Microelectromechanical Systems are ubiquitous in modern technology, with applications ranging from accelerometers in smartphones to ultra-high precision motion stages used for atomically-precise positioning. With the appropriate selection of materials and device design, MEMS resonators with ultra-high quality factors can be fabricated at minimal cost. As the sizes of such resonators decrease, however, their mechanical, electrical, and material properties can no longer be treated as linear, as can be done for larger-scale devices. Unfortunately, adding nonlinear effects to a system changes its dynamics from exactly-solvable to only solvable in specific cases, if at all. Despite (and because of) these added complications, nonlinear effects open up an entirely new world of behaviors that can be measured or taken advantage of to create even more advanced technologies. In our resonators, oscillations are induced and measured using aluminum nitride transducers. I used this mechanism for several separate highly-sensitive experiments. In the first, I demonstrate the incredible sensitivity of these resonators by actuating a mechanical resonant mode using only the force generated by the radiation pressure of a laser at room temperature. In the following three experiments, which use similar mechanisms, I demonstrate information transfer and force measurements by taking advantage of the nonlinear behavior of the resonators. When nonlinear resonators are strongly driven, they exhibit sum and difference frequency generation, in which a large carrier signal can be mixed with a much smaller modulation to produce signals at sum and difference frequencies of the two signals. These sum and difference signals are used to detect information encoded in the modulation signal using optical radiation pressure and acoustic pressure waves. Finally, in my experiments, I probe the nonlinear nature of the piezoelectric material rather than take advantage of the nonlinear resonator behavior. The relative sizes of the linear and nonlinear portions of the piezoelectric constant can be determined because the force applied to the resonator by a transducer is independent of the dielectric constant. This method allowed me to quantify the nonlinear constants.

The nonlinear dynamic characteristics and stability of floating vehicles are investigated theoretically and experimentally. Mathematical models of such floating bodies are used to investigate their complicated motions in regular waves. In particular, we address the phenomenon of indirectly exciting the roll motion of a vessel due to nonlinear couplings of the heave, pitch, and roll modes. In the analytical approach the method of multiple scales is used to determine first-order approximations to the solutions, yielding a system of nonlinear first-order equations governing the modulation of the amplitudes and phases of the system. The fixed-point solutions of these equations are determined and their bifurcations are investigated. Hopf bifurcations are found. Numerical simulations are used to investigate the bifurcations of the ensuing limit cycles and how they produce chaos. Experiments are conducted with tanker and destroyer models. They demonstrate some of the nonlinear effects, such as the jump phenomenon, the subcritical instability, and the coexistence of multiple solutions. The experimental results are qualitatively in good agreement with the results predicted by the theory. Coupling of the pitch and roll motions of a vessel when their frequencies are in the ratio of two-to-one is modeled by a two-degree-of-freedom system. The damping in the pitch mode is modeled by a linear viscous damping, whereas that of the roll mode is modeled by the sum of a linear viscous part and a quadratic viscous part. The effect of the quadratic damping is investigated when either mode is externally excited through a primary resonance. Force-response and frequency-response curves are generated. Coexistence of multiple solutions is found. The jump phenomenon continues to exist, whereas the saturation phenomenon ceases in the presence of quadratic damping. Hopf bifurcations are found. They indicate conditions for the nonexistence of steady-state periodic responses. Instead, the response is an amplitude- and phase-modulated motion consisting of both modes. Floquet theory is used to determine the stability of limit-cycle solutions. They undergo a pitchfork bifurcation followed by a cascade of period-doubling bifurcations, leading to chaos and hence chaotically modulated motions. When the roll mode is excited, the quadratic damping causes the region between the two Hopf bifurcation frequencies to shrink. However, the quadratic damping which may be introduced by attaching antirolling devices does not eliminate complicated motions completely in this region. The dynamic stability and excessive motion of the roll mode of a vessel in following or head regular waves is investigated theoretically and experimentally. The motion is modeled by a three-degree-of-freedom system with quadratic and cubic nonlinearities. The heave and pitch modes are linearized and their harmonic solutions are coupled into the roll mode. The resulting nonlinear ordinary-differential equation with time-varying coefficients is used to determine the stability of the roll mode for the case of principal parametric resonance. Experiments with a tanker model were conducted to validate the theory. They demonstrate the jump phenomenon and subcritical instability. They also reveal that the large-amplitude roll response depends not only on the encounter frequency but also on the position of the model relative to the waves. / Ph. D.

