Orientador: Orival Andries Junior / Dissertação (mestrado) - Universidade Estadual de Campinas, Faculdade de Educação Fisica / Made available in DSpace on 2018-08-14T17:22:27Z (GMT). No. of bitstreams: 1 Marques_AlessandroCustodio_M.pdf: 9033670 bytes, checksum: 8dee8cbe47cfcfd6eb7f6f540a902866 (MD5) Previous issue date: 2009 / Resumo: A utilização de protocolos não-invasivos na determinação das respostas metabólicas aeróbio-anaeróbio de atletas tem se tornado constante na busca de índices que possam auxiliar no controle de intensidade no treinamento. Além disso, muito pouco tem sido discutido com relação a diferença destas respostas entre os estilos. Os objetivos do trabalho foram: a) verificar a velocidade do limiar anaeróbio (vLAn) entre os nados costas e crawl; b) verificar a correlação entre a velocidade critica (VC) e velocidade do limiar anaeróbio (vLAn) nos nados crawl e costas. Para isso, foram selecionados 12 nadadores de costas de ambos os sexos com idade entre 15 a 26 anos com idade média de 20,25 ± 3,60 anos. Os sujeitos pertenciam às categorias juvenil II a sênior. A VC foi determinada através da inclinação da reta de regressão linear e as distâncias que compõe o teste e foram realizadas em velocidade máxima durante a sessão de treinamento em estímulos de 50, 100 e 200 metros nos nados costas e crawl de forma aleatória. Posterior a realização dos tiros, as distâncias foram combinadas em quatro modelos (VC1 - 50, 100 e 200m, VC2 - 50 e 100m, VC3 - 100 e 200m e VC4 - 50 e 200m). Para a determinação da vLAn foi utilizado o teste de duas distâncias (2 x 200m) sendo realizadas no nado costas e nado crawl com velocidades correspondentes a 85% e 100% da velocidade máxima para a distância e nado. As coletas de sangue foram realizadas no período de repouso (Rep.), final do estimulo (FT), um (1'), três (3'), cinco (5'), sete (7') e nove (9') minutos pós o término do teste, o período de repouso entre estímulos foi de trinta minutos. Todos os dados foram submetidos ao teste de normalidade (Shapiro-Wilk). A análise estatística utilizada foram a média, desvio padrão, valor máximo, valor mínimo e amplitude total. Foi utilizado o teste para comparação de duas medidas repetidas (t- Student) e a análise de variância para medidas repetidas (Anova Two-Way) seguido do Post-hoc de Tuckey para localização das diferenças. Para verificar a associação entre as variáveis foi utilizado o coeficiente de correlação linear produto-momento de Pearson. O nível de significância adotado durante toda a pesquisa foi de p_0,05. Através da análise dos dados podemos observar diferença entre vLAn nos nados costas e crawl (1,26 ± 0,08 e 1,37 ± 0,07 respectivamente) como também entre a vLAn e a VC em todas as combinações de distância para ambos os nados (VC1-VC4). Os valores da VC tanto para ambos os nados tendem a superestimar a vLAn. Apesar dos dados demonstrarem diferença estatisticamente significante entre a VC e vLAn a correlação foi muito expressiva, apresentando valores de r= 0,75 a 0,92. Podemos concluir que, apesar da VC nas diferentes combinações de distância terem demonstrado valores superiores aos da vLAn este método indireto é eficaz sendo uma boa ferramenta na verificação da sensibilidade ao treinamento como também uma ferramenta na avaliação de uma grande quantidade de atletas não necessitando diretamente de procedimentos invasivos. / Abstract: The use of protocols non-invasive in determination of the aerobic-anaerobic metabolic responses of athletes has become constant in the search for indicators that can assist in control of intensity in training. Furthermore, very little has been discussed with respect of these answers to between the differences styles. Therefore, the aim of this study were: a) verify the difference of the speed of the anaerobic threshold (vLAN) between swim backstroke and freestyle, b) assess the correlation between the critical velocity (VC) and velocity of the anaerobic threshold (vLAN) in swims backstroke and freestyle. For this, we selected 12 swimmer of swim backstroke of both gender with aged 15 to 26 years and with mean of 20,25 ± 3,60 years. The subjects belonged to the category youth II the senior. The VC was determined by