Otimização, análise dinâmica e de incertezas de uma treliça espacial utilizando o método dos elementos finitos
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Data
2017-03-28
Autores
Pires, Felipe Alves [UNESP]
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Editor
Universidade Estadual Paulista (Unesp)
Resumo
Devido à crescente demanda por sistemas de comunicação, monitoramento territorial e previsão climática, satélites foram lançados por agências espaciais e aproximadamente 2,271 orbitam a Terra. Com o objetivo de minimizar os custos de lançamento, estruturas espaciais devem possuir forma de sistemas do tipo treliça devido à considerável redução de peso por serem montadas em uma forma triangular e com materiais leves, por exemplo, alumínio. Como resultado, alguns problemas como flexibilidade e baixo amortecimento estrutural podem aparecer. Diante disso, um método de controle deve ser aplicado para manter os níveis de vibração em pequenas escalas. Neste trabalho, um método de controle passivo é aplicado a uma treliça espacial utilizando o método dos elementos finitos (MEF). MEF é uma das ferramentas computacionais mais utilizadas para analisar estruturas sujeitas a vibrações, tornando possível prever as respostas em frequência (FRFs) do sistema. Este trabalho utiliza a técnica de otimização \textit{simulated annealing} para otimizar a norma $\mathcal{H}_{2}$ para os seis primeiros modos de vibrar do sistema de maneira a encontrar as coordenadas de cada nó da treliça que minimizem o valor de norma $\mathcal{H}_{2}$. Nota-se que, com a minimização da norma $\mathcal{H}_{2}$, novas coordenadas das juntas podem ser obtidas e novas FRFs podem ser estudadas. Algumas amplitudes de vibração das FRFs diminuíram, porém algumas amplitudes aumentaram. Verifica-se que houve regiões que o controle aplicado foi efetivo e outras que a técnica não mostrou eficiência. O método estatístico simulação de Monte Carlo também é aplicado para estudar as incertezas associadas ao sistema. Para isto, histogramas são utilizados para verificação das distribuições das frequências naturais. É pertinente a necessidade de avaliar se as distribuições de frequências apresentam um comportamento de curvas normais e para isso alguns parâmetros estatísticos, como \textit{skewness}, \textit{kurtosis} e teste de qui-quadrado, são utilizados. Observa-se que, as incertezas relacionadas à geometria da estrutura afetam mais o sistema do que as incertezas ligadas às propriedades do material.
Due to the increasing demand for monitoring for telecommunication systems, weather and territorial monitoring, satellites have been launched by space agencies and 2,271 still orbit Earth. In order to minimize rocket launch costs, space structures should have the shape of trusses because of the significant weight reduction for being assembled in a triangular form and with elements made of light materials (e.g. aluminum). As a result of it, some problems such as flexibility and low structural damping may arise. For this reason, a control method must be applied to maintain the requirements of vibration levels in these types of structures. This work applies a passive vibration control to a space truss utilizing the Finite Element Method (FEM). FEM is one of the most used computational tools to analyze structures under vibrations and is also used to predict the system’s frequency response functions (FRFs). This work utilizes the optimization technique simulated annealing in order to optimize the norm H2 of the first six vibration modes of the system so that it’s possible to find the coordinates of each node of the space truss that minimize the value of H2. It has been noticed that with the minimization of the H2 norm, new coordinates of the joints can be obtained so that new FRFs can be studied. Some amplitudes of vibration in the FRFs diminished, however, some of them rose. It is verified that there are regions where the control method applied was effective and others where the control technique was not effective. The statistical method Monte Carlo simulation is also applied to study the uncertainties associated to the system. For this study, histograms are utilized to verify the natural frequencies distributions. It is pertinent the need to evaluate whether the frequencies distributions present the behavior of normal curves and to do this, some statistical parameters such as skewness, kurtosis and chi-square test are used. It has been noticed that uncertainties related to the geometry of the structure affect the system more than uncertainties related to the material properties.
Due to the increasing demand for monitoring for telecommunication systems, weather and territorial monitoring, satellites have been launched by space agencies and 2,271 still orbit Earth. In order to minimize rocket launch costs, space structures should have the shape of trusses because of the significant weight reduction for being assembled in a triangular form and with elements made of light materials (e.g. aluminum). As a result of it, some problems such as flexibility and low structural damping may arise. For this reason, a control method must be applied to maintain the requirements of vibration levels in these types of structures. This work applies a passive vibration control to a space truss utilizing the Finite Element Method (FEM). FEM is one of the most used computational tools to analyze structures under vibrations and is also used to predict the system’s frequency response functions (FRFs). This work utilizes the optimization technique simulated annealing in order to optimize the norm H2 of the first six vibration modes of the system so that it’s possible to find the coordinates of each node of the space truss that minimize the value of H2. It has been noticed that with the minimization of the H2 norm, new coordinates of the joints can be obtained so that new FRFs can be studied. Some amplitudes of vibration in the FRFs diminished, however, some of them rose. It is verified that there are regions where the control method applied was effective and others where the control technique was not effective. The statistical method Monte Carlo simulation is also applied to study the uncertainties associated to the system. For this study, histograms are utilized to verify the natural frequencies distributions. It is pertinent the need to evaluate whether the frequencies distributions present the behavior of normal curves and to do this, some statistical parameters such as skewness, kurtosis and chi-square test are used. It has been noticed that uncertainties related to the geometry of the structure affect the system more than uncertainties related to the material properties.
Descrição
Palavras-chave
Treliça espacial, Controle passivo, MEF, Simulated annealing, Simulação de Monte Carlo