Integrating damping and non-linearities in a vibration design process

Classical vibration design uses modes and transfer functions generated with the superposition principle to allow the verification of design objectives. If redesign is needed, one optimizes mass and stiffness in order to modify the transfer until the specification is met. Integrating damping and non-linearities in the optimization of detailed industrial models is however still considered a major difficulty, even though the physical mechanisms are well known. Approaches to handle viscoelastic damping and time domain modal damping are thus discussed. Distributed non-linearities, such as contact and friction, are becoming accessible to transient simulation, but lead to responses where modes are no longer defined. It is however illustrated that operational deflection shapes, associated with a singular value decomposition of the response, give similar information. Finally, a fundamental aspect of non-linear vibration simulation is the volume of output and the associated numerical cost. Model reduction is a key ingredient of practical approaches and a perspective on related issues is given

Solving an Elliptic PDE Eigenvalue Problem via Automated Multi-Level Substructuring and Hierarchical Matrices

We propose a new method for the solution of discretised elliptic PDE eigenvalue problems. The new method combines ideas of domain decomposition, as in the automated multi-level substructuring (short AMLS), with the concept of hierarchical matrices (short H-matrices) in order to obtain a solver that scales almost optimal in the size of the discrete space. Whereas the AMLS method is very effective for PDEs posed in two dimensions, it is getting very expensive in the three-dimensional case, due to the fact that the interface coupling in the domain decomposition requires dense matrix operations. We resolve this problem by use of data-sparse hierarchical matrices. In addition to the discretisation error our new approach involves a projection error due to AMLS and an arithmetic error due to H-matrix approximation. A suitable choice of parameters to balance these errors is investigated in examples. Mathematics Subject Classification (2000) 65F15, 65F30, 65F50, 65H17, 65N25, 65N5

Modelado de Multifractura Discreta en Materiales Quasi-Frágiles Monografía

In this work, a new modal reanalysis algorithm based on AMLS method is proposed for local, nontop ological,high rank modifications. Instead of using some perturbation technique[44, 85] or using the Kirsch Combined method[223, 226], the proposed reanalysis procedure uses AMLS method to perform the reanalysisexp lo itin g the concept of substructure. The modification affects a particular path on the hierarchical partitiontree, which traces back from the modified nodes to the root node. In our proposed modal reanalysis algorithmonly the modified substructures and affected substructures due to the propagation need to be recalculated. This algorithm can significantly improve the efficiency compared to the full recalculation. Some of the advantages are: 1. Larger substructure size increases moderately the accurate of the AMLS method. For medium substructure size, the efficiency of AMLS method can be improved using a sparse linear solver and sparse eigen solver. 2. If the modified substructures are recalculated using exact method, the reanalysis does not affect the precision of the final results by AMLS method. The eigen-values computed are accurate as the precision of AMLS method is. 3. The amplitude of modification is not limited to small modification change, as being required by approximate method. 4. It is only required to identify the corresponding modified and affected sub-structures for performing the recalculation and save the data of the non-modified sub-structures. In the worst case, the computational cost is no more than the fresh AMLS-solution. 5. It is more suitable for large-scale eigen value problem with local high-rank modifications. &nbsp

Secure random numbers from quantum images.

: Generazione di numeri casuali sicuri tramite l’implementazione di QRNG ottico basato sul modello PBS (Polarize Beam Splitter

Análise dinâmica de estruturas periódicas utilizando uma abordagem de propagação de ondas e técnicas de sub-estruturação

