The Fully compliant Tensural Bistable Mechanism (FTBM) class is introduced. The class consists of fully compliant linear bistable mechanisms that achieve much of their displacement and bistable behavior through tension loading of compliant segments. Multiple topologies of designs arising from the FTBM class were designed using a finite element analysis (FEA) model with optimization. In a coupled design approach, thermal actuators were optimized to the force and displacement requirements of the bistable mech-anisms, and selected FTBM devices were combined in switching systems with the result-ing Thermomechanical In-plane Microactuators (TIMs) and Amplified Thermomechanical In-plane Microactuators (ATIMs). Successful on-chip actuation was demonstrated. The bistable mechanisms and actuators in this work were fabricated in the MUMPs and SUMMiT V surface micromachining MEMS fabrication technologies. The Stacked Amplified Thermomechanical In-plane Microactuator (StATIM) is also introduced. The StATIM is a compact linear output actuator based on the ATIM that is capable of large displacements relative to the size of the actuator. The StATIMs presented in this thesis were fabricated in the SUMMiT V technology.

The objective of this work is to demonstrate the feasibility of on-chip sensing of bistable mechanism state using the piezoresistive properties of polysilicon, thus eliminating the need for electrical contacts. Changes in position are detected by observing changes in resistance across the mechanism. Sensing the state of bistable mechanisms is critical in their various applications. The research in this thesis advances the modeling techniques of MEMS devices which use piezoresistivity for position sensing. A fully compliant bistable micro mechanism was designed, fabricated, and tested to demonstrate the feasibility of this sensing technique. Testing results from two fabrication processes, Fairchild's SUMMiT IV and MUMPs, are compared. The Fairchild mechanism was then integrated into various Wheatstone bridge configurations to show the advantages of bridges and to demonstrate various design layouts. Repeatable and detectable results were found with independent mechanisms and with those integrated into Wheatstone bridges. Finite element models were constructed for the different Wheatstone bridges which were used to predict piezoresistive trends. A bistable mechanism for high-acceleration sensing was designed using uncertainty analysis optimization. The piezoresistive effects for this mechanism were also modeled. Discussion concerning nonvolatile memory applications is also presented.

Compliant bistable micromechanisms have been proposed for use in applications such as switches, relays, shutters, and sensing arrays. Unpublished laboratory testing suggests that off-axis forces may affect the bistable nature of fully compliant bistable micromechanisms (FCBMs). The actuation forces required to snap the FCBM from one stable equilibrium position to another can be altered if the off-axis forces are applied to the mechanism during transition between stable positions. Understanding the three-dimensional characteristics of these mechanisms and the effect of eccentric loading conditions would be helpful in design and analysis of FCBMs. Two 3-D FEA models were developed for analysis and validation purposes. The 3-D solid element model includes great detail regarding the geometry and boundary conditions of the FCBMs. Including fillets, residual stress, and anchors proved to generate more accurate results. The 3-D beam element model is greatly simplified, and primarily used to validate the results produced by the 3-D solid element model. Both models were validated through comparison to experimental data. A test suite of FEA runs was constructed to better understand the 3-D behavior of FCBMs. A chief discovery provided by the test suite results was the existence of two phenomenon conditions, defined as Phenomenon 1 and Phenomenon 2. Phenomenon 1 tended to occur when smaller off-axis forces were included in the model. When comparing the two phenomenon, larger pitch rotation, smaller out-of-plane motion, larger reaction forces, and a more consistent bistable mechanism was associated with Phenomenon 1. Phenomenon 2 tended to occur when larger applied forces were included in the model. Once this phenomenon was generated, the FCBM tended to remain in this condition. Reduced reaction forces, larger out-of-plane motion, and a tendency of non-bistability were characteristics of this phenomenon. The FCBMs could experience much larger in-plane applied forces before transitioning to Phenomenon 2. In contrast, relatively small out-of-plane forces caused the same transition. The FCBMs proved to be well behaved when being pulled into their alternate stable position rather than being pushed. A pushing motion caused the shuttle to roll, pitch and yaw in an inconsistent manner.