Off-road and racing motorcycles require a particular setup of the suspension to improve the comfort and the safety of the rider. Further, due to ground unevenness, off-road motorcycle suspensions usually experience extreme and erratic excursions in performing their function. In this regard, the adoption of nonlinear devices, such as progressive springs and hydro pneumatic shock absorbers, can help limiting both the acceleration experienced by the sprung mass and the excursions of the suspensions. For dynamic analysis purposes, this option involves the solution of the nonlinear differential equations that govern the motion of the motorcycle, which is excited by the stochastic road ground profile. In this study a 4 degrees-of-freedom (4-DOF) nonlinear motorcycle model is considered. The model involves suspension elements with asymmetric behaviour. Further, it is assumed that the motorcycle is exposed to loading of a stochastic nature as it moves with a specified speed over a road profile defined by a particular power spectrum. It is shown that a meaningful analysis of the motorcycle response can be conducted by using the technique of statistical linearization. The validity of the proposed approach is established by comparison with results from pertinent Monte Carlo studies. In this context the applicability of auto-regressive (AR) filters for efficient implementation of the Monte Carlo simulation is pointed out. The advantages of these methods for the synthesis of excitation signals from a given power spectrum, are shown by comparison with other methods. It is shown that the statistical linearization method allows the analysis of multi-degree-of-freedom (M-DOF) systems that present strong nonlinearities, exceeding other nonlinear analysis methods in both accuracy and applicability. It is expected that the proposed approaches, can be used for a variety of parameter/ride quality studies and as preliminary design tool by the motorcycle industry.

L’évolution du champ de localisation des déformations plastiques des métaux ductiles a été suivie par interférométrie de granularité laser (ESPI) au cours d’une sollicitation de traction uniaxiale. Il a été montré que le modèle mathématique utilisé, croisement de deux bandes rectilignes, décrit bien l’évolution du champ de vitesse de déformation depuis la striction diffuse jusqu'à rupture. Les caractéristiques physiques de la localisation, telles que la largeur des bandes, leur orientation et leur vitesse de déformation maximale ont été identifiées quantitativement. Leur évolution a été suivie et analysée sous plusieurs facteurs d’influence, qui sont à la fois microscopiques, tels que la taille de grains et la structure cristalline, et macroscopiques, comme la géométrie de l’éprouvette et la direction de son prélèvement par rapport à la direction de laminage, et la vitesse de traction. Il a été trouvé que les bandes de localisation rétrécissent au cours de la striction et leur orientation évolue également. Ces évolutions, le mode de striction et le moment de transition entre la striction diffuse et localisée sont influencés différemment par ces facteurs / The evolution of the plastic strain localization field of ductile metals was followed by electronic speckle pattern interferometry (ESPI) during a uniaxial tensile test. It was shown that the mathematical model, a system of two crossing straight bands, describes accurately the evolution of the strain rate field from diffuse necking up to rupture. The physical characteristics of the localization, such as the width of the bands, their orientations and maximum strain rates were identified quantitatively. Their evolutions were followed and analyzed from several influencing factors, which are both microscopic, such as grain size and crystal structure, and macroscopic, like the geometry of the specimen and the direction in which the specimen were cut with respect to the rolling direction, and the pulling speed. It has been found that the bands narrow down during the necking process and their orientations were also changing. These evolutions, the necking mode and the transition between the diffuse and localized necking are influenced differently by these factors

No description available.

