Orientador: Marcos Silveira / Resumo: O objetivo deste trabalho é explorar a atenuação da vibração de uma metaestrutura por meio da adição de absorvedores de forma periódica. Além disso é explorada a atenuação da vibração de uma metaestrutura quando um absorvedor com rigidez cúbica não linear é incluído sem aumentar a massa total. As metaestruturas, e especificamente as estruturas periódicas, apresentam características interessantes para atenuação da vibração que não são encontradas em estruturas clássicas. Estas características foram exploradas para aplicações automotivas e aeroespaciais, entre outras, pois estruturas com baixa massa são fundamentais para essas indústrias. Também é desejável manter baixos níveis de vibração em uma ampla faixa de frequência. Foi demonstrado que a adição de absorvedores de vibração em um arranjo periódico pode fornecer atenuação da vibração para entrada de choque sem aumentar a massa total de uma estrutura. Neste trabalho, a resposta dinâmica do sistema proposto é comparada a uma metaestrutura base sem absorvedores e uma metaestrutura com absorvedores lineares para entrada harmônica através da avaliação da norma H2 da resposta em frequência. Um procedimento de otimização é mostrado para encontrar a posição ideal e os coeficientes de rigidez do absorvedor não linear. A resposta dinâmica do sistema ideal é obtida numericamente e mostra que a adição de um absorvedor não linear pode melhorar a atenuação da vibração. / Abstract: The objective of this work is to explore the vibration attenuation of a metastructure by periodically adding absorbers, and the vibration attenuation of a metastructure is explored when a nonlinear cubic stiffness absorber is included without increasing the total mass. Metastructures, and specifically periodic structures, present interesting characteristics for vibration attenuation that are not found in classical structures. These characteristics have been explored for automotive and aerospace applications, among others, as structures with low mass are paramount for these industries, and keeping low vibration levels in wide frequency range is also desirable. It has been shown that the addition of vibration absorbers in a periodic arrangement can provide vibration attenuation for shock input without increasing the total mass of a structure. In this work, the dynamical response of the proposed system is compared to a base metastructure without absorbers and a metastructure with linear absorbers for harmonic input via the evaluation of the H2 norm of the frequency response. An optimisation procedure is shown to find the optimal position and stiffness coefficients of the nonlinear absorber. The dynamical response of the optimal system are obtained numerically, and shows that the addition of one nonlinear absorber can improve vibration attenuation. / Mestre

Orientador: Tamotsu Hirata / Banca: José Elias Tomazini / Banca: Luiz Fernando Costa Nascimento / Resumo: Um modelo fundamentado nos sistemas multicorpos, com sete corpos rígidos e oito corpos flexíveis, com três graus de liberdade para cada um dos corpos rígidos está sendo proposto. Os corpos rígidos são providos de inércia e os corpos flexíveis trabalham como juntas e não são providos de inércia. A solução numérica do modelo foi obtida com o método Runge-Kutta. Os parâmetros de influência, curvatura inicial da espinha lombar, posições dos centros geométricos das vértebras, tórax e da sacrum-pélvis, e o ponto de aplicação da força póstero-anterior (PA), foram obtidos de radiografia digital de cada paciente. O modelo foi simulado com dados de literaturas (obtidos de experimentos in vivo e em peças anatômicas). Os resultados foram satisfatórios do ponto de vista dos terapeutas e apresentam-se em conformidade com outros modelos propostos. O modelo oferece vantagem na aplicação individualizada a cada paciente pelos terapeutas, e foi construído com a metodologia de análise das forças aplicadas e suas reações diferentemente de outros modelos que apoiam-se nos métodos de análise das energias. O objetivo principal deste trabalho será o de avaliar o comportamento dinâmico do segmento lombar da coluna vertebral humana incluindo as massas do tórax e da pelve, por um modelo não-linear da rigidez viscoelástica estabelecido a partir da relação força-deslocamento obtida por experimentação in vivo. / Abstract: Evaluate a dynamic behavior of the human lumbar spine, with non-linear viscoelastic stiffness model followed by experimental data. Many of the techniques for the clinical treatment of dysfunction acting on lumber segments of the human spine have been based in the application of a postero anterior forces. Existing models to predict the state of lumber segments are restricted to evaluate general characteristic, furthermore, they use unrealistic boundary condition