the slope of the linear regression line, where the distances covered by the test were held in maximum speed during the training session on stimuli of 50, 100 and 200 meters in swim backstroke and freestyle at random, and combined in four models (VC1 - 50, 100 and 200m, VC2 - 50 and 100m, VC3 - 100 and 200m and VC4 - 50 and 200m). To determine the vLAN test was used for two different distances (2 x 200 m) were performed in swim backstroke (2 x 200m) and in freestyle (2 x 200 meters) with speeds corresponding to 85% and 100% of the maximum speed for the distance and swim. The blood samples were taken in the rest (Rep.), end of the stimulus (FT), one (1'), three (3'), five (5'), seven (7') and nine (9') minutes after the end of the test, the rest between stimuli was of thirty minutes. All data were subjected to the test of normality (Shapiro-Wilk). The statistical analysis used were the mean, standard deviation, maximum, minimum and total amplitude. Test was used for comparison of two repeated measures (t-Student) and analysis of variance for repeated measures (ANOVA two-way) followed by post-hoc Tuckey to locate the differences. The relationship between the variables we used the linear correlation coefficient product-moment of Pearson. The significance level throughout the study was p_0.05. Through data analysis we can see statistics differences vLAN between the swim as well the VC in all combinations of distance (VC1, VC2, VC3 and VC4). Both, swim backstroke and freestyle to the VC tends to overestimate the vLAN. Although the data show the difference between VC and vLAN in swim backstroke and freestyle the correlation was highly significant, showing values of r = 0.75 to 0.92. We conclude that although the VC away in various combinations have shown higher values for the vLAN that the indirect method is effective and can be a useful tool in checking the sensitivity to training but also a very useful tool in evaluating a large number of athletes not directly required for invasive procedimental. / Mestrado / Ciencias do Desporto / Mestre em Educação Física

Critical velocity is defined as projectile striking velocity that causes instantaneous rupture of the specimen under transverse impact. The main goal of this dissertation was to determine the critical velocities of a Twaron^® 2040 warp yarn impacted by different round indenters. Special attention was placed to develop models to predict the critical velocities when transversely impacted by the indenters. An MTS 810 load frame was utilized to perform quasi-static transverse and uniaxial tension experiments to examine the stress concentration and the constitutive mechanical properties of the yarn which were used as an input to the models. A gas/powder gun was utilized to perform ballistic experiments to evaluate the critical velocities of a Twaron^® 2040 warp yarn impacted by four different type of round projectiles. These projectiles possessed a radius of curvature of 2 μm, 20 μm, 200 μm and 2 mm. The results showed that as the projectile radius of curvature increased, the critical velocity also increased. However, these experimental critical velocities showed a demonstrated reduction as compared to the classical theory. Post-mortem analysis via scanning electron microscopy on the recovered specimens revealed that the fibers failure surfaces changed from shear to fibrillation as the radius of curvature of the projectile increased. To improve the prediction capability, two additional models, Euler-Bernoulli beam and Hertzian contact, were developed to predict the critical velocity. For the Euler–Bernoulli beam model, the critical velocity was obtained by assuming the specimen ruptured instantaneously when the maximum flexural strain reached the ultimate tensile strain of the yarn upon impact. On the other hand, for the Hertzian contact model, the yarn was assumed to fail when the indentation depth was equivalent to the diameter of the yarn. Unlike Smith theory, the Euler-Bernoulli beam model underestimated the critical velocity for all cases. The Hertzian model was capable of predicting the critical velocities of a Twaron^® 2040 yarn transversely impacted by 2 μm and 20 μm round projectiles.

