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The objective of this work is to develop mathematical simulation models for predicting the transient behaviour of strings and beams subjected to impacts. The developed models are applied to study the dynamics of the piano and the sitar. For simulating rigid point impacts on continuous systems, a new method is proposed based on the unit impulse response. The developed method allows one to relate modal velocities before and after impact, without requiring the integration of the system equations of motion during impact. The proposed method has been used to model the impact of a pinned-pinned beam with a rigid obstacle. Numerical simulations are presented to illustrate the inability of the collocation-based coefficient of restitution method to predict an accurate and energy-consistent response. The results using the unit-impulse-based coefficient of restitution method are also compared to those obtained with a penalty approach,with good agreement. A new moving boundary formulation is presented to simulate wrapping contacts in continuous systems impacting rigid distributed obstacles. The free vibration response of an ideal string impacting a distributed parabolic obstacle located at its boundary is analyzed to understand and simulate a sitar string. The portion of the string in contact with the obstacle is governed by a different partial differential equation (PDE) from the free portion represented by the classical string equation. These two PDEs and corresponding boundary conditions, along with the transversality condition that governs the dynamics of the moving boundary, are obtained using Hamilton's principle. A Galerkin approximation is used to convert them into a system of nonlinear ordinary differential equations, with time-dependent mode-shapes as basis functions. The advantages and disadvantages of the proposed method are discussed in comparison to the penalty approach for simulating wrapping contacts. Finally, the model is used to investigate the mechanism behind the generation of the buzzing tone in a sitar. An alternate formulation using the penalty approach is also proposed, and the results are contrasted with those obtained using the moving boundary approach. A model for studying the interaction between a flexible beam and a string at a point including friction has also been developed. This model is used to study the interaction between a piano hammer and the string. A realistic model of the piano hammer-string interaction must treat both the action mechanism and the string. An elastic stiff string model is integrated with a dynamic model of a compliant piano action mechanism with a flexible hammer shank. Simulations have been used to compare the mechanism response for impact on an elastic string and a rigid stop. Hammer head scuffing along the string, as well as length of time in contact, were found to increase where an elastic string was used, while hammer shank vibration amplitude and peak contact force decreased. Introducing hammer-string friction decreases the duration of contact and reduces the extent of scuffing. Finally, significant differences in hammer and string motion were predicted for a highly flexible hammer shank. Initial contact time and location, length of contact period, peak contact force, hammer vibration amplitude, scuffing extent, and string spectral content were all influenced.

The objective of this work is to develop mathematical simulation models for predicting the transient behaviour of strings and beams subjected to impacts. The developed models are applied to study the dynamics of the piano and the sitar. For simulating rigid point impacts on continuous systems, a new method is proposed based on the unit impulse response. The developed method allows one to relate modal velocities before and after impact, without requiring the integration of the system equations of motion during impact. The proposed method has been used to model the impact of a pinned-pinned beam with a rigid obstacle. Numerical simulations are presented to illustrate the inability of the collocation-based coefficient of restitution method to predict an accurate and energy-consistent response. The results using the unit-impulse-based coefficient of restitution method are also compared to those obtained with a penalty approach,with good agreement. A new moving boundary formulation is presented to simulate wrapping contacts in continuous systems impacting rigid distributed obstacles. The free vibration response of an ideal string impacting a distributed parabolic obstacle located at its boundary is analyzed to understand and simulate a sitar string. The portion of the string in contact with the obstacle is governed by a different partial differential equation (PDE) from the free portion represented by the classical string equation. These two PDEs and corresponding boundary conditions, along with the transversality condition that governs the dynamics of the moving boundary, are obtained using Hamilton's principle. A Galerkin approximation is used to convert them into a system of nonlinear ordinary differential equations, with time-dependent mode-shapes as basis functions. The advantages and disadvantages of the proposed method are discussed in comparison to the penalty approach for simulating wrapping contacts. Finally, the model is used to investigate the mechanism behind the generation of the buzzing tone in a sitar. An alternate formulation using the penalty approach is also proposed, and the results are contrasted with those obtained using the moving boundary approach. A model for studying the interaction between a flexible beam and a string at a point including friction has also been developed. This model is used to study the interaction between a piano hammer and the string. A realistic model of the piano hammer-string interaction must treat both the action mechanism and the string. An elastic stiff string model is integrated with a dynamic model of a compliant piano action mechanism with a flexible hammer shank. Simulations have been used to compare the mechanism response for impact on an elastic string and a rigid stop. Hammer head scuffing along the string, as well as length of time in contact, were found to increase where an elastic string was used, while hammer shank vibration amplitude and peak contact force decreased. Introducing hammer-string friction decreases the duration of contact and reduces the extent of scuffing. Finally, significant differences in hammer and string motion were predicted for a highly flexible hammer shank. Initial contact time and location, length of contact period, peak contact force, hammer vibration amplitude, scuffing extent, and string spectral content were all influenced.