for its analysis. Periodic oscillatory posteroanterior forces were applied on each vertebra with initial lordotic curvature of the lumbar spine. A model is based on the multibody system of seven rigid bodies and eight deformable bodies representing human spine composed of thoratic, lumber and sacrum-pelvis segments. On each lumber were considered three degree of freedom(posterior - anterior, axial and flexion - extension). The rigid bodies are provided with inerti and the deformable bodies, wich would as joints with no inertia provided. Numerical solution of proposed model was solved with Ringe-Kutta methods. Parameter of influence, initial lordotic curvature, positions of the geometric centers of the vertebras, thorax and of the sacrum-pelvis, and point of application of the posteroanterior force (PA) were evaluated from x-ray image of patients. Nonlinear stiffness character introducedin the model affects the motion stability when periodic posteroanterior forces are applied to one vertebra. / Doutor

Made available in DSpace on 2014-06-11T19:34:58Z (GMT). No. of bitstreams: 0 Previous issue date: 2006-04-24Bitstream added on 2014-06-13T19:04:57Z : No. of bitstreams: 1 duque_lhm_dr_guara.pdf: 1861000 bytes, checksum: 826224c8ed71ff732f9aa6af40eab143 (MD5) / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES) / Um modelo fundamentado nos sistemas multicorpos, com sete corpos rígidos e oito corpos flexíveis, com três graus de liberdade para cada um dos corpos rígidos está sendo proposto. Os corpos rígidos são providos de inércia e os corpos flexíveis trabalham como juntas e não são providos de inércia. A solução numérica do modelo foi obtida com o método Runge-Kutta. Os parâmetros de influência, curvatura inicial da espinha lombar, posições dos centros geométricos das vértebras, tórax e da sacrum-pélvis, e o ponto de aplicação da força póstero-anterior (PA), foram obtidos de radiografia digital de cada paciente. O modelo foi simulado com dados de literaturas (obtidos de experimentos in vivo e em peças anatômicas). Os resultados foram satisfatórios do ponto de vista dos terapeutas e apresentam-se em conformidade com outros modelos propostos. O modelo oferece vantagem na aplicação individualizada a cada paciente pelos terapeutas, e foi construído com a metodologia de análise das forças aplicadas e suas reações diferentemente de outros modelos que apoiam-se nos métodos de análise das energias. O objetivo principal deste trabalho será o de avaliar o comportamento dinâmico do segmento lombar da coluna vertebral humana incluindo as massas do tórax e da pelve, por um modelo não-linear da rigidez viscoelástica estabelecido a partir da relação força-deslocamento obtida por experimentação in vivo. / Evaluate a dynamic behavior of the human lumbar spine, with non-linear viscoelastic stiffness model followed by experimental data. Many of the techniques for the clinical treatment of dysfunction acting on lumber segments of the human spine have been based in the application of a postero anterior forces. Existing models to predict the state of lumber segments are restricted to evaluate general characteristic, furthermore, they use unrealistic boundary condition for its analysis. Periodic oscillatory posteroanterior forces were applied on each vertebra with initial lordotic curvature of the lumbar spine. A model is based on the multibody system of seven rigid bodies and eight deformable bodies representing human spine composed of thoratic, lumber and sacrum-pelvis segments. On each lumber were considered three degree of freedom(posterior - anterior, axial and flexion - extension). The rigid bodies are provided with inerti and the deformable bodies, wich would as joints with no inertia provided. Numerical solution of proposed model was solved with Ringe-Kutta methods. Parameter of influence, initial lordotic curvature, positions of the geometric centers of the vertebras, thorax and of the sacrum-pelvis, and point of application of the posteroanterior force (PA) were evaluated from x-ray image of patients. Nonlinear stiffness character introducedin the model affects the motion stability when periodic posteroanterior forces are applied to one vertebra.

This thesis is focused on design of piezoelectric energy harvester with additional nonlinear stiffness. Linear generator has very narrow resonance frequency bandwidth. It makes the resonance mechanism very sensitive to tuning up of the resonance frequency and it can be tuned only for one narrow vibration peak. The main idea for using of the vibration energy harvester with nonlinear stiffness is to make resonance frequency bandwidth wider, so the generator will be useable for more excitation frequencies. In this thesis is used generator Midé V21BL and additional nonlinear stiffness is realized with permanent magnets.