The prediction of material behavior and its microstructural evolution during high velocity impacts has been investigated for decades. The application of this topic can be observed in various engineering applications such as the cold spray process. Cold spray (CS) is an additive manufacturing method in which solid particles are accelerated using a low temperature supersonic inert gas flow, prior to their impact onto a substrate and adhesion/consolidation. In this process, unlike other thermal spray processes, the particles are kept well below their melting point prior to impact. This allows the CS process to be used for the manufacturing of high quality, specialized products at a low energy input. In CS, the deformation and bonding processes happen in a very short time (less than 100 ns). With the current technology, in-situ investigation is almost impossible. In this situation, numerical modeling methods are the best alternative to study the deposition process. There are several factors influencing the particle deposition, such as particle/substrate material properties, particle size, material temperature, particle velocity and so on, but it has been shown that the particle impact velocity has the major role during the deposition process. In fact, despite the type of bonding, i.e., mechanical or chemical, particle is sticking to the substrate after experiencing severe plastic deformation that occurs upon the impact at high velocities. Therefore, in order to develop the understating of the CS process, investigating the deformation behavior of material during high velocity impacts, and also bonding mechanisms involved during particle deposition must be investigated. III Although numerous studies have been done to explore the mechanisms occurring during particle deposition, the details of this process are still unclear. Therefore, the purpose of this research is to study the fundamental aspects of material behavior during the deformation and deposition processes with the aim of improving the understating of the CS process. Two different numerical approaches will be used to achieve the objective of the study, i.e., Finite Element Method (FEM) and Molecular Dynamics (MD) method. FEM will be used to study the metallic bonding occurring between the particle and the substrate. A physically based model to predict this phenomenon will be implemented into ABAQUS/Explicit FEM software. MD simulations will be performed to investigate the microstructure evolution during high velocity impacts. In order to characterize the deformation behavior of materials at a fundamental level, analysis will be focused on the basic mechanisms of plasticity and hardening in metals, i.e., the multiplication, glide and locking of dislocations, and also solid-state amorphization that happens at high strain rate deformations.

As velocidades críticas de resfriamento necessárias à obtenção de percentuais definidos de martensita, presentes em amostras de aços temperados em óleo, foram determinadas por meio de curvas de resfriamento. As amostras constituíram-se de barras de aço AISI 4140 e 8640 com seções circulares de 25,4; 38,1 e 50,8 mm e barras quadradas com 25,4 e 38,1 mm de lado e comprimento igual a 5 vezes o diâmetro ou lado. Visando-se à obtenção de padrões de comparação para essas velocidades, foram também obtidas as curvas em U das durezas ao longo das seções transversais das barras e as curvas Jominy desses aços. Os resultados apresentaram boa coerência, o que garantiu a eficiência do processo. Os resultados concernentes ao teor específico de 50% de martensita foram comparados com os obtidos a partir de equações constantes na literatura. As equações não se mostraram diretamente adequadas, requerendo a obtenção de um fator de correção, que uma vez obtido mostrou-se eficiente na adequação dos valores empíricos de velocidade crítica aos determinados por meio das curvas de resfriamento. / The criticaI cooling velocities necessary to obtaining specific contents of martensite, present in test specimens of hardened steels in oil, were evaluated by means of cooling curves. The samples were constituted of bars of AISI 4140 and 8640 steels with 25,4; 38,1 and 50,8 mm diameter and squared bars with 25,4 and 38,1 mm in side by 5 times the diameter or side long. Aiming at obtaining comparison patterns for those velocities, they were also obtained the curves in U of the hardness along the traverse sections of the bars and the Jominy curves of those steels. The results presented good agreement, what guaranteed the efficiency of the process. The concerning results achieving a 50 pct martensitic microstructure were compared with those obtained from equations presented in the literature. The equations did not show good approaches, requesting the determination of a correction factor, that once obtained it was shown efficient in the adaptation of the empirical values of critical velocities to those determined by means of the cooling curves.

