The application of robotic manipulators in machining systems has gained a great interest in manufacturing because of their lower prices, higher kinematic flexibility and larger workspace compared to conventional CNC machine tools. However, their performance is limited due to the much lower structural rigidity which makes them more susceptible to excessive and unstable vibrations, known as chatter, during the machining process. Highly effective chatter modeling and avoidance methods that have been developed for CNC machining in the past decades are now being used by the industry to design high-performance chatter-free machining operations. The available methods, however, face major difficulties when applied to robotic machining, mainly due to the high flexibility and pose-dependency of the vibration response in robots. High flexibility leads to high-amplitude vibrations which affect the process dynamics and excite structural nonlinearities. The existing approaches to modeling machining vibrations assume linearity of the structural dynamics of the robotic manipulator. This assumption, considering the inherent nonlinearities in the robot’s revolute joints, may cause considerable inaccuracies in predicting the stability of vibrations during the process. This thesis studies the high flexibility and nonlinearity of the robot’s structural dynamics and their effects on chatter vibrations. The research starts with investigating the effects of high flexibility of robot's structure in the process dyamics by considering the modulation of cutting forces by axial vibrations, which is normally ignored in CNC milling due to high rigidity of the machine in this direction. The results of chatter prediction considering this effect are shown and discussed. The rest of the thesis focuses on the structural nonlinearity. Firstly, an experimental study is presented to investigate the extent of nonlinearity in structural dynamics of the robot. The results confirm that structural nonlinearities in robotic machining systems can be effectively excited in the presence of high-amplitude vibrations due to milling forces, such that they cause remarkable differences in chatter prediction. The following step is modeling the structural nonlinearities. For this purpose, the variation of restoring forces with the dynamic response (displacement and velocity) are observed when the robot is subjected to harmonic excitation. Based on the experimental observations, the nonlinear effects are modeled by cubic stiffness and damping characteristics. Parameters of the nonlinear model are then identified using Higher-order Frequency Response Functions (HFRF) extracted from measurements. The identified model can predict the vibration behavior of the robotic machining system when subjected to periodic loads such as milling forces. The developed model of nonlinear structural dynamics is then coupled with the chatter model. Consequently, the system is described by nonlinear Delay Differential Equations (DDE) with periodic coefficients. Bifurcation diagrams for the forced vibrations in the described system are developed using the numerical continuation method. The effects of cutting parameters such as feedrate as well as the nonlinear parameters are studied. The thesis is concluded by proposing the use of in-process FRF in the linear model of chatter stability for quick prediction of stability limits. In this approach, the exact characteristics of the nonlinear mechanisms are not studied; instead, the measured FRF during the milling process are used, which are assumed to represent the nonlinear structural dynamics that are linearized about the applied operational conditions. Two methods of measuring in-process FRF are proposed and employed in the robotic milling system. The measured FRF are then used in the linear chatter model to develop the Stability Lobes Diagram (SLD) which shows the combination of cutting parameters that lead to stable or unstable vibrations. Experimental chatter tests show that better agreement with predictions can be achieved by using in-process FRF instead of FRF measured at the idle state of the system. The results of this thesis contribute to better characterization of vibrations in robotic machining with high-amplitude forces and selecting suitable strategies to enhance productivity of the operation. / Graduate

