Submitted by VIVIANE CASSOL MARQUES null (vivicm@gmail.com) on 2018-01-19T17:29:04Z No. of bitstreams: 1 DefesaTese_Viviane_Cassol_Marques_LibraryVersion.pdf: 2942887 bytes, checksum: f212fcfebf6c7edc3efed2df80579420 (MD5) / Approved for entry into archive by Cristina Alexandra de Godoy null (cristina@adm.feis.unesp.br) on 2018-01-19T18:31:18Z (GMT) No. of bitstreams: 1 marques_vc_dr_ilha.pdf: 2942887 bytes, checksum: f212fcfebf6c7edc3efed2df80579420 (MD5) / Made available in DSpace on 2018-01-19T18:31:18Z (GMT). No. of bitstreams: 1 marques_vc_dr_ilha.pdf: 2942887 bytes, checksum: f212fcfebf6c7edc3efed2df80579420 (MD5) Previous issue date: 2017-12-12 / Grandes estruturas, como aviões, navios e até mesmo sistemas de refrigeração, que possuem muitos componentes podem ser substruturados, com o intuito de agilizar e facilitar o cálculo da transmissão vibratória entre seus componentes. Existem diversas formas e domínios em que esta substruração pode ser realizada, sendo a utilizada nesta tese a substruturação no domínio da frequência utilizando para o cálculo as mobilidades medidas nos pontos de acoplamento dos componentes. Esta tese se concentra na substruturação de sistemas dinâmicos que possuem áreas flexíveis de contato como o que ocorre no acoplamento de amortecedores de borracha em sistemas vibratórios, sendo que para estes casos foi verificado que os métodos de substruturação mais usuais não apresentaram bons resultados para frequências superiores a primeira frequência natural do sistema completo, mesmo quando utilizados vários pontos de acoplamento no amortecedor de borracha. Utilizando o cálculo do comprimento de onda em diferentes materiais, neste caso o aço e a borracha, foi possível determinar uma relação entre a distância dos pontos de acoplamento e o comprimento de onda em que a metodologia de substruturação apresenta resultados acurados. Devido a estas limitações dos métodos de substruração, quando acoplamentos flexíveis existem nos subsistemas considerados, uma nova forma de substruração foi apresentada a qual mostrou resultados muito melhores, especialmente quando comparados com os resultados do sistema completo quando substruturado no acoplamento flexível. / Large structures, such as airplanes, ships and even refrigeration systems, which have many components, can be substructured in order to speed up and facilitate the process of calculating the vibratory transmission between the system components. There are several methods and domains in which the substructuring can be done. In this thesis the substructuring method in the frequency domain is chosen to do the calculations, with the mobilities measured at the coupling points of the components. This thesis focuses on the substructuring of dynamic systems that have flexible distributed connections, such as those which occur in the coupling with rubber isolators in vibratory systems. For these cases, the most usual substructuring methods are shown not to give good results for frequencies higher than the first natural frequency of the complete system, even when several coupling points are used for the rubber isolator. Using the calculation of the flexural wavelength in different materials, in this case steel and rubber, it is possible to determine a relationship between the distance of the coupling points within the isolator and the wavelengths of the component materials, at which the substructuring methodology gives accurate results. Due to these limitations of current substructuring methods, when soft flexible couplings exist in the subsystems, a new substructuring approach is presented, and is shown to really improve the results, especially when compared to the when the complete system is substructured at the flexible coupling.