Os elementos de combustível de um reator nuclear de pesquisa tipo MTR (\"Material Testing Reactor\") são, em sua grande maioria, formados por placas de combustível revestidas com alumínio contendo no cerne silicileto de urânio (U3Si2) disperso em matriz de alumínio. Essas placas possuem espessura da ordem de milímetros e comprimentos muito maiores em relação à sua espessura. Elas são dispostas paralelamente no conjunto que forma o elemento combustível, de maneira a formar canais entre elas com poucos milímetros de espessura, por onde escoa o fluido de refrigeração (água leve ou água pesada). Essa configuração, associada à necessidade de um escoamento com altas vazões para garantir o resfriamento das placas em operação, pode gerar problemas de falhas mecânicas das placas de combustível devido às vibrações induzidas pelo escoamento nos canais e, consequentemente, acidentes de proporções graves no caso de velocidade crítica que possa gerar o colapso das placas. Embora não haja ruptura das placas de combustível durante o colapso, as deflexões permanentes excessivas das placas podem causar bloqueio do canal de escoamento no núcleo do reator e levar ao superaquecimento nas placas. Para este trabalho, foram desenvolvidas uma bancada experimental com capacidade para altas vazões volumétricas (Q=100 m3/h) e uma seção de testes que simula um elemento combustível do tipo placa com três canais de resfriamento. A seção de testes foi construída com placas de alumínio e acrílico e foi instrumentada com sensores de deformação, sensores de pressão, um acelerômetro e um tubo de pitot. As dimensões da seção de testes foram baseadas nas dimensões do Elemento Combustível do Reator Multipropósito Brasileiro (RMB), cujo projeto está sendo coordenado pela Comissão Nacional de Energia Nuclear - CNEN. Os experimentos realizados alcançaram o objetivo de chegar à condição de velocidade crítica de Miller com o colapso das placas. A velocidade crítica foi atingida com 14,5 m/s levando a consequente deformação plástica das placas que formam o canal do escoamento. O canal central na entrada da seção de testes apresentou uma abertura de 3 mm em seu centro, causando um grande bloqueio do escoamento nos canais laterais. Este comportamento foi v constatado visualmente durante a desmontagem da seção de testes, ilustrado e discutido na análise de resultados apresentado neste trabalho. O bloqueio dos canais também foi observado por meio de gráficos de queda de pressão e por gráficos das deformações da entrada, centro e saída das placas contra a velocidade média da seção de testes. Observou-se uma queda da resistência hidráulica da seção de testes devido ao aumento da seção transversal de escoamento no canal central e um aumento exponencial das deformações quando da ocorrência da velocidade crítica. Comparativamente, o valor experimental obtido para velocidade crítica na seção de testes foi da ordem de 85% do valor obtido por cálculo com a expressão teórica de Miller. Os experimentos realizados permitiram um melhor entendimento da interação fluido estrutura em elementos de combustível tipo placa como: valores de frequências de vibrações naturais, instabilidade fluido elástica e desenvolvimento de técnicas para a detecção de valores de velocidade crítica. / The fuel elements of a MTR (Material Testing Reactor) type nuclear reactor are mostly composed of aluminum-coated fuel plates containing the core of uranium silica (U3Si2) dispersed in an aluminum matrix. These plates have a thickness of the order of millimeters and are much longer in relation to their thickness. They are arranged in parallel in the assembly forming the fuel element to form channels between them a few millimeters in thickness, through which there is a flow of the coolant (light water or heavy water). This configuration, combined with the need for a flow at high flow rates to ensure the cooling of the fuel element in operation, may create problems of mechanical failure of fuel plate due to the vibration induced by the flow in the channels. In the case of critical velocity may cause collapse of the plates. Although there is no rupture of the fuel plates during collapse, excessive permanent deflections of the plates can cause blockage of the flow channel in the reactor core and lead to overheating in the plates. For this study were developed an experimental bench capable of high volume flows (Q = 100 m3/h) and a test section that simulates a plate-like fuel element with three cooling channels. The test section was constructed with aluminum and acrylic plates and was instrumented with straingauge sensors, pressure sensors, accelerometer and a tube of pitot. The dimensions of the test section were based on the dimensions of the Fuel Element of the Brazilian Multipurpose Reactor (RMB), whose project is being coordinated by the National Commission of Nuclear Energy (CNEN). The experiments performed attained the objective of reaching Miller\'s critical velocity condition with the collapse of the plates. The critical velocity was reached with 14.5 m/s leading to the consequent plastic deformation of the plates forming the flow channel. The central channel had a 3mm aperture in its center, causing a large blockage of the flow in the lateral channels. This behavior was observed visually during the disassembly of the test section, illustrated and discussed in the results analysis presented in this work. Blocking of the channels was also observed by means of graphs of pressure drop and graphs of the deformations of the entrance, center and exit of the plates against the average speed vii of the section of tests. It was observed a decrease of the hydraulic resistance of the section of tests due to the increase of the transversal section of flow in the central channel and an exponential increase of the deformations when the critical speed occurrence. Comparatively, the value obtained for critical velocity in the test section through the experiments was of the order of 85% of the value obtained by calculation with Miller\'s theoretical expression. The experiments allowed a better understanding of the structure fluid interaction in plate type fuel elements such as: natural vibration frequency values, elastic fluid instability and development of techniques for the detection of critical velocity values.