[pt] Este trabalho tem por objetivo apresentar um sistema integrado para otimização de forma de estruturas planas que tenham comportamento elasto-plástico. A metodologia implementada propõe uma alternativa à forma conservadora com que tradicionalmente as estruturas têm sido otimizadas, ou seja, admitindo-se que as mesmas possuam comportamento linear elástico. O sistema computacional é denominado integrado pois reúne diversos módulos distintos para o tratamento do problema, como modelagem geométrica, geração de malhas de elementos finitos, análise não-linear da resposta da estrutura, análise de sensibilidade,programação matemática e otimização de estruturas. A geometria do contorno da estrutura plana é definida por meio de curvas (paramétricas)B-splines cúbicas. Estas, por sua vez, são determinadas em função de um conjunto de pontos de interpolação (pontos-chave) e condições de contorno em seus vértices extremos. A correta definição da geometria da estrutura é responsável pelo sucesso do processo de otimização. A resposta da estrutura às solicitações do carregamento externo é avaliada pelo método dos elementos finitos. Para isso, é necessário que o domínio da estrutura seja discretizado. No presente trabalho foi empregado um gerador automático de malhas não estruturadas de elementos finitos isoparamétricos. A configuração de equilíbrio da estrutura é obtida através de um procedimento iterativo/incremental envolvendo o método de Newton-Raphson. Localmente, o equilíbrio é satisfeito pela aplicação de um algoritmo implícito de integração de tensões nos pontos que violarem o critério de plastificação do material. A matriz tangente de rigidez é atualizada a cada iteração da análise e é obtida de forma consistente com o algoritmo de integração das tensões, preservando as características de convergência quadrática assintótica inerentes ao método de Newton- Raphson. No procedimento iterativo de otimização é empregado um algoritmo de programac¸ ão quadrática recursiva que requer a avaliação dos gradientes da função-objetivo e restrições. Para tal, foi implementado um método semi-analítico para a determinação das sensibilidades da resposta estrutural envolvidas nas expressôes dos gradientes citados. O método leva em consideração os efeitos da plastificação ocorrida durante o carregamento da estrutura e é dito -exato- por apresentar imprecisões apenas nos casos em que a magnitude da perturbação da variável é muito pequena, não podendo ser representada corretamente pelo hardware. Os exemplos analisados mostram que a consideração do comportamento elastoplástico da estrutura na otimização de sua forma leva a configurações mais eficientes do que aquelas obtidas admitindo-se a relação linear elástica entre deformações e tensões. / [en] The main goal of this work is to present an integrated system for the optimization of plane structures with elastoplastic behavior. The methodology proposes an alternative for the conservative way in which structures traditionally have been optimized, i.e., that they present linear elastic behavior. The computational system is said to be integrated because it congregates distinct modules for the solution of the problem, such as geometric modelling, finite element mesh generation, non-linear structural response analysis, sensitivity analysis, mathematical programming and optimization of structures. The geometry of the plane structure`s boundary is defined by cubic (parametric) B-splines curves. Those, in turn, are determined by a set of interpolation points (key points) and boundary constraints at their ends. The correct definition of the structure`s geometry is responsible for the success of the optimization process.The structural response to the applied loading is evaluated by the finite element method. For that, the domain of the structure must be discretized. In the present work, an automatic unstructured mesh generator of isoparametric finite elements has been used. The equilibrium layout of the structure is obtained by an iterative/incremental procedure using the standard Newton-Raphson method. Locally, the equilibrium is satisfied by applying an implicit stress return mapping algorithm at points which violate the yield criterion of the material. The tangent stiffness matrix is updated at each analysis iteration and it is obtained in a way which is consistent with the return mapping algorithm, so that the asymptotic quadratic rate of convergence of the Newton-Raphson method is preserved. The use of a quadratic recursive programming algorithm in the optimization procedure involves the gradient evaluation of the objective function and constraints. For that, a semi-analytical method for the calculation of the response sensitivities, which appear in the gradient expressions, has been implemented. The technique takes into account the plastic effects which take place during the loading of the structure and is considered - exact- up to round-off errors, which occurs when the magnitude of the perturbation is so small that the hardware cannot accurately represent it.The examples presented demonstrate that the consideration of the elastoplastic behavior of the material during the optimization process leads to structural layouts which are more efficient than of those obtained under the assumption of linear elastic relationship between strains and stresses. / [es] Este trabajo tiene por objetivo presentar un sistema integrado para otimización de forma de extructuras planas que tengan comportamiento elástico-plástico. LA metodología implementada propone una alternativa a la forma conservadora con que tradicionalmente las extructuras han sido optimizadas, o sea, admitiendo que las poseen um comportamiento lineal-elástico. EL sistema computacional se denomina integrado pues reúne diversos módulos para el tratamiento del problema, como modelage geométrica, generación de mallas de elementos finitos, análisis no lineal de la respuesta de la extructura, análisis de sensibilidad,programación matemática y otimización de extructuras. LA geometría del contorno de la extructura plana es definida por medio de curvas (paramétricas)B splines cúbicas. Estas, por su vez, son determinadas en función de un conjunto de puntos de interpolación (puntos claves) y condiciones de contorno en sus vértices extremos. La definición correta de la geometría de la extructura es responsable por el éxito del proceso de otimización. La respuesta de la extructura a las solicitudes de carga externa se evalúa por el método de los elementos finitos. Para esto, es necesario que el dominio de la extructura sea discretizado. En este trabajo se utiliza un generador automático de mallas no extructuradas de elementos finitos isoparamétricos. La configuración de equilíbrio de la extructura se obtiene a través de un procedimiento iterativo/incremental que envuelve el método de Newton Raphson. Localmente, el equilíbrio es satisfecho por la aplicación de un algoritmo implícito de integración de tensiones en los puntos que violen el critério de plastificación del material. La matriz tangente de rigidez se actualiza a cada iteración del análisis y se obtiene de forma consistente con el algoritmo de integración de las tensiones, preservando las características de convergencia cuadrática asintótica inherentes al método de Newton Raphson. En el procedimiento iterativo de otimización se utiliza un algoritmo de programación cuadrática recursiva que requiere la evaluación de los gradientes de la función objetivo y restricciones. Para tal, se implementó un método semi analítico para la determinación de las sensibilidades de la respuesta extructural envolvidas en las expresóes de los gradientes citados. EL método lleva en consideración el hecho de que la plastificación que ocurre durante la carga de la extructura y se dice exacta por presentar imprecisiones apenas en los casos en que la magnitud de la perturbación de la variable es muy pequeña, no puede ser representada correctamente por el hardware. Los ejemplos analizados muestran que la consideración del comportamiento elástico-plástico de la extructura en la otimización de su forma lleva la configuraciones más eficientes de que aquellas obtenidas admitiendo la relación lineal elástica entre deformaciones y tensiones.

