Análise robusta de modelos estruturais utilizando métodos probabilísticos

Dissertação (mestrado) - Universidade Federal de Santa Catarina, Centro Tecnológico, Programa de Pós-Graduação em Engenharia Mecânica, Florianópolis, 2015.Na modelagem da dinâmica de estruturas, um modelo mecânico-matemático é construído com a finalidade de determinar o comportamento de estruturas reais. Nesse processo, duas fontes de incertezas podem ser destacadas: as limitações dos processos de manufatura que, por mais complexos e modernos, não podem eliminar as variabilidades de produção e a incapacidade de representar matematicamente processos físicos complexos de maneira exata. Esta dissertação tem como principal objetivo a determinação numérica do comportamento dinâmico de um tubo de descarga acoplado à carcaça de um compressor hermético considerando as incertezas do modelo. Inicialmente, é construído um modelo linear determinístico para cada componente estrutural e, a partir desse modelo médio, desenvolve-se um modelo probabilístico não paramétrico. Essa abordagem estocástica, bastante recente, encontra-se amparada no Princípio de Máxima Entropia, levando em conta as restrições físicas de um sistema dinâmico como vínculos em um problema de otimização. Em uma primeira análise, a resposta dinâmica de cada componente é avaliada separadamente, enquanto a dispersão do modelo de cada estrutura, controlada por três parâmetros, é determinada utilizando resultados experimentais. Por fim, a determinação do comportamento dinâmico do tubo de descarga acoplado à carcaça é calculada através de um método de síntese modal de componentes. Essa metodologia permite acessar a resposta robusta do sistema quando as incertezas não estão distribuídas de maneira homogênea no modelo. Os resultados mostram que a determinação da velocidade quadrática média na superfície da carcaça do compressor, quando excitada através de uma extremidade do tubo de descarga, é bastante sensível às incertezas no modelo numérico do tubo. Esse resultado sugere que a construção de modelos mais representativos para o tubo de descarga é parte fundamental para a obtenção de modelos mais fiéis às respostas reais do sistema. Além disso, a aplicação da abordagem probabilística não paramétrica juntamente com o método de síntese modal de componentes mostrou-se uma ferramenta interessante para o projeto de novos tubos de descarga, uma vez que tal metodologia é capaz de considerar as variabilidades do processo de manufatura e, de maneira conjunta, as limitações do modelo numérico utilizado.Abstract : During structural modeling process, a mathematical-mechanical model is constructed to determine the dynamical behavior of physical structures. In this process, two sources of uncertainties should be highlighted: the limitations of the manufacturing processes, even complex and modern ones, which cannot eliminate production variabilities, and the incapability to represent, mathematically, complex physical processes accurately. The main purpose of this master thesis is to evaluate the dynamical behavior of a discharge pipe coupled with an hermetic compressor shell considering the uncertainties of the numerical model. Firstly, a linear deterministic model is constructed for each compressor's component and, from this mean model, a nonparametric probabilistic model is implemented. This recent stochastic approach is derived from the maximum entropy principle, which considers the physical properties of the dynamical system as constraints in an optimization problem. In a first analysis, the dynamical responses from the compressor components are individually analyzed, while the dispersion of each numerical model, controlled by three parameters, are fitted by using experimental results. Finally, the dynamical responses of the discharge pipe coupled with the compressor's shell are calculated according to a component mode synthesis method, which is able to represent nonhomogeneous uncertainties in the numerical model. The obtained result shows that the averaged square velocity on the housing surface, due to an excitation on the discharge pipe, is very sensitive with respect to the tube model uncertainties. This result suggests that a more representative discharge pipe model is very important to achieve a better model for the coupled system. Moreover, the nonparametric probabilistic approach, together with the component mode synthesis method, seems to be an interesting tool to design new discharge pipes considering the limitations of the numerical model as well as the variability of the manufacturing processes

Computation of quasi-periodic localised vibrations in nonlinear cyclic and symmetric structures using harmonic balance methods

In this paper we develop a fully numerical approach to compute quasi-periodic vibrations bifurcating from nonlinear periodic states in cyclic and symmetric structures. The focus is on localised oscillations arising from modulationally unstable travelling waves induced by strong external excitations. The computational strategy is based on the periodic and quasi-periodic harmonic balance methods together with an arc-length continuation scheme. Due to the presence of multiple localised states, a new method to switch from periodic to quasi-periodic states is proposed. The algorithm is applied to two different minimal models for bladed disks vibrating in large amplitudes regimes. In the first case, each sector of the bladed disk is modelled by a single degree of freedom, while in the second application a second degree of freedom is included to account for the disk inertia. In both cases the algorithm has identified and tracked multiple quasi-periodic localised states travelling around the structure in the form of dissipative soliton

