It is found that the quarter embedded piles produce greater vibration amplitudes as compared to the half and fully embedded piles. Larger amplitudes of vibrations are encountered on the ground surface for shorter pile embedment lengths. In the third analysis, three different impact forces consisting of 2,000 kN (F), 6,000 kN (3F) and 10,000 kN (5F) are applied on the pile head. It is concluded that increase in hammer energy causes increase in the peak particle velocities.

Le contrôle de vibrations est devenu un enjeu majeur dans de nombreuses applications industrielles où l'augmentation de la durée de vie nécessite de réduire les vibrations. Dans le cas de structures embarquées, les vibrations doivent être amorties efficacement tout en limitant la masse et le volume du contrôleur. Cet objectif peut être atteint en minimisant voire en supprimant l'énergie nécessaire à ce contrôle. Dans ce contexte, les recherches présentées consistent à utiliser des céramiques piézoélectriques comme capteurs et actionneurs. Légères et peu encombrantes, elles sont constituées de matériaux dont la bande fréquentielle est importante ce qui les rend bien adaptées au contrôle de structures embarquées. Afin d'atteindre les objectifs de performance et d'énergie nécessaires au contrôle des structures embarquées, une stratégie de contrôle semi-actif modal a été développée. La méthode est basée sur une stratégie de contrôle qui ne nécessite que très peu d'énergie pour fonctionner mais est efficace uniquement lorsque l'excitation est ciblée sur un mode unique. Afin d'améliorer les performances du contrôle semi-actif dans le cas d'une excitation large bande, une approche modale est proposée. Cette méthode modale permet de minimiser l'énergie nécessaire au contrôle en ciblant celui-ci sur des modes choisis. De plus, l'approche modale permet d'utiliser moins de capteurs et d'actionneurs que de modes à contrôler. Les résultats numériques et expérimentaux montrent que le contrôle semi-actif modal développé est performant et bien qu'un modèle soit nécessaire, il s'avère robuste en stabilité et en performance. Le contrôle de vibrations consiste en un compromis entre performance et énergie de contrôle. Comparés à d'autre type de contrôle tel que le contrôle actif, les performances obtenues par la méthode semi-active modale s'avèrent être en retrait. Cependant, la méthode semi-active modale ne nécessite qu'une énergie très faible pour fonctionner contrairement au contrôle actif qui nécessite des amplificateurs souvent lourds et encombrants limitant fortement les applications notamment dans le domaine des structures embarquées. Afin de bénéficier des avantages respectifs des deux méthodes, le contrôle proposé consiste à associer le contrôle actif au contrôle semi-actif modal. Cette méthode hybride permet de contrôler les modes de vibrations de la structure avec des performances identiques à celle du contrôle actif tout en consommant moins d'énergie. Une application expérimentale de cette méthode est réalisée sur une poutre encastrée-libre. L'analyse énergétique de la commande active permet de quantifier le gain en énergie du contrôle hybride face aux différentes méthodes de contrôle. Cette réduction de l'énergie de contrôle se traduit par une diminution de la masse des amplificateurs. Cette technique pourra trouver des applications dans le domaine des transports pour améliorer la durée de vie des systèmes.vibrations