In 1995 was published a regulation from RCAR company which determines rules for crash tests in maximum speed of 15 km/h on vehicles lighter than 2,5 ton. The main reason was to reduce costs for car reparation in case of crash in low speed. My diploma thesis is focused on the modifications of deformation part in the car alias absorption part of the vehicle. In the first part of my diploma thesis has been done a research about organisations doing basic car crashes as well as topic focused on nonlinear mechanics and description of explicit FEM. In the second part of my work are settled conditions for crash simulation of a barrier into the car. There is an evaluation of critical force on the stringer. Afterwards the calculating simulation simplified on loading of absorption part and there are some material and form adjustments. In the final part of my diploma thesis is done a result comparison and development of the absorption part.

Cette thèse vise à contribuer à l'adoption du virtual testing, pratique industrielle encore embryonnaire qui consistera à optimiser et certifier par la simulation numérique le dimensionnement de pièces industrielles critiques. Le virtual testing permettra des économies colossales dans la conception des pièces mécaniques et un plus grand respect de l'environnement grâce à des designs optimisés. Afin d'atteindre un tel objectif, de nouvelles méthodes de calcul doivent être mises en place, plus sûres, plus respectueuses des architectures matérielles, plus rapides, compatibles avec les contraintes temporelles de l'ingénierie. Nous nous intéressons à la résolution parallèle de problèmes non linéaires de grande taille par des méthodes de décomposition de domaine. Notre objectif est d'atteindre une approximation de la solution exacte en minimisant les communications entre les sous-domaines. Pour cela nous souhaitons maximiser les calculs réalisés indépendamment par sous-domaine à l'aide d'approches de relocalisation non linéaire, contrôler les critères de convergence des solveurs imbriqués de manière à éviter la sur-résolution et les divergences, améliorer la construction de conditions d'interface mixtes, et non linéariser l'étape de préconditionnement du solveur. L'objectif à terme étant de traiter des problèmes de complexité industrielle, la robustesse des méthodes sera un souci constant. De manière classique, les problèmes non linéaires sont résolus en construisant une suite de systèmes linéaires qui peuvent être résolus en parallèle à l'aide de méthodes itératives, telles que les solveurs de Krylov. Nous souhaitons remettre en question cette procédure usuelle en essayant de construire une suite de petits systèmes non linéaires indépendants à résoudre en parallèle. Une telle technique implique l'utilisation de solveurs itératifs imbriqués dont les critères de convergence doivent être syntonisés dynamiquement de manière à éviter à la fois la sur-résolution et la perte de convergence. La robustesse de la méthode pourra notamment être assurée par l'emploi de conditions d'interface mixtes bien construites et de préconditionneurs bien choisis. / This thesis is aimed to contribute to the adoption of virtual testing, an industrial practice still embryonic which consists in optimizing and certifying by numerical simulations the dimensioning of critical industrial structures. The virtual testing will allow colossal savings in the design of mechanical parts and a greater respect for the environment, thanks to optimized designs. In order to achieve this goal, new calculation methods must be implemented, satisfying more requirements concerning safety, respect for hardware architectures, fastness, and compatibility with the time constraints of engineering.We are interested in the parallel resolution of large nonlinear problems by domain decomposition methods. Our goal is to approximate the exact solution by minimizing communication between subdomains. In order to do this, we want to maximize the computations performed independently by subdomain, using nonlinear relocation approaches. We also try to control the convergence criteria of the nested solvers in order to avoid over-resolution and divergences, to improve the construction of conditions Of mixed interface, and non-linearizing the preconditioning step of the solver. The ultimate objective being to deal with problems of industrial complexity, the robustness of the methods we develop will be a constant concern.Conventionally, non-linear problems are solved by constructing a sequence of linear systems that can be solved in parallel using iterative methods, such as Krylov solvers. We wish to question this usual procedure by trying to construct a sequence of small independent nonlinear systems to be solved in parallel. Such a technique involves the use of interleaved iterative solvers, whose convergence criteria must be dynamically tuned in order to avoid both over-resolution and loss of convergence. The robustness of the method can be ensured in particular by the use of well-constructed mixed interface conditions and well-chosen preconditioners;