Fully compliant bistable mechanisms have been proposed to be used as threshold accelerometers. The advantages to using these devices are that they require no external power to operate and maintain their sensing state. Using this characteristic the devices can be integrated with passive radio frequency identification tags (RFID). This allows for the sensing package to lay dormant with no maintenance needed until the sensor is read by the RFID reader. This thesis presents a successfully fabricated and integrated threshold accelerometer with a passive RFID tag. This in turn has been successfully read with an RFID reader and shown to act as a wireless passive sensor indicating whether or not a threshold acceleration has been exceeded. It is shown that in general plastics are not a suitable material to use in threshold accelerometers due to variability in fabrication, temperature and prolonged stresses inducing stress relaxation in the material. Multiple methods for testing the switching forces of these threshold accelerometers are developed and a frequency response for the switching forces of these devices is explored. A straight-leg bistable mechanism design model is introduced and used to design metal bistable devices to reduce the variations seen in the plastic threshold accelerometers. With this metal design a new fabrication process is introduced to attain thin metal compliant flexures with little variation in the thickness of the compliant flexures. This method allows for a more economical method of producing compliant flexures. The metal bistable mechanism designs presented show significant improvement over the plastic bistable designs. These improvements include minimizing the effects of stress relaxation, minimizing variation in switching forces and minimizing variation between fabricated devices. The cost, however, with the metal bistable mechanism design would be more than the plastic bistable mechanism design.

Origami is making an impact in engineering as solutions to problems are being found by applying origami principles (eg. flat-foldability) and using specific crease patterns as inspiration. This thesis presents an in-depth analysis of a particular origami fold -- the waterbomb base -- to facilitate its use in future engineering problems. The watebomb base is of interest due to its familiarity to the origami community, simple topology (can be made by folding a single sheet of paper four times), scalability, generalizability, and interesting kinetic behavior. It can behave as a nonlinear spring as well as a one- or two-way bistable mechanism. This thesis presents models of the kinetic behavior of the traditional waterbomb base as well as some non-traditional variants to be used as tools in future development of waterbomb-base-inspired mechanisms. In all cases considered here, developability as well as rotational symmetry in both the geometry and motion of the mechanisms are assumed. The thesis provides an introduction to origami and reviews some of the ways in which it has been studied and applied in engineering fields. The waterbomb base is also presented as a specific origami fold with practical application potential. Models for the behavior of the traditional waterbomb base are introduced and its potential usefulness as a testbed for actuation methods is discussed. Models are developed for its kinematic and bistable behavior, including the forces needed to transition between stable states. These models are validated by comparison to physical prototype testing and finite element analysis. The thesis introduces the generalized waterbomb base (WB) and generalized split-fold waterbomb base (SFWB). The WB maintains the pattern of alternating mountain and valley folds around the vertex but in this generalized case any even number of folds greater than or equal to 6 is allowed. An SFWB is created by splitting each fold of a WB into two “half folds”, effectively doubling the number of folds and links but halving the deflection at each fold. The same models that were developed for the traditional waterbomb base are developed for the WB and the SFWB and a few potential applications are discussed.

Cette thèse est consacrée à l'étude d'équations de réaction-diffusion dans un environnement périodique en temps. Ces équations modélisent l'évolution d'une tumeur cancéreuse en présence d'un traitement qui correspond à une immunothérapie dans la première partie du manuscrit, et à une chimiothérapie cytotoxique dans la suite.On considère dans un premier temps des nonlinéarités périodiques en temps pour lesquelles 0 et 1 sont des états d'équilibre linéairement stables. On étudie l'unicité, la monotonie et la stabilité de fronts pulsatoires. On exhibe également des cas d'existence et de non-existence de telles solutions. Dans la deuxième partie de la thèse, on commence par travailler sur des nonlinéarités périodiques en temps qui sont la somme d'une fonction positive traduisant la croissance de la tumeur et d'un terme de mort de cellules cancéreuses du au traitement. On s'intéresse aux états d'équilibres de telles nonlinéarités, et on va déduire de cette étude des propriétés de propagation de perturbations et l'existence de fronts pulsatoires. On raffine ensuite le modèle en considérant des nonlinéarités qui sont la somme d'une fonction asymptotiquement périodique en temps et d'un terme perturbatif. On prouve notamment que les propriétés relatives à la propagation de perturbations restent valables dans ce cadre là. Pour finir, on s'intéresse à l'influence du protocole de traitement. / This phD thesis investigates reaction-diffusion equations in a time periodic environment. These equations model the evolution of a cancerous tumor in the presence of a treatment that corresponds to an immunotherapy in the firs part of the manuscript, and to a cytotoxic chemotherapy after. We begin by considering time-periodic nonlinearities for which 0 and 1 are linearly stable equilibrium states. We study uniqueness, monotonicity and stability of pulsating fronts. We also provide some conditions for the existence and non-existence of such solutions.In the second part of the manuscript, we begin by working on time-periodic nonlinearities which are the sum of a positive function which stands for the growth of the tumor in the absence of treatment and of a death term of cancerous cells due to treatment. We are interested in equilibrium states of such nonlinearities, and we will infer from this study spreading properties and existence of pulsating fronts. We then refine the model by considering nonlinearities which are the sum of an asymptotic periodic nonlinearity and of a small perturbation. In particular we prove that the spreading properties remain valid in this case. To finish, we are interested in the influence of the protocol of the treatment.