This thesis deals with the design of a dynamic model of a harmonic drive. It includes a theoretical study aimed at the analysis of the harmonic drive gearing principle and its nonlinear properties. The first part of the practical section deals with the analytical calculation of the nondeformed geometry of the Flexspline. Based on these results, several simulations in ANSYS are created to identify torsional characteristics of a harmonic drive. These simulation models are further enhanced by the analysis of clearance, backlash and inaccuracies and their impact on torsional properties. By using MATLAB /Simulink, several dynamic submodels are created representing the individual characteristics of nonlinearities in harmonic drives. Furthermore, a comprehensive dynamic model is created of the mechatronic system which is describing all nonlinearities and kinematic error of the transmission. The dynamic model is also experimentally verified based on its damping properties.

The use of continuously welded rails (CWR) governs the longitudinal stress caused by seasonal temperature changes, bending of supporting structure and braking/accelerating due to passing trains. Those three loads have been regulated in Eurocode1 and accomplished by the national codes like DIN Fb-101 in Germany. An additional loading case identified and treated in this thesis is the load due to a change of the coupling stiffness in longitudinal direction between the track and bridge. This additional load occurs as a consequence of the employment of a nonlinear stiffness law which increases the restoring force by a factor of 3 when the situation of the track changes from ‘unloaded’ to ‘loaded’ due to a passing train. This particular phenomenon has not been mentioned in the codes so far though it is a natural consequence of fundamental conditions in those codes. For CWR the longitudinal coupling between the rail and bridge plays an important role. This coupling interface is created either by a ballast, for a ballasted track, or by a fastening system in the case of slab track. The deformation state of the coupling interface characterizes the behaviour of the system, whether elastic or plastic. Therefore, the nonlinear behaviour is valid for the system. To accommodate the nonlinear nature, a sequential loading analysis is used, taking into account the loading history. As the change situation due to a passing train happens in a short time, the influence of the mass acceleration should be taken into account in the system’s equilibrium. This aspect is investigated by treating the dynamic load as an impulse-like load. However, a realistic load needs some time to affect the whole bridge, thus the continuous change of stiffness is used to simulate the dynamic analysis. There is a lack of information on determining the value of coupling stiffness in longitudinal direction caused by a passing train. Therefore, it is important to evaluate the coupling stiffness from field measurements in order to find reliable values. The implementation of the load onto several typical bridges shows that the change of the coupling stiffness increases the stresses and it should not be neglected. The evaluation of the load due to a change of the coupling stiffness accompanied by bending of the supporting structure gives satisfactory results by using the static analysis only. Thus, a dynamic analysis can be avoided. Multiple cycles of passing trains occurring after seasonal temperature change indicate a significant increase of elastic parts along the track-bridge coupling interface and a decrease in stresses in the rails. Thus the danger of deterioration is reduced significantly. / Die Verwendung von durchgehend geschweißten Schienen auf Brücken führt zu zusätzlichen Längsspannungen infolge der Lastfälle jahreszeitliche Temperaturänderung, Brückendurchbiegung und Bremsen/Anfahren. Diese drei Lasten sind durch den Eurocode 1 vorgegeben und in die nationale deutsche Norm DIN Fb-101 integriert. In dieser Arbeit wird erstmals ein weiterer Lastfall identifiziert und behandelt, der durch den Wechsel der Koppelsteifigkeit in Längsrichtung zwischen Gleis und Tragwerk bei der Zugüberfahrt begründet wird. Dieser Lastfall wird hier mit „Ruck“ bezeichnet und ist eine zwangsläufige Konsequenz des nichtlinearen Längsverschiebewiderstandes, wie er im EC 1 und im DIN Fb-101 vorgegeben ist. Dennoch wurden die