La vitesse critique de flottement est un facteur essentiel à la conception aéronautique car elle caractérise le régime de vol au-delà duquel l’aéronef risque de subir un mécanisme de ruine. L’objectif de cette thèse est d’étudier l’impact des incertitudes d’origines aléatoires et épistémiques sur la limite de stabilité linéaire pour des configurations aéroélastiques idéalisées. Dans un premier temps, un problème de propagation directe d’incertitudes aléatoires relatives à des paramètres de fabrication d’une aile en forme de plaque en matériau composite stratifié a été considéré. La représentation du matériau par la méthode polaire lève la contrainte de grande dimensionnalité du problème stochastique initial et permet l’utilisation du Chaos Polynômial. Cependant, la corrélation introduite par cette paramétrisation nécessite une adaptation de la base polynômiale. Enfin, un algorithme d’apprentissage automatique a été employé pour traiter des discontinuités dans le comportement modal des instabilités aéroélastiques. Le second volet de la thèse concerne la quantification d’incertitudes de modélisation de caractère épistémique qui sont introduites au niveau de l’opérateur aérodynamique. Ces travaux, menés à partir d’un formalisme Bayésien, permettent non seulement d’établir des probabilités de modèle, mais aussi de calibrer les coefficients des modèles dans un contexte stochastique afin d’obtenir des prédictions robustes pour la vitesse critique. Enfin, une étude combinée des deux types d’incertitude permet d’améliorer le processus de calibration. / The critical flutter velocity is an essential factor in aeronautic design because it caracterises the flight envelope outside which the aircraft risks to be destroyed. The goal of this thesis is the study of the impact of uncertainties of aleatory and epistemic origin on the linear stability limit of idealised aeroelastic configurations. First, a direct propagation problem of aleatory uncertainties related to manufacturing parameters of a rectangular plate wing made of a laminated composite material was considered. The representation of the material through the polar method alleviates the constraint of the high number of dimensions of the initial stochastic problem, which allows the use of polynomial chaos. However, the correlation which is introduced by this parametrisation requires an adaption of the polynomial basis. Finally, a machine learning algorithm is employed for the treatment of discontinuities in the modal behaviour of the aeroelastic instabilities. The second part of the thesis is about the quantification of modelling uncertainties of epistemic nature which are introduced in the aerodynamic operator. This work, which is conducted based on a Bayesian formalism, allows not only to establish model probabilities, but also to calibrate the model coefficients in a stochastic context in order to obtain robust predictions for the critical velocity. Finally, a combined study of the two types of uncertainty allows to improve the calibration process.