The application of polynomial reproducing methods has been explored in the context of linear and non linear problems. Of specific interest is the application of a recently developed reproducing scheme, referred to as the error reproducing kernel method (ERKM), which uses non-uniform rational B-splines (NURBS) to construct the basis functions, an aspect that potentially helps bring in locall support, convex approximation and variation diminishing properties in the functional approximation. Polynomial reproducing methods have been applied to solve problems coming under the class of a simplified theory called Cosserat theory. Structures such as a rod which have special geometric properties can be modeled with the aid of such simplified theories. It has been observed that the application of mesh-free methods to solve the aforementioned problems has the advantage that large deformations and exact cross-sectional deformations in a rod could be captured exactly by modeling the rod just in one dimension without the problem of distortion of elements or element locking which would have had some effect if the problem were to be solved using mesh based methods. Polynomial reproducing methods have been applied to problems in fracture mechanics to study the propagation of crack in a structure. As it is often desirable to limit the use of the polynomial reproducing methods to some parts of the domain where their unique advantages such as fast convergence, good accuracy, smooth derivatives, and trivial adaptivity are beneficial, a coupling procedure has been adopted with the objective of using the advantages of both FEM and polynomial reproducing methods. Exploration of SMW (Sherman-Morrison-Woodbury) in the context of polynomial reproducing methods has been done which would assist in calculating the inverse of a perturbed matrix (stiffness matrix in our case). This would to a great extent reduce the cost of computation. In this thesis, as a first step attempts have been made to apply Mesh free cosserat theory to one dimensional problems. The idea was to bring out the advantages and limitations of mesh free cosserat theory and then extend it to 2D problems.

Orientador: Paulo Roberto Gardel Kurka / Tese (doutorado) - Universidade Estadual de Campinas, Faculdade de Engenharia Mecânica / Made available in DSpace on 2018-08-23T11:40:22Z (GMT). No. of bitstreams: 1 Izuka_JaimeHideo_D.pdf: 4550690 bytes, checksum: d283c500cecbc7a038784ba35f0f73df (MD5) Previous issue date: 2013 / Resumo: A utilização de braços manipuladores flexíveis em veículos de exploração foi o motivador deste trabalho. Estas estruturas têm como vantagens a sua massa reduzida e a capacidade de suportar grandes deformações sem que o limite de elasticidade seja excedido. O controle das vibrações de sua extremidade livre é essencial para uma aplicação prática. Neste contexto, este trabalho tem como objetivo a determinação de um modelo dinâmico para uma estrutura longa e flexível, visando o seu controle de vibração. A estrutura considerada possui seção variável, semelhante a uma viga telescópica. Considera-se ainda que a estrutura esteja sujeita a uma grande deformação causada pelas ações de tendão de tração, peso próprio e cargas concentradas. O modelo dinâmico consiste na adaptação de uma malha de elementos finitos de baixa ordem à configuração da linha de deformação estática da viga. A vibração a ser controlada consiste das pequenas oscilações que ocorrem em torno da posição de equilíbrio da viga deformada. O modelo dinâmico encontrado para a estrutura é utilizado no projeto de um controlador de vibrações, ativado por forças exercidas no tendão de tração, responsável pela deformação estática da própria viga. Comparações com a literatura, bem como resultados experimentais comprovam a validade do modelo empregado para a caracterização do sistema. Simulações numéricas mostram o sucesso de uso do modelo no projeto de um controlador ativo de vibrações / Abstract: The use of flexible manipulator arms in exploration vehicles was the motivation of this work. The advantages of such structures are their light weight and the capability to withstand large displacements without exceeding their specified elastic limit. The control of vibrations of its free end is essential for a practical application. In this context, the objective of this study is to determine a dynamic model for a long and flexible structure, aiming its vibration control. The structure has a variable section, similar to a telescopic beam. Large deformation behavior of the structure is considered. Concentrated loads, self-weight of the structure and tendon traction are the loads applied to the structure. The model dynamics is described by a low order finite element mesh, which is adapted to the geometry defined by the static deformation of the beam. The vibrations to be controlled are the small oscillations about the equilibrium position of the deformed beam. The dynamic model found for the structure is applied to design an active vibration controller. The controller forces are applied though the tendon traction cables, which is also responsible for the static deformation of the beam itself. Comparison with literature as well as experimental results prove the validity of the model used to characterize the system. Numerical simulations show the success of using the model in the design of an active vibration controller / Doutorado / Mecanica dos Sólidos e Projeto Mecanico / Doutor em Engenharia Mecânica