Auswirkungen auf das Systemverhalten bisher nicht untersucht. Bei einem Wechsel vom unbelasteten Gleis zum belasteten Gleis während einer Zugüberfahrt erhöht sich zum Beispiel der Längsverschiebewiderstand für ein Schottergleis um den Faktor 3! Die dadurch bedingte Veränderung des Zusammenwirkens zwischen Gleis und Tragwerk führt zu einer Veränderung des Systemzustandes und damit zu veränderten Schienenspannungen. Für durchgehend geschweißte Schienen spielt die Längskopplung zwischen Schiene und Brücke eine wesentliche Rolle. Beim Schottergleis wird sie dargestellt durch die Einbettung des Gleisrostes im Schotterbett im Zusammenwirken mit der Schienenbefestigung. Bei der festen Fahrbahn durch das Befestigungssystem. Für kleine Deformationen ist die Koppelsteifigkeit proportional zur Relativverschiebung zwischen Gleis und Brücke. Darüberhinaus geht das linear elastische Verhalten in ein quasi plastisches Verhalten mit konstanter Koppelkraft über. Folgerichtig ist die Behandlung einer Lastenfolge nur in inkrementeller Weise unter Einbeziehung der Verformungsgeschichte mechanisch korrekt. Die Lastfälle Bremsen/Anfahren, Brückendurchbiegung und Ruck ereignen sich nur während der Zugüberfahrt; also in relativ kurzer Zeit, dann allerdings mit einem erheblichen Lastgradienten. Somit stellt sich die Frage nach dem Einfluss der Massenbeschleunigungen, die in dieser Arbeit geklärt wird. Die im Fachbericht genanntenWerte für den Längsverschiebewiderstand des belasteten Gleises basieren auf einer relativ geringen Datenmenge. Aus diesem Grund werden die Messdaten einer umfangreichen Feldmessung mit Zugüberfahrten zu Aussagen über den Längsverschiebewiederstand herangezogen und die Problematik derartiger Messungen beleuchtet. Die unterschiedlichen Modellierungen des Lastfalls „Ruck“, einmal rein statisch und zum anderen dynamisch, ergeben übereinstimmende Schienenlängsspannungen für die statische und die kontinuierliche dynamische Variante. Somit kann auf die aufwändige dynamische Analyse verzichtet werden. Mehrere Zyklen von Zugüberfahrten im Anschluss an eine jahreszeitliche Temperaturänderung bewirken einen signifikanten Abbau der Durchrutschbereiche, also eine Erhöhung der elastischen Abschnitte in der Koppelfuge zwischen Bauwerk und Gleis verbunden mit einer Abnahme der Schienendruckspannungen. Somit hilft dieser Effekt dem System, der jahreszeitlichen Temperaturänderung zu widerstehen.

This thesis deals with modifications to the construction of vibration-to-electricity energy converter, which is one of possible solutions to problem of sustainable and stable energy source for wireless sensor supply. Upon the exploration of the present state of this problem, new construction of generator is proposed. The aim of this proposal is to enhance the existing generator properties with respect to retention of its dimensions and its weight. Results obtained by simulations of model with proposed parameters are presented and analysed.

The use of continuously welded rails (CWR) governs the longitudinal stress caused by seasonal temperature changes, bending of supporting structure and braking/accelerating due to passing trains. Those three loads have been regulated in Eurocode1 and accomplished by the national codes like DIN Fb-101 in Germany. An additional loading case identified and treated in this thesis is the load due to a change of the coupling stiffness in longitudinal direction between the track and bridge. This additional load occurs as a consequence of the employment of a nonlinear stiffness law which increases the restoring force by a factor of 3 when the situation of the track changes from ‘unloaded’ to ‘loaded’ due to a passing train. This particular phenomenon has not been mentioned in the codes so far though it is a natural consequence of fundamental conditions in those codes. For CWR the longitudinal coupling between the rail and bridge plays an important role. This coupling interface is created either by a ballast, for a ballasted track, or by a fastening system in the case of slab track. The deformation state of the coupling interface characterizes the behaviour of the system, whether elastic or plastic. Therefore, the nonlinear behaviour is valid for the system. To accommodate the nonlinear nature, a sequential loading analysis is used, taking into account the loading history. As the change situation due to a passing train