Cette thèse concerne les phénomènes de propagation de certaines équations d'évolution dans des habitats périodiques. Dans la première partie, nous étudions les phénomènes d'expansion de certaines équations d'intégro-différence spatialement périodiques. Tout d'abord, nous établissons une théorie générale sur l'existence des vitesses de propagation pour des systèmes d'évolution noncompacts, sous l'hypothèse que les systèmes linéarisés ont des valeurs propres principales. Ensuite, nous introduisons la notion d'irréductibilité uniforme des mesures de Radon finies sur le cercle. On démontre que tout opérateur de convolution généré par une telle mesure admet une valeur propre principale. Enfin, nous prouvons l'existence de vitesses de propagation pour certains équations d'intégro-différence avec des noyaux de dispersion uniformément irréductibles. Dans la deuxième partie, nous étudions les phénomènes de propagation de front pour des équations de réaction-diffusion spatialement périodiques avec des non-linéarités bistables. Nous nous concentrons d'abord sur les solutions de type fronts pulsatoires. Sous diverses hypothèses, il est prouvé que les fronts pulsatoires existent lorsque la période spatiale est petite ou grande. Nous caractérisons aussi le signe des vitesses et nous montrons la stabilité exponentielle globale des fronts pulsatoires de vitesse non nulle. Nous étudions ensuite les solutions de type fronts de transition. Sous des hypothèses convenables, on prouve que les fronts de transition se ramènent aux fronts pulsatoires avec une vitesse non nulle. Mais nous montrons aussi l'existence de nouveaux types de fronts de transition qui ne sont pas des fronts pulsatoires. / This dissertation is concerned with propagation phenomena of some evolution equations in periodic habitats. The main results consist of the following two parts. In the first part, we investigate the spatial spreading phenomena of some spatially periodic integro-difference equations. Firstly, we establish a general theory on the existence of spreading speeds for noncompact evolution systems, under the hypothesis that the linearized systems have principal eigenvalues. Secondly, we introduce the notion of uniform irreducibility for finite Radon measures on the circle. It is shown that, any generalized convolution operator generated by such a measure admits a principal eigenvalue. Finally, applying the above general theories, we prove the existence of spreading speeds for some integro-difference equations with uniformly irreducible dispersal kernels. In the second part, we study the front propagation phenomena of spatially periodic reaction-diffusion equations with bistable nonlinearities. Firstly, we focus on the propagation solutions in the class of pulsating fronts. It is proved that, under various assumptions on the reaction terms, pulsating fronts exist when the spatial period is small or large. We also characterize the sign of the front speeds and we show the global exponential stability of the pulsating fronts with nonzero speed. Secondly, we investigate the propagation solutions in the larger class of transition fronts. It is shown that, under suitable assumptions, transition fronts are reduced to pulsating fronts with nonzero speed. But we also prove the existence of new types of transition fronts which are not pulsating fronts.