If air is entrained in a bottom outlet of a dam in an uncontrolled way, the resulting air pockets may cause problems such as blowback, blowout and loss of discharge capacity. In order to provide guidance for bottom outlet design and operation, this study examines how governing parameters affect air entrainment, air-pocket transport and de-aeration and the surrounding flow structure in pipe flows. Both experimental and numerical approaches are used. Air can be entrained into the bottom outlet conduit due to vortex formation at the intake if the intake submergence is not sufficient. The influent of the intake entrance profiles and channel width on the critical submergence were studied in the experiment. The experimental study was performed to investigate the incipient motion of air pockets in pipes with rectangular and circular cross sections. The critical velocity is dependent on pipe slope, pipe diameter, pipe roughness and air-pocket volume. If the pipe is horizontal, air removal is generally easier in a rectangular pipe than in a circular pipe. However, if the pipe is downward-inclined, air removal is easier in a circular pipe. When a bottom outlet gate opens, air can become entrained into the conduit in the gate shaft downstream of the gate. Using FLUENT software, the transient process of air entrainment into a prototype bottom outlet during gate opening is simulated in three dimensions. The simulations show in the flow-pattern changes in the conduit and the amount of air entrainment in the gate shaft. The initial conduit water level affects the degree of air entrainment. A de-aeration chamber is effective in reducing water surface fluctuations at blowout. High-speed particle image velocimetry (HSPIV) were applied to investigate the characteristics of the flow field around a stationary air pocket in a fully developed horizontal pipe flow. The air pocket generates a horseshoe vortex upstream and a reverse flow downstream. A shear layer forms from the separation point. Flow reattachment is observed for large air pockets. The air―water interface moves with the adjacent flow. A similarity profile is obtained for the mean streamwise velocity in the shear layer beneath the air pocket. / <p>QC 20140211</p>

Grandes esforços vêm sendo realizados atualmente com o objetivo de diagnosticar vibrações em estruturas e equipamentos, para máquinas rotativas se requer atenção ainda maior, pois correm o risco de se auto excitarem. Este trabalho tem por objetivo expor uma metodologia em dinâmica de rotores para diminuição da amplitude da resposta no domínio da frequência. Com essa finalidade, o rotor utiliza uma discretização de elementos finitos de viga de Timoshenko com funções da classe C0. A programação é implementada no programa acadêmico Meflab desenvolvida na plataforma do software MATLAB®, e no software ANSYS® Workbench para algumas validações. Os resultados numéricos são comparados com os resultados do modelo de literatura. A implementação da otimização se dá com o uso do toolbox de algoritmos genéticos existente no software MATLAB®, onde os parâmetros do algoritmo de otimização são escolhidos como sendo os diâmetros da seção transversal de cada elemento finito. A função objetivo escolhida está associada à diminuição da resposta no domínio da frequência para excitações do tipo desbalanceamento ou a evitar o posicionamento de alguma velocidade crítica dentro de um intervalo de frequências predeterminado. As restrições do problema encontram-se associadas às dimensões máximas e mínimas das seções transversais dos elementos do eixo. Em geral, para a rotação onde se requeria a diminuição da amplitude da resposta no domínio da frequência, havia uma tendência das antirressonâncias mais próximas se deslocarem para o ponto requerido. / Great efforts are been made recently in order to diagnose vibrations in structures and equipments. Rotary machines require even greater attention, for they carry the risk of auto-excitation. This paper has as an objective the exposition a rotor dynamics methodology to minimize the response amplitude in the frequency domain. With this goal, the rotor is discretized using finite Timoshenko Beams elements, with C0 class functions. The programming is implemented in the academic software Meflab, coded in the MATLAB® platform, and in the software ANSYS® Workbench to validate some results. The numerical results are compared with the results from literature model. The optimization is made utilizing the genetic algorithms toolbox existing in the MATLAB® software, where the optimization algorithms parameters are chosen as being the transverse section diameters of each finite element. The objective function chosen is associated with the response minimization in the frequency domain for unbalanced type excitations or to avoid the existence of a critical velocity within a predetermined frequency range. The problem restrictions are associated to maximum and minimum transverse section dimensions of the axis elements, as well as its total volume variation. In general, for the rotation where the frequency domain amplitude response minimization was required, there was a tendency for the closest anti-resonances to shift themselves to the required point.