Orientadores: José Roberto de França Arruda, Jean-Mathieu MencikTese (doutorado) - Universidade Estadual de Campinas, Faculdade de Engenharia MecânicaResumo: Nesta tese de doutorado, o método dos elementos finitos ondulatórios é utilizado para cálculo da resposta harmônica de sistemas mecânicos envolvendo estruturas com periodicidade unidimensional, i.e., estruturas compostas por subestruturas idênticas arranjadas ao longo de uma direção. Tais sistemas mecânicos podem ser complexos e são comumente encontrados em aplicações de engenharia como, por exemplo, nas fuselagens de aviões. A primeira parte da tese é dedicada ao cálculo das ondas que se propagam ao longo dessas estruturas. Uma breve revisão da literatura sobre as formulações disponíveis para o problema de autovalor associado ao método dos elementos finitos ondulatórios é apresentada, assim como um estudo dos erros numéricos induzidos por estes problemas de autovalor no caso de um guia de ondas sólido. Na segunda parte desta tese, modelagens de superelementos para estruturas periódicas são propostas. Neste contexto, matrizes de rigidez dinâmica e de receptância ou flexibilidade de estruturas periódicas são expressas a partir dos modos de onda. Comparadas às matrizes de rigidez dinâmica e receptância obtidas pelo método dos elementos finitos convencional, as matrizes baseadas no método dos elementos finitos ondulatórios são calculadas de forma bastante rápida e sem perda de acuracidade. Ademais, uma estratégia eficiente de redução de ordem de modelo é apresentada. Comparada às formulações que utilizam a base completa de ondas, esta estratégia proporciona redução do tempo computacional requerido para cálculo da resposta forçada de estruturas periódicas. De fato, é mostrado que elementos espectrais numéricos de alta ordem podem ser construídos a partir do método dos elementos finitos ondulatórios. Isto constitui uma alternativa ao método dos elementos espectrais convencional, cuja utilização está limitada a estruturas simples para as quais soluções analíticas por ondas existam. A motivação por trás das formulações de matrizes de superelementos a partir do método dos elementos finitos ondulatórios está na utilização do conceito de ondas numéricas para calcular a resposta harmônica de sistemas mecânicos acoplados que envolvam estruturas com periodicidade unidimensional e junções elásticas a partir de procedimentos de montagem clássicos de elementos finitos ou técnicas de decomposição de domínio. Este assunto é tratado na terceira parte desta tese. Nesse caso, o método de Craig-Bampton é usado para expressar as matrizes de superelementos de junções por meio de modos estáticos e de interface fixa. Um critério baseado no método dos elementos finitos ondulatórios é considerado para a seleção dos modos da junção que mais contribuem para a resposta forçada do sistema. Isto também contribui para o aumento da eficiência da simulação numérica de sistemas acoplados. Finalmente, na quarta parte desta tese, o método dos elementos finitos ondulatórios é utilizado para mostrar que é possível projetar estruturas periódicas com potencial para funcionar como filtros de vibração em bandas de frequência específicas. Com o intuito de destacar a relevância dos desenvolvimentos propostos nessa tese, ensaios numéricos envolvendo guias de onda sólidos, pórticos planos e estruturas tridimensionais do tipo fuselagem aeronáutica são realizadosAbstract: In this thesis, the wave finite element (WFE) method is used for assessing the harmonic forced response of mechanical systems that involve structures with one-dimensional periodicity, i.e., structures which are made up of several identical substructures along one direction. Such mechanical systems can be quite complex and are commonly encountered in engineering applications, e.g., aircraft fuselages. The first part of the thesis is concerned with the computation of wave modes traveling along these structures. A brief literature review is presented regarding the available formulations for the WFE eigenproblem, which need to be solved for expressing the wave modes, as well as a study of the numerical errors induced by these eigenproblems in the case of a solid waveguide. In the second part of the thesis, the WFE-based superelement modeling of periodic structures is proposed. In this context, the dynamic stiffness matrices and receptance matrices of periodic structures are expressed in terms of wave modes. Compared to the conventional FE-based dynamic stiffness and receptance matrices, the WFE-based matrices can be computed in a very fast way without loss of accuracy. In addition, an accurate strategy for WFE-based model order reduction is presented. It provides significant computational time savings for the forced response analysis of periodic structures compared to WFE-based superelement modeling, which makes use of the full wave basis. Indeed, it is shown that higher-order numerical spectral elements can be built by means of the WFE method. This is an alternative to the conventional spectral element method, which is limited to simple structures for which closed-form wave solutions exist. The motivation behind the formulation of WFE-based superelement matrices is the use of the concept of numerical wave modes to assess the forced response of coupled mechanical systems that involve structures with one-dimensional periodicity and coupling elastic junctions through classic finite element assembly procedures or domain decomposition techniques. This issue is addressed in the third part of this thesis. In this case, the Craig-Bampton method is used to express superelement matrices of coupling junctions by means of static and fixed-interface modes. A WFE-based criterion is considered to select among junction modes those that contribute most to the system forced response. This also contributes to enhancing the efficiency of the numerical simulation of coupled systems. Finally, in the fourth part of this thesis, the WFE method is used to show the potential of designing periodic structures which work as vibration filters within specific frequency bands. In order to highlight the relevance of the developments proposed in this thesis, numerical experiments which involve solid waveguides, two-dimensional frame structures, and three-dimensional aircraft fuselage-like structures are carried outDoutoradoMecanica dos Sólidos e Projeto MecanicoDoutora em Engenharia Mecânica2010/17317-9FAPES

Shapes & DOF: on the use of modal concepts in the context of parametric non-linear studies

Physical responses tend to lie within restricted subspaces even for parametric problems. For a given subspace, the choice of a basis defines Degree Of Freedom (DOF) and this choice may give interesting meaning to the associated amplitudes. Classical modal analysis builds subspaces combining modeshapes and static responses. Parametric loads for non-linear, damped, variable, ... structures are discussed to extend the theory and illustrated for test and simulation cases. Challenges in shape extraction and basis generation techniques are then detailed. Introducing the ability to manipulate models with variable junction properties, component material and geometry, load and operating conditions, ... opens new questions on the quantification and tracking of changes and objectives throughout design exploration. The definition of a reference linear system and the use of global and/or local modal DOF are shown to provide an interesting perspective

Bootstrap Based Surface Reconstruction

Surface reconstruction is one of the main research areas in computer graphics. The goal is to find the best surface representation of the boundary of a real object. The typical input of a surface reconstruction algorithm is a point cloud, possibly obtained by a laser 3D scanner. The raw data from the scanner is usually noisy and contains outliers. Apart from creating models of high visual quality, assuring that a model is as faithful as possible to the original object is also one of the main aims of surface reconstruction. Most surface reconstruction algorithms proposed in the literature assess the reconstructed models either by visual inspection or, in cases where subjective manual input is not possible, by measuring the training error of the model. However, the training error underestimates systematically the test error and encourages overfitting. In this thesis, we provide a method for quantitative assessment in surface reconstruction. We integrate a model averaging method from statistics called bootstrap and define it into our context. Bootstrapping is a resampling procedure that provides statistical parameter. In surface fitting, we obtained error estimate which detect error caused by noise or bad fitting. We also define bootstrap method in context of normal estimation. We obtain variance and error estimates which we use as a quality measure of normal estimates. As application, we provide smoothing algorithm for point clouds and normal smoothing that can handle feature area. We also developed feature detection algorithm