Orientador: Michael John Brennan / Resumo: Grandes estruturas, como aviões, navios e até mesmo sistemas de refrigeração, que possuem muitos componentes podem ser substruturados, com o intuito de agilizar e facilitar o cálculo da transmissão vibratória entre seus componentes. Existem diversas formas e domínios em que esta substruração pode ser realizada, sendo a utilizada nesta tese a substruturação no domínio da frequência utilizando para o cálculo as mobilidades medidas nos pontos de acoplamento dos componentes. Esta tese se concentra na substruturação de sistemas dinâmicos que possuem áreas flexíveis de contato como o que ocorre no acoplamento de amortecedores de borracha em sistemas vibratórios, sendo que para estes casos foi verificado que os métodos de substruturação mais usuais não apresentaram bons resultados para frequências superiores a primeira frequência natural do sistema completo, mesmo quando utilizados vários pontos de acoplamento no amortecedor de borracha. Utilizando o cálculo do comprimento de onda em diferentes materiais, neste caso o aço e a borracha, foi possível determinar uma relação entre a distância dos pontos de acoplamento e o comprimento de onda em que a metodologia de substruturação apresenta resultados acurados. Devido a estas limitações dos métodos de substruração, quando acoplamentos flexíveis existem nos subsistemas considerados, uma nova forma de substruração foi apresentada a qual mostrou resultados muito melhores, especialmente quando comparados com os resultados do sistema completo... (Resumo completo, clicar acesso eletrônico abaixo) / Abstract: Large structures, such as airplanes, ships and even refrigeration systems, which have many components, can be substructured in order to speed up and facilitate the process of calculating the vibratory transmission between the system components. There are several methods and domains in which the substructuring can be done. In this thesis the substructuring method in the frequency domain is chosen to do the calculations, with the mobilities measured at the coupling points of the components. This thesis focuses on the substructuring of dynamic systems that have flexible distributed connections, such as those which occur in the coupling with rubber isolators in vibratory systems. For these cases, the most usual substructuring methods are shown not to give good results for frequencies higher than the first natural frequency of the complete system, even when several coupling points are used for the rubber isolator. Using the calculation of the flexural wavelength in different materials, in this case steel and rubber, it is possible to determine a relationship between the distance of the coupling points within the isolator and the wavelengths of the component materials, at which the substructuring methodology gives accurate results. Due to these limitations of current substructuring methods, when soft flexible couplings exist in the subsystems, a new substructuring approach is presented, and is shown to really improve the results, especially when compared to the when the complete sy... (Complete abstract click electronic access below) / Doutor

This work aims at enhancing the understanding and to provideimproved models of the dynamic behavior of rubber vibrationisolators which are widely used in mechanical systems.Initially, a time domainmodel relating compressions tocomponent forces accounting for preload effects, frequency anddynamic amplitude dependence is presented. The problem ofsimultaneously modelling the elastic, viscoelastic and frictionforces are removed by additively splitting them, where theelastic force response is modelled either by a fully linear ora nonlinear shape factor based approach, displaying resultsthat agree with those of a neo-Hookean hyperelastic isolatorunder a long term precompression. The viscoelastic force ismodelled by a fractional derivative element, while the frictionforce governs from a generalized friction element displaying asmoothed Coulomb force. This is a versatile one-dimensionalcomponent model effectively using a small number of parameterswhile exhibiting a good resemblance to measured isolatorcharacteristics. Additionally, the nonlinear excitationeffects on dynamic stiffness and damping of a filled rubberisolator are investigated through measurements. It is shownthat the well-known Payne effect - where stiffness is high forsmall excitation amplitudes and low for large amplitudes whiledamping displays a maximum at intermediate amplitudes -evaluated at a certain frequency, is to a large extentinfluenced by the existence of additional frequency componentsin the signal. Finally, a frequency, temperature and preloaddependent dynamic stiffness model is presented covering theranges from 20 to 20 000 Hz, -50 to +50 °C at 0 to 20 %precompression. A nearly incompressible, thermo-rheologicallysimple material model is adopted displaying viscoelasticitythrough a time - strain separable relaxation tensor with asingle Mittag-Leffler function embodying its time dependence.This fractional derivative based function successfully fitsmaterial properties throughout the whole audible frequencyrange. An extended neo-Hookean strain energy function, beingdirectly proportional to the temperature and density, isapplied for the finite deformation response with componentproperties solved by a nonlinear finite element procedure. Thepresented work is thus believed to enlighten workingconditions’impact on the dynamic properties of rubbervibration isolators, while additionally taking some of thesemost important features into account in the presentedmodels.

