The objective of this research work was to develop a design tool to analyze and design undamped beam and rotor systems in two dimensions. Systems modeled in two dimensions, such as beams with different moments of inertia, could produce varying responses in the each direction of motion. A coupling between the vertical and horizontal motions also exists in rotor systems mounted of fluid film bearings. The computer program called 2DBEAM has been developed to model and provide analyses of such systems in two dimensions. The tool has been based on an existing design package, BEAM9, which in its present state provides the response of beams and rotors in one plane of motion. The 2DBEAM program has the capability of performing the static response, free vibration, forced dynamic response, and frequency response analyses of a system. The Transfer Matrix Method has been used in the development of the software and an explanation of the method is included in this thesis. Mathematical problems and solutions encountered while developing 2DBEAM are also documented in this study. The code has been tested against analytical and published solutions for the types of analysis mentioned above and on coupled and uncoupled system models. / Master of Science

The purpose of this research is to analyze the statics and dynamics of steel smoke stacks subject to excitation by aerodynamic forces. The wind loads experienced by smoke stacks arise from various phenomenon, the most prominent of which are static drag load, vortex shedding, and atmospheric turbulence. The nature of these loading sources around a cylinder are studied in detail. Both static and dynamic loads are capable of producing large tip deflections, and are of the most prominent design criteria for stack designers. A computer program, STACK1, has been created by modifying an existing analysis code, BEAM8, to be used specifically for stack analysis. This analysis code utilizes the transfer matrix method to perform detailed bending and vibration analyses. This new software has been developed to check stack designs for compliance with appropriate steel stack standards, and provide the designer with information regarding the static and dynamic response of the structure. A detailed analysis is performed to demonstrate the validity of approximating a tapered Timoshenko beam with a series of continuous, constant cross-section beams. / Master of Science

A theoretical study has been carried out on different methods available to analyze complex mufflers. Segmentation methods have been discussed in detail. The latest two port segmentation method has been discussed and employed for a few common muffler configurations, describing its implications and limitations. A new transfer matrix based method has been developed in view of the lacunae of the available approaches. This Integrated Transfer Matrix (ITM) method has been developed particularly to analyze complex mufflers. An Integrated transfer matrix relates the state variables across the entire cross-section of the muffler shell, as one moves along the axis of the muffler, and can be partitioned appropriately in order to relate the state variables of different tubes constituting the cross-section. The method presents a 1-D approach, using transfer matrices of simple acoustic elements which are available in the literature. Results from the present approach have been validated through comparisons with the available experimental and three dimensional FEM based results. The total pressure drop across perforated muffler elements has been measured experimentally and generalized expressions have been developed for the pressure loss across cross-flow expansion, cross-flow contraction elements, etc. These have then been used to derive empirical expressions for flow-acoustic resistance for use in the Integrated Transfer Matrix Method in order to predict the flow-acoustic performance of commercial mufflers. A flow resistance model has been developed to analytically determine the flow distribution and thereby pressure drop of mufflers. Generalized expressions for resistance across the perforated elements have been derived by means of flow experiments as mentioned above. The derived expressions have been implemented in a flow resistance network that has been developed to determine the pressure drop across any given complex muffler. The results have been validated with experimental data.

O trabalho tem por objetivo avaliar diferentes métodos para identificar zeros na matriz de transferência de sistemas MIMO e propor um método novo baseado em análise de correlação. Estes métodos são utilizados durante a etapa de pré-identificação, a fim de se obter informações relevantes que possam ser utilizadas para se reduzir o tempo dos experimentos, diminuir a variabilidade dos parâmetros dos modelos e melhorar a eficácia dos modelos remanescentes. Estes métodos são aplicados a sistemas MIMO lineares, com dados coletados em malha aberta e em malha fechada. É avaliado o ganho obtido em relação à capacidade de predição dos modelos, a redução do tempo de identificação e o ganho de desempenho do controlador MPC que utiliza estes modelos. O trabalho conclui que a informação de zeros resulta em melhorias no tempo de identificação e no desempenho do controlador MPC. / This work aims to evaluate different methods to identify zeros in the transfer matrix of MIMO systems and to propose a new method based on correlation analysis. These methods are used during the pre-identification stage in order to identify relevant information that can be used to reduce the duration of the experiment, decrease model parameter variability and improve the accuracy of the remaining models. These methods are applied to MIMO linear systems, with data collected in open and closed-loop. The gains obtained in relation to the predictive ability of the models, the reduction of identification time and the performance gain of the MPC using these models are evaluated. This work concludes that the zero information results in improvements in identification time and in performance gain of the MPC controller.