Solitons in cyclic and symmetric structures

The main aim of this thesis is to investigate the emergence of localised vibrations in cyclic and perfectly symmetric structures due to the effect of nonlinearity. The application is on vibrations of bladed disks of aircraft engines, i.e. mechanical structures composed of ideally symmetric sectors assembled in a cyclic configuration. Firstly, a minimal model of a bladed disk vibrating under the effect of geometric nonlinearities is introduced. The system is composed of a chain of Duffing oscillators, and the cubic-type stiffening effect represents, physically, a first-order correction for an underlying nonlinear stress-strain dependence. The analysis starts from a weakly nonlinear and slowly varying approximation, where the system can be studied using insights from a continuum wave mechanics approach. The investigation shows that homogeneous solutions might become unstable when nonlinear effects are large, leading to strong and stable localised vibrations. In order to solve more complex physical models, where the weakly nonlinear and slowly varying approximation might not be valid, a fully numerical approach is proposed. The strategy is based on the periodic and quasi-periodic harmonic balance methods, and thus the displacement of each degree of freedom of the model is assumed to be written as a truncated Fourier series. Firstly, the same chain of Duffing oscillators investigated before is readdressed, and the results obtained from the fully numerical implementation are discussed. In the following, a more complex physical model for a bladed disk, where each sector is modelled by two degrees of freedom, is addressed numerically. The results show similar features compared to the simple chain of Duffing oscillators, i.e. large engine order excitations might lead to localised vibrations due to geometric nonlinearities. In order to study a real geometry, a dummy bladed disk is introduced and solutions of this physical system are computed from fully nonlinear finite elements. The results show that localised solutions might bifurcate from homogeneous states when the displacement levels are about 10\% of the blade thickness. Finally, the effect of impacts is considered. The main motivation is to investigate the possibility of energy localisation when nonlinearities go beyond the cubic-type stiffening effects. The results show that homogeneous states might self-modulate and localise, spontaneously, through envelope dynamics even if nonlinearity arises due to non-smooth interactions. Lastly, the emergence of localised vibrations due to nonlinear effects is investigated experimentally. A test rig composed of two weakly coupled beams impacting against rigid stoppers is designed. The results show that strong localised regimes might be observed, and the final configuration depends on the underlying initial conditions only. A minimal model with piecewise linear springs is then developed in order to study, phenomenologically, the observed results. The theoretical analysis shows that the measured localised regimes might be seen as results of bifurcated normal modes if the system is analysed from a modal analysis perspective.Open Acces

Reconstruction of governing equations from vibration measurements for geometrically nonlinear systems

Data-driven system identification procedures have recently enabled the reconstruction of governing differential equations from vibration signal recordings. In this contribution, the sparse identification of nonlinear dynamics is applied to structural dynamics of a geometrically nonlinear system. First, the methodology is validated against the forced Duffing oscillator to evaluate its robustness against noise and limited data. Then, differential equations governing the dynamics of two weakly coupled cantilever beams with base excitation are reconstructed from experimental data. Results indicate the appealing abilities of data-driven system identification: underlying equations are successfully reconstructed and (non-)linear dynamic terms are identified for two experimental setups which are comprised of a quasi-linear system and a system with impacts to replicate a piecewise hardening behavior, as commonly observed in contacts.Deutsche ForschungsgemeinschaftItalian Ministry of Education, University and Research (MIUR

Reconstruction of Governing Equations from Vibration Measurements for Geometrically Nonlinear Systems

Data-driven system identification procedures have recently enabled the reconstruction of governing differential equations from vibration signal recordings. In this contribution, the sparse identification of nonlinear dynamics is applied to structural dynamics of a geometrically nonlinear system. First, the methodology is validated against the forced Duffing oscillator to evaluate its robustness against noise and limited data. Then, differential equations governing the dynamics of two weakly coupled cantilever beams with base excitation are reconstructed from experimental data. Results indicate the appealing abilities of data-driven system identification: underlying equations are successfully reconstructed and (non-)linear dynamic terms are identified for two experimental setups which are comprised of a quasi-linear system and a system with impacts to replicate a piecewise hardening behavior, as commonly observed in contacts

Relatórios de Estágios de 2011 (A)

Neste arquivo contém os RAENOS dos estagiários do Curso de Física que apresentaram na Coordenadoria de Estágio no período de Agosto de 2011 À Dezembro de 2011.UFS

Termos de Compromisso de Estágio de 2011 (H)

Neste arquivo contém os TCEs de 25 estagiário no período de 08/08/2011 à 23/01/2012UFS