Grandes esforços vêm sendo realizados atualmente com o objetivo de diagnosticar vibrações em estruturas e equipamentos, para máquinas rotativas se requer atenção ainda maior, pois correm o risco de se auto excitarem. Este trabalho tem por objetivo expor uma metodologia em dinâmica de rotores para diminuição da amplitude da resposta no domínio da frequência. Com essa finalidade, o rotor utiliza uma discretização de elementos finitos de viga de Timoshenko com funções da classe C0. A programação é implementada no programa acadêmico Meflab desenvolvida na plataforma do software MATLAB®, e no software ANSYS® Workbench para algumas validações. Os resultados numéricos são comparados com os resultados do modelo de literatura. A implementação da otimização se dá com o uso do toolbox de algoritmos genéticos existente no software MATLAB®, onde os parâmetros do algoritmo de otimização são escolhidos como sendo os diâmetros da seção transversal de cada elemento finito. A função objetivo escolhida está associada à diminuição da resposta no domínio da frequência para excitações do tipo desbalanceamento ou a evitar o posicionamento de alguma velocidade crítica dentro de um intervalo de frequências predeterminado. As restrições do problema encontram-se associadas às dimensões máximas e mínimas das seções transversais dos elementos do eixo. Em geral, para a rotação onde se requeria a diminuição da amplitude da resposta no domínio da frequência, havia uma tendência das antirressonâncias mais próximas se deslocarem para o ponto requerido. / Great efforts are been made recently in order to diagnose vibrations in structures and equipments. Rotary machines require even greater attention, for they carry the risk of auto-excitation. This paper has as an objective the exposition a rotor dynamics methodology to minimize the response amplitude in the frequency domain. With this goal, the rotor is discretized using finite Timoshenko Beams elements, with C0 class functions. The programming is implemented in the academic software Meflab, coded in the MATLAB® platform, and in the software ANSYS® Workbench to validate some results. The numerical results are compared with the results from literature model. The optimization is made utilizing the genetic algorithms toolbox existing in the MATLAB® software, where the optimization algorithms parameters are chosen as being the transverse section diameters of each finite element. The objective function chosen is associated with the response minimization in the frequency domain for unbalanced type excitations or to avoid the existence of a critical velocity within a predetermined frequency range. The problem restrictions are associated to maximum and minimum transverse section dimensions of the axis elements, as well as its total volume variation. In general, for the rotation where the frequency domain amplitude response minimization was required, there was a tendency for the closest anti-resonances to shift themselves to the required point.

Grandes esforços vêm sendo realizados atualmente com o objetivo de diagnosticar vibrações em estruturas e equipamentos, para máquinas rotativas se requer atenção ainda maior, pois correm o risco de se auto excitarem. Este trabalho tem por objetivo expor uma metodologia em dinâmica de rotores para diminuição da amplitude da resposta no domínio da frequência. Com essa finalidade, o rotor utiliza uma discretização de elementos finitos de viga de Timoshenko com funções da classe C0. A programação é implementada no programa acadêmico Meflab desenvolvida na plataforma do software MATLAB®, e no software ANSYS® Workbench para algumas validações. Os resultados numéricos são comparados com os resultados do modelo de literatura. A implementação da otimização se dá com o uso do toolbox de algoritmos genéticos existente no software MATLAB®, onde os parâmetros do algoritmo de otimização são escolhidos como sendo os diâmetros da seção transversal de cada elemento finito. A função objetivo escolhida está associada à diminuição da resposta no domínio da frequência para excitações do tipo desbalanceamento ou a evitar o posicionamento de alguma velocidade crítica dentro de um intervalo de frequências predeterminado. As restrições do problema encontram-se associadas às dimensões máximas e mínimas das seções transversais dos elementos do eixo. Em geral, para a rotação onde se requeria a diminuição da amplitude da resposta no domínio da frequência, havia uma tendência das antirressonâncias mais próximas se deslocarem para o ponto requerido. / Great efforts are been made recently in order to diagnose vibrations in structures and equipments. Rotary machines require even greater attention, for they carry the risk of auto-excitation. This paper has as an objective the exposition a rotor dynamics methodology to minimize the response amplitude in the frequency domain. With this goal, the rotor is discretized using finite Timoshenko Beams elements, with C0 class functions. The programming is implemented in the academic software Meflab, coded in the MATLAB® platform, and in the software ANSYS® Workbench to validate some results. The numerical results are compared with the results from literature model. The optimization is made utilizing the genetic algorithms toolbox existing in the MATLAB® software, where the optimization algorithms parameters are chosen as being the transverse section diameters of each finite element. The objective function chosen is associated with the response minimization in the frequency domain for unbalanced type excitations or to avoid the existence of a critical velocity within a predetermined frequency range. The problem restrictions are associated to maximum and minimum transverse section dimensions of the axis elements, as well as its total volume variation. In general, for the rotation where the frequency domain amplitude response minimization was required, there was a tendency for the closest anti-resonances to shift themselves to the required point.