O escopo desta dissertação é o desenvolvimento de uma metodologia para identificar os modelos de canais da matriz dinâmica que estejam degradando o desempenho de controladores preditivos, ou MPC (Model Predictive Control), baseado nas técnicas de auditoria e diagnóstico deste tipo de controlador propostas por BOTELHO et al. (2015) e BOTELHO; TRIERWEILER; FARENZENA (2016) e CLARO (2016). A metodologia desenvolvida contempla dois métodos distintos. O primeiro, chamado método direto compensado, tem como base o método direto de identificação em malha fechada (LJUNG, 1987)e compensa cada saída medida do processo de modo a se reter apenas a contribuição do canal que se deseja identificar. O segundo, chamado método do erro nominal, utiliza a definição de saída nominal do processo, proposta por BOTELHO et al. (2015), como métrica para se quantificar o quão próximo o modelo está do comportamento da planta através da minimização do erro nominal. Os métodos foram aplicados ao sistema de quatro tanques cilíndricos (JOHANSSON, 2000) para dois cenários distintos, sendo o primeiro um sistema 2x2 em fase não mínima contendo um MPC trabalhando com setpoint e o segundo um sistema 4x4 em fase mínima com o MPC atuando por faixas. Para o sistema 2x2, se avaliou a influência da localização do canal discrepante (dentro ou fora da diagonal principal da matriz dinâmica de transferência) na eficácia dos métodos. Para o sistema 4x4, o estudo foi voltado para a eficácia dos métodos frentes a controladores que atuam dentro de limites para as variáveis. Os modelos identificados foram comparados pela capacidade de identificar um modelo que capturasse o zero de transmissão da planta e o RGA dinâmico, par ao sistema 2x2, e pelas respostas degrau e diagrama de Bode para o sistema 4x4. O método direto compensado resultou em baixo erro relativo no valor do zero para a discrepância na diagonal principal da matriz dinâmica e alto valor quando a discrepância se encontrava fora da diagonal principal. O método do erro nominal, por sua vez, foi capaz de identificar um modelo cujo zero de transmissão possuía baixo erro relativo frente ao zero da planta em ambos os cenários. No cenário do controlador atuando por faixas, os métodos propostos obtiveram melhores estimativas dos modelos quando comparados com o método concorrente, uma vez que apresentou alto percentual de aderência das saídas simuladas com as saídas medidas. Em todos os cenários estudados, o método do erro nominal se mostrou capaz de identificar um modelo mais robusto, pois este apresentou RGA dinâmico compatível com a planta em todo o range de frequências analisado. / The objective of this dissertation is to develop a method to identify the model for the channel of the dynamic matrix that are affecting the performance of model predictive controllers (MPC), based on the assessment and diagnosis techniques for this type of controller proposed by BOTELHO et al. (2015) e BOTELHO; TRIERWEILER; FARENZENA (2016) and CLARO (2016). The proposed methodology includes two different methods. The first, called the compensated direct method, is based on the closed-loop direct identification method (LJUNG, 1987) and compensates each process measured output in order to retain only the contribution of the channel being identified. The second, called nominal error method, uses the definition of the process nominal output, proposed by BOTELHO et al. (2015), as a metric to quantify how close the model is to the actual plant behavior by minimizing the nominal error. The proposed methods were applied to the quadruple-tank system (JOHANSSON, 2000) for two distinct scenarios, the first being a nonminimum-phase 2x2 system containing a MPC working with setpoint and the second a minimum-phase 4x4 system with the MPC working by ranges. For the 2x2 system, the influence of the model mismatch location (inside or outside the main diagonal of the dynamic transfer matrix) on the effectiveness of the methods was evaluated. For the 4x4 system, the study was focused on the effectiveness of the methods with controllers that operate within limits for the variables. The identified models were compared by the capability of identifying a model with accurate plant transmission zero and dynamic RGA, for the 2x2 system, and by the step responses and Bode diagram for the 4x4 system. The compensated direct method resulted in low relative error in the value of the transmission zero for the model mismatch located in the main diagonal of the dynamic matrix and high relative error when the mismatch was outside the main diagonal. On the other hand, the nominal error method was able to identify a model whose transmission zero had low relative error against the plant zero in both scenarios. In the scenario of a controller working by range, the proposed methods obtained better estimates of the models when compared to the concurrent method, since it presented a high percentage of adherence of the simulated outputs with the measured outputs. In all the studied scenarios, the nominal error method was able to identify a more robust model, since it presented dynamic RGA compatible with the plant in the entire range of analyzed frequencies.