Constrained negative stiffness elements in volume concentrations (1% to 2%) embedded within viscoelastic materials have been shown to provide greater energy absorption than conventional materials [Lakes et al., Nature (London) 410, 565–567 (2001)]. This class of composite materials, called meta-materials, could be utilized in a variety of applications including noise reduction, anechoic coatings and transducer backings. The mechanism underlying the meta-material's behavior relies on the ability of the negative stiffness element to locally deform the viscoelastic material, dissipating energy in the process. The work presented here focuses specifically on the design of the negative stiffness elements, which take the form of buckled beams. By constraining the beam in an unstable, S-shaped configuration, the strain energy density of the beam will be at a maximum and the beam will accordingly display negative stiffness. To date, physical realization of these structures has been limited due to geometries that are difficult to construct and refine with conventional manufacturing materials and methods. By utilizing the geometric freedoms allowed by the Selective Laser Sintering (SLS) machines, these structures can be built and tuned for specific dynamic properties. The objective of this research was to investigate the dynamic behavior of SLS-constructed meso-scale negative stiffness elements with the future intention of miniaturizing the elements to create highly absorptive meta-materials. This objective was accomplished first through the development and analysis of a mathematical model of the buckled beam system. A characterization of the Nylon 11 material was performed to obtain the material properties for the parts that were created using SLS. Applying the mathematical model and material properties, a tuned meso-scale negative stiffness structure was fabricated. Transmissibility tests of the meso-scale structure revealed that the constrained negative stiffness system was able to achieve overall higher damping and vibration isolation than an unconstrained system. Quasistatic behavior of the system indicated that these elements would be ideal for implementation within meta-materials. Based on the results of the meso-scale system, a method to test a representative volume element for a negative stiffness meta-material was developed for future completion. / text

Au cours de la dernière décennie, des travaux de recherche importants ont été effectués dans le domaine de la microrobotique. Ces travaux concernent la conception, la fabrication et la commande de microrobots destinés à exécuter diverses tâches dans le micromonde (le monde des objets de taille micrométrique). Il s'agit notamment de tâches de manipulation d'objets artificiels ou biologiques à des fins de positionnement, de caractérisation ou de tri mais aussi pour le micro-assemblage industriel. Les recherches effectuées ont montré l'efficacité des matériaux actifs pour l'actionnement des microrobots. Toutefois, en dépit de leur haute résolution intrinsèque, ces matériaux présentent des inconvénients qui rendent la commande des microrobots difficile. Le comportement de ces matériaux et plus généralement des actionneurs qui les utilisent est souvent complexe, non linéaire et parfois non stationnaire. L'implantation de lois de commande nécessite donc l'emploi de capteurs et d'instruments coûteux et encombrants pour le traitement des signaux et l'exécution en temps réel. Dans le but de lever les difficultés citées précédemment et d'ouvrir des perspectives nouvelles pour la conception et la commande de microrobots, nous proposons une nouvelle approche pour la microrobotique appellée « microrobotique numérique » qui utilise un concept de modularité et une commande en boucle ouverte. Ces nouveaux microrobots sont construits à partir de « modules élémentaires » possédant deux états mécaniques stables et répétables. La position de l'extrémité du microrobot dépend de l'état des différents modules bistables qui le composent. Cette approche introduit un nouveau paradigme en microrobotique permettant la conception de cinématiques diverses adaptées au micromonde. Les principaux avantages de cette nouvelle microrobotique sont la modularité, l'absence de capteurs, la flexibilité, la possibilité de réaliser des robots microfabriqués et l'absence d'asservissement. Cette thèse propose la conception, la microfabrication et la caractérisation d'un module bistable.

<p>In recent years portable electronic devices, such as mobile phones and personal digital assistants, have increased the demand for high performance displays with low power consumption. An interesting candidate with the potential of fulfilling these demands is the reflective single-polarizer surface controlled bistable twisted nematic liquid crystal display. The main focus of this work involves the optical properties of displays based on these bistable structures. In the investigations, the display is considered as an integrated optical system, containing not only the liquid crystal cell, but also components such as polarizers and retardation films. The specific aim of the thesis was to derive new optical modes of the reflective single-polarizer bistable twisted nematic device using the Jones matrix method to study the interaction between the polarization of light and the optically anisotropic media. The electro-optical properties of the derived modes have been studied and evaluated both theoretically and experimentally. The modes possess excellent brightness and high contrast ratio. By introducing a quarter-wave retardation film into the optical configuration, the contrast ratio can be significantly increased by preventing spectral leakage of light in the dark state. To experimentally realize the derived optical modes, special layers for the alignment of the liquid crystal molecules on the cell substrate surface have been proved needed. Therefore, also the photo-alignment technology of nematic liquid crystals on novel alignment materials has been studied with the aim to control liquid crystal cell parameters such as pretilt angle and anchoring energy, both critical for the bistable switching. The results of this thesis will increase the understanding of the optical properties of the reflective single-polarizer bistable twisted nematic liquid crystal display and will be valuable when considering this type of device for practical applications.</p>