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One of the most intriguing properties of light-matter interaction is the ability of an electromagnetic field to exert mechanical forces on polarizable objects. This phenomenon is a direct consequence of the fact that light carries momentum, which in turn can be transferred to matter. Mediated by scattering, this interaction usually manifests itself as a “pushing force” in the direction of beam propagation. However, it is possible to judiciously engineer these optical forces, either by tailoring particle polarizability, and/or by structuring the incident light field. As a simple example, a tightly focused laser beam demonstrates strong gradient forces, which may attract and even trap particles with positive polarizability in the focal volume. The opposite occurs in the regime of negative polarizability, where particles are expelled from the regions of highest intensity. Based on this fundamental principle, one can actively shape the beam using spatial light modulators to manipulate individual objects as well as ensembles of particles suspended in a liquid. In the latter case, a modulation of the local particle concentration is associated with changes of the effective refractive index. The result is an artificial nonlinear medium, whose Kerr-type response can be readily tuned by the parameters of its constituent particles. In the course of this work, we introduce a new class of synthetic colloidal suspensions exhibiting negative polarizabilities, and observe for the first time robust propagation and enhanced transmission of self-trapped light over long distances. Such light penetration in strongly scattering environments is enabled by the interplay between optical forces and self-activated transparency effects. We explore various approaches to the design of negative-polarizability arrangements, including purely dielectric as well as metallic and hybrid nanoparticles. In particular, we find that plasmonic resonances allow for extremely high and spectrally tunable polarizabilities, leading to unique nonlinear light-matter interactions. Here, for the first time we were able to observe plasmonic resonant solitons over more than 25 diffraction lengths, in colloidal nanosuspensions.

A Displacement Based Optimization (DBO) approach was applied to truss design problems with material nonlinearities, to explore feasibility and verify efficiency of the approach to solve such problem. Various truss sizing problems with holonomic (path-independent) elastoplastic laws were investigated. This type of material nonlinearity allows us to naturally extend the linear elastic truss sizing in the DBO setting to nonlinear problems. A computer program that uses the commercially available optimizer DOT by VR&D and IMSL Linear Programming solver by Visual Numerics was developed to solve this type of problems. For comparison, we chose an important class of minimum-weight truss design problems, where holonomic linear strain hardening behavior was used. Additional examples of optimum design of trusses with elastic perfectly plastic material response that could be easily solved by Limit Design approach using linear programming were investigated for comparison. All demonstrated examples were tested successfully using the DBO approach. Solutions of comparable examples were consistent with the available results by other methods. Computational effort associated with the DBO approach was minimal for all the examples studied. Optimum solutions of several examples proved that the DBO approach is particularly suited for truss topology design where removal of truss members is essential. / Master of Science

The focus of this dissertation is the existence, stability, and resulting dynamical evolution of localized stationary solutions to Nonlinear Schr¨odinger (NLS) equations with periodic confining potentials in 2(+1) dimensions. I will make predictions about these properties based on a discrete lattice model of coupled ordinary differential equations with the appropriate symmetry. The latter has been justified by Wannier function expansions in a so-called tight-binding approximation in the appropriate parametric regime. Numerical results for the full 2(+1)-D continuum model will be qualitatively compared with discrete model predictions as well as with nonlinear optics experiments in optically induced photonic lattices in photorefractive crystals. The predictions are also relevant for BECs (Bose-Einstein Condensates) in optical lattices.

This work examines the relationship between Alfred North Whitehead’s process philosophy and the nonlinear dynamical systems framework for studying cognition. I argue that the nonlinear dynamical systems approach to cognitive science presupposes many key elements of his process philosophy. The process philosophical interpretation of nature posits events and the dynamic relations between events as the fundamental substrate of reality, as opposed to static physical substances. I present a brief history of the development of substance thought before describing Whitehead’s characterization of nature as a process. In following, I will examine the both the computational and nonlinear dynamical systems frameworks for investigating cognition. I will show that the computational paradigm is subject to many of the same criticisms as substance. Conversely, I will show that nonlinear dynamical cognitive science avoids these criticisms and is congenial to Whitehead’s philosophy insofar as it is suitable for describing emergent processes. To conclude, I suggest that the nonlinear dynamical cognitive science confirms and validates Whitehead’s philosophy. Furthermore, I argue that process philosophy is an appropriate characterization of nature for guiding inquiry in cognitive science.

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