O trabalho tem por objetivo avaliar diferentes métodos para identificar zeros na matriz de transferência de sistemas MIMO e propor um método novo baseado em análise de correlação. Estes métodos são utilizados durante a etapa de pré-identificação, a fim de se obter informações relevantes que possam ser utilizadas para se reduzir o tempo dos experimentos, diminuir a variabilidade dos parâmetros dos modelos e melhorar a eficácia dos modelos remanescentes. Estes métodos são aplicados a sistemas MIMO lineares, com dados coletados em malha aberta e em malha fechada. É avaliado o ganho obtido em relação à capacidade de predição dos modelos, a redução do tempo de identificação e o ganho de desempenho do controlador MPC que utiliza estes modelos. O trabalho conclui que a informação de zeros resulta em melhorias no tempo de identificação e no desempenho do controlador MPC. / This work aims to evaluate different methods to identify zeros in the transfer matrix of MIMO systems and to propose a new method based on correlation analysis. These methods are used during the pre-identification stage in order to identify relevant information that can be used to reduce the duration of the experiment, decrease model parameter variability and improve the accuracy of the remaining models. These methods are applied to MIMO linear systems, with data collected in open and closed-loop. The gains obtained in relation to the predictive ability of the models, the reduction of identification time and the performance gain of the MPC using these models are evaluated. This work concludes that the zero information results in improvements in identification time and in performance gain of the MPC controller.

Neste trabalho estudamos alguns modelos com conservacao de particulas, que apresentam uma transicao de fase entre um estado estacionario ativo e infinitos estados absorventes. Os estados ativos de cada modelo sao compostos por configuracoes equiprovaveis, correspondendo, de acordo com a formulacao gibbsiana da Mecanica Estatistica, a um ensemble microcanonico. Efetuando uma mudanca de ensemble, podemos calcular as grandezas fisicas para cada um destes modelos utilizando a tecnica de matrizes de transferencia, explicada neste trabalho. Realizamos simulacoes destes modelos e confirmamos as hipoteses que sustentam o uso desta tecnica. Por fim, analisamos dois modelos derivados dos anteriores que nao podem ser estudados com base nesta tecnica. / In this work we studied some models with particle conservation which present a phase transition between an active stationary state and infinitely many absorbing states. The active states of each model consist of equiprobable configurations, corresponding, according to Gibbs's formulation of Statistical Mechanics, to a microcanonical ensemble. Carrying out an ensemble change, we can calculate the physical quantities for each one of these models using the transfer matrix technique, explained in this work. We performed simulations of these models and confirmed the hypothesis that sustain the use of this technique. Finally, we analysed two models derived from the previous ones for which this technique cannot be applied.

This research deals with determining the acoustic attenuation of heating, ventilation, and air conditioning (HVAC) ductwork. A finite element approach was developed for calculating insertion loss and breakout transmission loss. Procedures for simulating the source and receiving rooms were developed and the effect of structureborne flanking was included. Simulation results have been compared with measurements from the literature and the agreement is very good. With a good model in place, the work was extended in three ways. 1) Since measurements on full-scale equipment are difficult, scale modeling rules were developed and validated. 2) Two different numerical approaches were developed for evaluating the transmission loss of silencers taking into account the effect of higher order modes. 3) A power transfer matrix approach was developed to assess the acoustic performance of several duct components connected in series.

The present thesis reviews my scientific works on disordered systems from 1995 until today. They can be roughly categorized into three main classes: (1) non-interacting disordered systems, (2) the two-interacting particle problem, and (3) the interplay of disorder and many-particle interaction. A (4)th chapter is concerned with the implementation of the numerical algorithms. The structure of the thesis reflects this division. The reprints have been added at the end of these main divisions according to their context. For the convenience of the reader, I have ordered them in each chapter alphabetically according to the names of the authors. Furthermore, in each citation of my work, the starting page number in the thesis is given, e.g, Ref.\ \cite{EPR97} refers to a paper of Eckle, Punnoose and myself and can be found on page \pageref{EPR97}. Citations which do not refer to my work are numbered and are ordered in the bibliography according to the names of the authors.

With a new range of water jet assemblies under development, CWF Hamilton & Co. Ltd. highlighted the need to establish a validated model for predicting critical speeds. A review of the relevant literature revealed a significant lack of information concerning the operating properties of a lightly loaded, water lubricated marine bearing. Therefore, an instrumented test rig based on a CWF Hamilton & Co. Ltd. ‘HJ364’ water jet assembly was established to evaluate critical speeds and validate the predictive models. A number of analytical and numerical models for predicting critical speeds were investigated. Geometric modifications were made to the test rig and the changes in critical speeds were observed. The ability of the predictive models to measure these observed critical speeds was examined. Driveline mass and driveline overhang were found to have the most significant effects on critical speeds. Modifications to the thrust bearing housing, the impeller mass, the tailpipe stiffness and the marine bearing resulted in no significant shift in critical speeds. However, a change to the geometry of the thrust bearing resulted in a significant shift. This indicated that the thrust bearing was not performing ideally in the test rig. All three models predicted changes in critical speeds relatively accurately. However, the estimates of the critical speeds themselves were somewhat conservative; approximately 10 to 15 percent lower than those measured. Linearisation of the thrust bearing geometry is recommended if greater accuracy is to be achieved. Of all the predictive methods, the Myklestad-Prohl transfer-matrix and the Isolated-Mainshaft finite-element were deemed to be the most flexible and suitable for CWF Hamilton & Co. Ltd.