Orientador: Janito Vaqueiro Ferreira / Dissertação (mestrado) - Universidade Estadual de Campinas, Faculdade de Engenharia Eletrica / Made available in DSpace on 2018-08-04T09:11:42Z (GMT). No. of bitstreams: 1 Mariano_SilvioLuiz_M.pdf: 10538477 bytes, checksum: b5e594a3783a5571c8face1a74dae202 (MD5) Previous issue date: 2005 / Resumo: Este trabalho apresenta a análise numérica e experimental do índice de vibro-impacto em alavancas de transmissão mecânica. Foram desenvolvidos modelos de alavanca que consideram não-linearidades na estrutura. Métodos para quantificação do vibro-impacto foram obtidos na literatura e implementados para o levantamento de curvas, as quais indicam a variação do índice de Vibro-impacto com relação à variação dos parâmetros dos modelos desenvolvidos. A técnica da Transformada de Hilbert também foi implementada para levantamento das forças não-lineares atuantes nos modelos. Foram utilizadas três bancadas para identificação das forças não-lineares atuantes e validação da técnica salientada, que utiliza sinais de força, deslocamento, velocidade e aceleração. As curvas de rigidez não-Hnear foram identificadas coerentemente, as quais tiveram validação pelo levantamento da rigidez das mesmas bancadas por medições estáticas. Dois modelos numéricos de alavanca, utilizando massas concentradas, foram estudados. Nestes identificaram-se curvas de força não-Hnear e levantaram-se curvas de sensibilidade do índice de Vibro-impacto à variação dos parâmetros dos modelos. Mostrou-se que a técnica da Transformada de Hilbert pode ser utilizada para a identificação de sistemas não-lineares e que o estudo de sensibilidade em modelos de vibro-impacto pode ser obtido sem muita dificuldade / Abstract: This work presents a study about a numerical and experimental vibro-impact level analisys in mechanical gearshift levers. It was developed gearshift lever models which consider nonlinearities in the structure. Methods to vibro-impact quantification were obtained in the available literature and were implemented to obtain curves which show the vibro-impact level change with the modification of the parameters of the developed models. Hubert Transform techniques were also implemented to obtain nonlinear forces implemented on the models. To verify the efficiency of these techniques, three test rigs with nonlinearities were developed and the nonlinear forces were identified. The techniques need the displacement, velocity and acceleration signals to calculate the forces. The nonlinear forces curves were identified and validated with the static forces measured. Two models of gearshift levers were developed, using lumped masses. In these models the nonlinear forces curves and the sensibility to the vibro-impact level with modifications in the model parameters were obtained. It was showed that the Hubert Transform techniques are reliable to identify nonlinear systems and that the sensibility study in vibro-impact can be obtained easily / Mestrado / Mecanica dos Sólidos e Projeto Mecanico / Mestre em Engenharia Mecânica