Orientador: Gilberto Pechoto de Melo / Banca: Vicente Lopes Júnior / Banca: Raquel Santini Leandro Rade / Resumo: Hoje em dia um dos fatores de interesse das indústrias no desenvolvimento de novas técnicas de detecção e localização de falhas é a preocupação com a segurança de seus sistemas, tendo-se a necessidade de supervisão e monitoramento de modo que as falhas sejam detectadas e corrigidas o mais rápido possível. Verifica-se na prática que determinados parâmetros dos sistemas podem variar durante o processo, devido a características específicas ou o desgaste natural de seus componentes. Sabe-se também que, mesmo nos sistemas bem projetados, a ocorrência de trincas em alguns componentes pode provocar perdas econômicas ou conduzir a situações perigosas. Os observadores de estado podem reconstruir os estados não medidos do sistema, desde que os mesmos sejam observáveis, tornando possível, desta forma, estimar as medidas nos pontos de difícil acesso. A técnica dos observadores de estado consiste em desenvolver um modelo para o sistema em análise e comparar a estimativa da saída com a saída medida, a diferença entre os dois sinais presentes resulta em um resíduo que é utilizado para análise. Neste trabalho foi montado um banco de observadores associado a um modelo de trinca de modo a acompanhar o progresso da mesma. Os resultados obtidos através de simulações computacionais em uma placa engastada discretizada pela técnica dos elementos finitos e as análises experimentais realizadas foram bastante satisfatórios, validando a metodologia desenvolvida. / Abstract: Nowadays a main factor of interest in industries in the development of new techniques for detection and localization of faults is the concern with the security of its systems. There is the need of supervising and monitoring the machines to detect and correct the fault as soon as possible. In practice it is verified that some determined parameters of the systems can vary during the process, due to the specific characteristics or the natural wearing of its components. It is known that even in well-designed systems the occurrence of cracks in some components can induce economic losses or lead to dangerous situations. The state observers methodology can reconstruct the unmeasured states of the system, since they are observable, becoming possible in this way to estimate the measures at points of difficult access. The technique of state observers consists of developing a model for the system under analysis and to compare the estimated with the measured exit, and the difference between these two signals results in a residue that is used for analysis. In this work was set up a bank of observers associated to a model of crack in order to follow its progress. The results obtained through computational simulations in a cantilever plate discretized by using the finite elements technique and the accomplished experimental analysis were sufficiently satisfactory, validating the developed methodology. / Mestre

Les travaux effectués, dans le cadre de cette thèse, concernent l’analyse et la synthèse de systèmes dynamiques continus complexes de grande dimension. Pour la classe des systèmes étudiés, est mise en exergue en particulier l’importance du choix de la description des systèmes sur l’étendue des résultats pouvant être obtenus lorsque la méthode d’étude de la stabilité est fixée.L’utilisation des normes vectorielles comme fonction d’agrégation et du critère pratique de Borne et Gentina pour l’étude de la stabilité, associée à la description des systèmes par des matrices caractéristiques de forme en flèche, a permis l’élaboration de nouvelles conditions suffisantes de stabilisabilité de systèmes dynamiques continus non linéaires, monovariables et multivariables, formulées en théorèmes et corollaires.Ces résultats obtenus, pour une classe de processus, pouvant être caractérisés par des matrices instantanées de forme en flèche mince, ont été généralisés au cas des matrices quelconques, pouvant être mises sous forme en flèche mince généralisée ou en flèche épaisse.Les critères élaborés, soit pour l’analyse de la stabilité soit pour la synthèse d’une loi de commande stabilisante, sont ensuite exploités, avec succès, pour la formulation de nouvelles conditions suffisantes de vérification des propriétés de synchronisation, d’anti-synchronisation et de synchronisation hybride de systèmes chaotiques du type maître-esclave, d’un grand intérêt, en particulier, pour garantir une transmission sécurisée / This Thesis deals with the analysis and the synthesis of dynamic large scale continuous systems depending on the choice of the system description.Stability and stabilisability proposed studies are based on the use of vector norms as an aggregation function and of the practical Borne-Gentina criterion, associated to the description of the system by instantaneous characteristic matrix in arrow form.Practical stability conditions, easy to use, are obtained for both dynamic nonlinear continuous single input single output systems and multiple inputs multiple outputs ones, formulated by means of theorems and corollaries. These obtained results for thin arrow form, are generalized to the case of matrices, which can be putted under thin generalized arrow form or thick arrow form. The proposed stability and stabilisability criteria are afterwards, successfully, exploited to formulate new sufficient conditions, guaranteeing the synchronization, the anti-synchronization and the hybrid synchronization properties, for chaotic master-slave systems, having an increasing interest throughout their application in the secure communication field