happens in a short time, the influence of the mass acceleration should be taken into account in the system’s equilibrium. This aspect is investigated by treating the dynamic load as an impulse-like load. However, a realistic load needs some time to affect the whole bridge, thus the continuous change of stiffness is used to simulate the dynamic analysis. There is a lack of information on determining the value of coupling stiffness in longitudinal direction caused by a passing train. Therefore, it is important to evaluate the coupling stiffness from field measurements in order to find reliable values. The implementation of the load onto several typical bridges shows that the change of the coupling stiffness increases the stresses and it should not be neglected. The evaluation of the load due to a change of the coupling stiffness accompanied by bending of the supporting structure gives satisfactory results by using the static analysis only. Thus, a dynamic analysis can be avoided. Multiple cycles of passing trains occurring after seasonal temperature change indicate a significant increase of elastic parts along the track-bridge coupling interface and a decrease in stresses in the rails. Thus the danger of deterioration is reduced significantly. / Die Verwendung von durchgehend geschweißten Schienen auf Brücken führt zu zusätzlichen Längsspannungen infolge der Lastfälle jahreszeitliche Temperaturänderung, Brückendurchbiegung und Bremsen/Anfahren. Diese drei Lasten sind durch den Eurocode 1 vorgegeben und in die nationale deutsche Norm DIN Fb-101 integriert. In dieser Arbeit wird erstmals ein weiterer Lastfall identifiziert und behandelt, der durch den Wechsel der Koppelsteifigkeit in Längsrichtung zwischen Gleis und Tragwerk bei der Zugüberfahrt begründet wird. Dieser Lastfall wird hier mit „Ruck“ bezeichnet und ist eine zwangsläufige Konsequenz des nichtlinearen Längsverschiebewiderstandes, wie er im EC 1 und im DIN Fb-101 vorgegeben ist. Dennoch wurden die Auswirkungen auf das Systemverhalten bisher nicht untersucht. Bei einem Wechsel vom unbelasteten Gleis zum belasteten Gleis während einer Zugüberfahrt erhöht sich zum Beispiel der Längsverschiebewiderstand für ein Schottergleis um den Faktor 3! Die dadurch bedingte Veränderung des Zusammenwirkens zwischen Gleis und Tragwerk führt zu einer Veränderung des Systemzustandes und damit zu veränderten Schienenspannungen. Für durchgehend geschweißte Schienen spielt die Längskopplung zwischen Schiene und Brücke eine wesentliche Rolle. Beim Schottergleis wird sie dargestellt durch die Einbettung des Gleisrostes im Schotterbett im Zusammenwirken mit der Schienenbefestigung. Bei der festen Fahrbahn durch das Befestigungssystem. Für kleine Deformationen ist die Koppelsteifigkeit proportional zur Relativverschiebung zwischen Gleis und Brücke. Darüberhinaus geht das linear elastische Verhalten in ein quasi plastisches Verhalten mit konstanter Koppelkraft über. Folgerichtig ist die Behandlung einer Lastenfolge nur in inkrementeller Weise unter Einbeziehung der Verformungsgeschichte mechanisch korrekt. Die Lastfälle Bremsen/Anfahren, Brückendurchbiegung und Ruck ereignen sich nur während der Zugüberfahrt; also in relativ kurzer Zeit, dann allerdings mit einem erheblichen Lastgradienten. Somit stellt sich die Frage nach dem Einfluss der Massenbeschleunigungen, die in dieser Arbeit geklärt wird. Die im Fachbericht genanntenWerte für den Längsverschiebewiderstand des belasteten Gleises basieren auf einer relativ geringen Datenmenge. Aus diesem Grund werden die Messdaten einer umfangreichen Feldmessung mit Zugüberfahrten zu Aussagen über den Längsverschiebewiederstand herangezogen und die Problematik derartiger Messungen beleuchtet. Die unterschiedlichen Modellierungen des Lastfalls „Ruck“, einmal rein statisch und zum anderen dynamisch, ergeben übereinstimmende Schienenlängsspannungen für die statische und die kontinuierliche dynamische Variante. Somit kann auf die aufwändige dynamische Analyse verzichtet werden. Mehrere Zyklen von Zugüberfahrten im Anschluss an eine jahreszeitliche Temperaturänderung bewirken einen signifikanten Abbau der Durchrutschbereiche, also eine Erhöhung der elastischen Abschnitte in der Koppelfuge zwischen Bauwerk und Gleis verbunden mit einer Abnahme der Schienendruckspannungen. Somit hilft dieser Effekt dem System, der jahreszeitlichen Temperaturänderung zu widerstehen.