<p>This work aims at enhancing the understanding and to provideimproved models of the dynamic behavior of rubber vibrationisolators which are widely used in mechanical systems.Initially, a time domainmodel relating compressions tocomponent forces accounting for preload effects, frequency anddynamic amplitude dependence is presented. The problem ofsimultaneously modelling the elastic, viscoelastic and frictionforces are removed by additively splitting them, where theelastic force response is modelled either by a fully linear ora nonlinear shape factor based approach, displaying resultsthat agree with those of a neo-Hookean hyperelastic isolatorunder a long term precompression. The viscoelastic force ismodelled by a fractional derivative element, while the frictionforce governs from a generalized friction element displaying asmoothed Coulomb force. This is a versatile one-dimensionalcomponent model effectively using a small number of parameterswhile exhibiting a good resemblance to measured isolatorcharacteristics. Additionally, the nonlinear excitationeffects on dynamic stiffness and damping of a filled rubberisolator are investigated through measurements. It is shownthat the well-known Payne effect - where stiffness is high forsmall excitation amplitudes and low for large amplitudes whiledamping displays a maximum at intermediate amplitudes -evaluated at a certain frequency, is to a large extentinfluenced by the existence of additional frequency componentsin the signal. Finally, a frequency, temperature and preloaddependent dynamic stiffness model is presented covering theranges from 20 to 20 000 Hz, -50 to +50 °C at 0 to 20 %precompression. A nearly incompressible, thermo-rheologicallysimple material model is adopted displaying viscoelasticitythrough a time - strain separable relaxation tensor with asingle Mittag-Leffler function embodying its time dependence.This fractional derivative based function successfully fitsmaterial properties throughout the whole audible frequencyrange. An extended neo-Hookean strain energy function, beingdirectly proportional to the temperature and density, isapplied for the finite deformation response with componentproperties solved by a nonlinear finite element procedure. Thepresented work is thus believed to enlighten workingconditions’impact on the dynamic properties of rubbervibration isolators, while additionally taking some of thesemost important features into account in the presentedmodels.</p>

Conventional isolation models deal with massless isolators, which tend to overestimate the isolator performance because they neglect the internal resonances (IRs) due to the inertia of the isolator. Previous researches on the IR problem is not adequate because they only discussed this problem in terms of vibration based on single degree-of-freedom (SDOF) models. These studies did not reveal the importance of the IRs, especially from the perspective of the noise radiation. This dissertation is novel compared to previous studies in the following ways: (a) a three-DOF (3DOF) model, which better represents practical vibration systems, is employed to investigate the importance of the IRs; (b) the IR problem is studied considering both vibration and noise radiation; and (c) passive and hybrid control approaches using dynamic vibration absorbers (DVAs) to suppress the IRs are investigated and their potential demonstrated. The 3DOF analytical model consists of a rigid primary mass connected to a flexible foundation through three isolators. To include the IRs, the isolator is modeled as a continuous rod with longitudinal motion. The force transmissibility through each isolator and the radiated sound power of the foundation are two criteria used to show the effects and significance of the IRs on isolator performance. Passive and hybrid DVAs embedded in the isolator are investigated to suppress the IRs. In the passive approach, two DVAs are implemented and their parameters are selected so that the IRs can be effectively attenuated without significantly degrading the isolator performance at some other frequencies that are also of interest. It is demonstrated that the passive DVA enhanced isolator performs much better than the conventional isolator in the high frequency range where the IRs occur. The isolator performance is further enhanced by inserting an active force pair between the two passive DVA masses, forming the hybrid control approach. The effectiveness and the practical potential of the hybrid system are demonstrated using a feedforward control algorithm. It is shown that this hybrid control approach not only is able to maintain the performance of the passive approach, but also significantly improve the isolator performance at low frequencies. / Ph. D.

This thesis, gathering four papers, concerns the enhancement in understanding and modelling of the audible dynamic stiffness of vibration rubber isolators including experimental measurements. Paper A studies the performances of three different types of vibration isolator using an indirect measurement technique to estimate the blocked dynamic transfer stiffness of each specimen. The measurements are performed over a wide audible frequency range of 200 to 1000 Hz in a specially designed test rig enabling the investigation of arbitrary preload influences. Paper B addresses the modelling of the audible-frequency stiffness of the rubber conical mount experimentally appraised in Paper A accounting for preload effects. The model is based on a simpliflied waveguide approach approximating the nonlinearities attributed to the predeformations by adopting shape factor considerations. The carbon black filled rubber is assumed incompressible, displaying a viscoelastic behavior based on a fractional derivative Kelvin-Voigt model efficiently reducing the number of required material parameters. In Paper C the focus is on the axial dynamic stiffness modelling of an arbitrary long rubber bushing within the audible frequency range. The problems of simultaneously satisfying the locally non-mixed boundary conditions at the radial and end surfaces are solved by adopting a waveguide approach, using the dispersion relation for axially symmetric waves in thick-walled infinite plates, while fulfilling the radial boundary conditions by mode-matching. The results obtained are successfully compared with simpliflied models but display discrepancies when increasing the diameter-to-length ratios since the influence of higher order modes and dispersion augments. Paper D develops an effective waveguide model for a pre-compressed cylindrical vibration isolator within the audible frequency domain at arbitrary compressions. The original, mathematically arduous problem of simultaneously modelling the preload and frequency dependence is solved by applying a novel transformation of the pre-strained isolator into a globally equivalent homogeneous and isotropic configuration enabling the straightforward application of a waveguide model to satisfy the boundary conditions. The results obtained present good agreement with the non-linear finite element results for a wide frequency range of 20 to 2000 Hz at different preloads. / QC 20101001