Made available in DSpace on 2014-06-11T19:27:14Z (GMT). No. of bitstreams: 0 Previous issue date: 2008-04-19Bitstream added on 2014-06-13T18:55:45Z : No. of bitstreams: 1 zacarias_at_me_ilha.pdf: 587117 bytes, checksum: 4a907603292d52ff41cf7df3b7718be5 (MD5) / Hoje em dia um dos fatores de interesse das indústrias no desenvolvimento de novas técnicas de detecção e localização de falhas é a preocupação com a segurança de seus sistemas, tendo-se a necessidade de supervisão e monitoramento de modo que as falhas sejam detectadas e corrigidas o mais rápido possível. Verifica-se na prática que determinados parâmetros dos sistemas podem variar durante o processo, devido a características específicas ou o desgaste natural de seus componentes. Sabe-se também que, mesmo nos sistemas bem projetados, a ocorrência de trincas em alguns componentes pode provocar perdas econômicas ou conduzir a situações perigosas. Os observadores de estado podem reconstruir os estados não medidos do sistema, desde que os mesmos sejam observáveis, tornando possível, desta forma, estimar as medidas nos pontos de difícil acesso. A técnica dos observadores de estado consiste em desenvolver um modelo para o sistema em análise e comparar a estimativa da saída com a saída medida, a diferença entre os dois sinais presentes resulta em um resíduo que é utilizado para análise. Neste trabalho foi montado um banco de observadores associado a um modelo de trinca de modo a acompanhar o progresso da mesma. Os resultados obtidos através de simulações computacionais em uma placa engastada discretizada pela técnica dos elementos finitos e as análises experimentais realizadas foram bastante satisfatórios, validando a metodologia desenvolvida. / Nowadays a main factor of interest in industries in the development of new techniques for detection and localization of faults is the concern with the security of its systems. There is the need of supervising and monitoring the machines to detect and correct the fault as soon as possible. In practice it is verified that some determined parameters of the systems can vary during the process, due to the specific characteristics or the natural wearing of its components. It is known that even in well-designed systems the occurrence of cracks in some components can induce economic losses or lead to dangerous situations. The state observers methodology can reconstruct the unmeasured states of the system, since they are observable, becoming possible in this way to estimate the measures at points of difficult access. The technique of state observers consists of developing a model for the system under analysis and to compare the estimated with the measured exit, and the difference between these two signals results in a residue that is used for analysis. In this work was set up a bank of observers associated to a model of crack in order to follow its progress. The results obtained through computational simulations in a cantilever plate discretized by using the finite elements technique and the accomplished experimental analysis were sufficiently satisfactory, validating the developed methodology.

Les travaux effectués dans le cadre de cette thèse présentent une nouvelle approche permettant d’estimer et si possible minimiser l’écart maximum de la sortie par rapport à l’objectif dans le cas des processus non linéaires pour lesquels il n’est pas toujours possible de déterminer une commande permettant d’atteindre exactement un objectif donné.Le concept de norme vectorielle, associé à la définition des systèmes de comparaison par l'approche de la stabilité Borne et Gentina, et le choix de la représentation matricielle qui s’avère particulièrement importante pour l’étude de la stabilité, est proposé dans ce travail, avec succès, pour étudier la stabilité des processus complexes de modèles éventuellement incertainsNous avons défini une technique d’estimation des attracteurs caractérisant le maximum de l’erreur par rapport à l’objectif et par la prise en compte des résultats ainsi obtenus de les affiner par des itérations successives de la procédure présentée.Dans la recherche de commandes, l’approche a été réalisée en définissant celle-ci par retours d’état calculés soit directement, soit à partir d’une linéarisation du modèle du processus dans le voisinage de l’objectif. Une attention toute particulière a été accordée aux processus du type Lur’e Postnikov / A new approach of the estimation of the error between the desired output of a nonlinear complex system and the real one’s is studied by the use of Borne-Gentina vector norm approach and the Benrejeb arrow form description.A new technique of definition of the attractors characterizing the precision of control laws is defined, implementing successive improved determinations. The research of control laws by various types of state or output feedback in presence of uncertainties is proposed, based on a local linearization and control of the system.A special attention has been devoted to the control of nonlinear Lur’e Postnikov type systems

This master's thesis discourse the proposal of the strategy of increasing efficiency of the enterprise. It includes the analysis of the present efficiency level of the company and also a file of math-economical issues, like the riverbed of interconnected flows, whose correct modelling will improve the current entrepreneurial situation.