Ces travaux de thèse portent sur l'étude expérimentale et numérique de structures mécaniques non-linéaires soumises à des vibrations sinusoïdales et aléatoires. L'étude prend en compte l'existence d'incertitudes au sein du protocole expérimentale et de la modélisation. Les études expérimentales menées au CEA/CESTA montrent que la réponse des structures assemblées à des sollicitations vibratoires est fortement dépendante du niveau d'excitation d'une part, et que la réponse obtenue possède une variabilité, parfois importante. Ces résultats expérimentaux ne peuvent pas être reproduits en simulation avec la méthode de simulation vibratoire linéaire déterministe classique.L'objectif de ces travaux est de proposer et de mettre en place des méthodes numériques pour étudier ces réponses non-linéaires, et de quantifier et propager les incertitudes pertinentes au sein des calculs. Cet objectif passe par l'étude de maquettes d'essai de complexité croissante et sujettes aux mêmes phénomènes vibratoires que les objets d'étude industriels du CEA/CESTA. Les méthodes de simulation vibratoire non-linéaires et les techniques numériques développées dans le monde académique sont adaptées et utilisées dans le contexte industriel du CEA/CESTA.Le premier objet d'étude est une poutre métallique bi-encastrée, dont la non-linéarité est d'origine géométrique. Le modèle associé à cette poutre est un oscillateur de Duffing à un degré de liberté très détaillé dans la littérature scientifique, et qui permet de valider les développements numériques effectués, sur les aspects de l'excitation aléatoire et de la propagation d'incertitudes. Dans un premier temps, les méthodes de tir et d'équilibrage harmonique sont étendues au cas de l'excitation aléatoire et validées sur cette structure académique par comparaison à l'expérience. Dans un second temps, une méthode de propagation d'incertitude non-intrusive est implémentée pour prendre en compte les incertitudes de modélisation identifiées.Le second objet d'étude est une maquette comportant un plot élastomère reliant une masselotte à un bâti. Le comportement non-linéaire de l'élastomère est au c\oe ur de ces travaux de thèse. De nombreux essais vibratoires sont réalisés dans un premier temps pour identifier un modèle non-linéaire de l'élastomère juste suffisant. Dans un second temps, le modèle développé est validé par comparaison aux essais en utilisant et adaptant les méthodes étendues lors de l'étude de la poutre bi-encastrée.Enfin, une maquette d'étude se rapprochant d'un cas d'application industriel est étudiée : la maquette Harmonie-Gamma. Elle compte des interfaces frottantes et des liaisons élastomères. Les essais vibratoires réalisés permettent d'identifier le comportement dynamique linéaire et non-linéaire du système et d'étudier l'évolution de la réponse en fonction du niveau d'excitation. Un modèle numérique est réalisé par éléments finis puis réduit par une méthode de sous-structuration. Les relations non-linéaires sont introduites au niveau des liaisons frottantes et élastomères. La réponse vibratoire de la structure est simulée par la méthode d'équilibrage harmonique couplée à un algorithme de continuation. Les comparaisons essais / calculs sont menées pour les excitations de type sinus balayé et aléatoire, et permettent d'analyser l'apport de chaque non-linéarité dans la réponse de la structure. / This PhD work focuses on the experimental and numerical study of nonlinear structures subjected to both harmonic and random vibrations, in the presence of modeling and experimental uncertainties. Experimental studies undertaken at the CEA / CESTA show a strong dependence of the jointed structures towards the excitation level, as well as a variability in the response for a given excitation level. These experimental results cannot be simulated using the classical determinist linear vibration simulation method.The objective of this work is to propose and set up numerical methods to study these nonlinear responses, while quantifying and propagating the relevant uncertainties in the simulations. This objective involves the study of structural assemblies of increasing complexity and subjected to the same vibratory phenomena as CEA / CESTA industrial structures. Advanced nonlinear numerical methods developed in academia are applied in the CEA / CESTA industrial context.The first test structure is a clamped-clamped steel beam that has a geometrical nonlinearity. The beam is modeled by a Duffing oscillator which is a widely studied model in the field of nonlinear dynamics. This allows for a validation of the numerical developments proposed in this work, first on the issue of random vibrations, and second on the issue of the propagation of uncertainties. The simulations are based on two techniques of reference (shooting method and harmonic balance method). Firstly, the simulation results are validated by comparison with the experimental results for random vibrations. Secondly, the harmonic balance method is used in adequation with a non-intrusive polynomial chaos in order to take into accounts the modeling uncertainties.The second test structure is a mass linked to a solid casing via a vibration-absorbing elastomeric material of biconical shape surrounded by a cage of aluminum. The nonlinear behavior of the elastomer is at the heart of this work. Various vibration tests were performed on this structure in order to identify the simplest nonlinear model possible to answer our queries. The identified model is validated through comparisons between the simulation results and the experimental results for both sine-swept and random vibrations.The central assembly of this work is an industrial assembly with friction joints and vibration-absorbing elastomeric joints, named Harmonie-Gamma. The vibration tests performed exhibit resonance modes as well as a strong dependency of the response with the excitation level. A numerical finite element model is developed and reduced with a substructuration technique. The resulting nonlinear reduced model is simulated using an harmonic balance method with a continuation method. The simulated responses are compared with the experiments and allow for an analysis of coupled nonlinearities in the CEA / CESTA industrial context.