The goal of this thesis is to investigate the biophysical basis underlying the nonlinear relationship between firing response and current stimulation in single motor neurons. After reviewing the relevant motoneuron physiology and theories that describe complex dendritic signaling properties, I hypothesize that at least five passive electrical properties must be considered to better understand the physiological input-output properties of motor neurons in vivo: input resistance, system time constant, and three signal propagation properties between the soma and dendrites that depend on the signal direction (i.e. soma to dendrites or vice versa) and type (i.e. direct (DC) or alternating (AC) current). To test my hypothesis, I begin with characterizing the signal propagation of the dendrites, by directly measuring voltage attenuations along the path of dendrites of the type-identified anatomical neuron models. Based on this characterization of dendritic signaling, I develop the novel realistic reduced modeling approach by which the complex geometry and passive electrical properties of anatomically reconstructed dendrites can be analytically mapped into simple two-compartment modeling domain without any restrictive assumptions. Combining mathematical analysis and computer simulations of my new reduced model, I show how individual biophysical properties (system input resistance, time constant and dendritic signaling) contribute to the local excitability of the dendrites, which plays an essential role in activating the plateau generating membrane mechanisms and subsequent nonlinear input-output relations in a single neuron. The biophysical theories and computer simulations in this thesis are primarily applied to motor neurons that compose the motor neuron pool for control of movement. However, the general features of the new reduced neuron modeling approach and important insights into neuronal computations are not limited to this area. My findings can be extended to other areas including artificial neural networks consisting of single compartment processors. / Medical Sciences – Biomedical Engineering

Doctor of Philosophy / A detailed theoretical and numerical investigation of the behaviour of reactive systems under the influence of chaotic stirring is presented. These systems exhibit stationary solutions arising from the balance between chaotic advection and diffusion. Excessive stirring of such systems results in the termination of the reaction via a saddle-node bifurcation. The solution behaviour of these systems is analytically described using a recently developed nonperturbative, non-asymptotic variational method. This method involves fitting appropriate parameterised test functions to the solution, and also allows us to describe the bifurcations of these systems. This method is tested against numerical results obtained using a reduced one-dimensional reaction-advection-diffusion model. Four one- and two-component reactive systems with multiple homogeneous steady-states are analysed, namely autocatalytic, bistable, excitable and combustion systems. In addition to the generic stirring-induced saddle-node bifurcation, a rich and complex bifurcation scenario is observed in the excitable system. This includes a previously unreported region of bistability characterised by a hysteresis loop, a supercritical Hopf bifurcation and a saddle-node bifurcation arising from propagation failure. Results obtained with the nonperturbative method provide a good description of the bifurcations and solution behaviour in the various regimes of these chaotically stirred reaction-diffusion systems.

This study aims to comprehend the bistable and multi-stable behaviour of flexible straws with the intention of utilising it for future engineering applications. This behaviour is achieved by the multiple inversions of conical frustum shells within the corrugation of a flexible straw. This study examined the effects of various material models, geometry variables and loading methods on the inversion of close-top and open-top conical frustum shells via experiments and FEM simulations. This thesis consists of three main parts, and the second and the third parts are complementary to each other: First, we investigated the effects of applying a uniform vertical load to the upper rim of open-top frustum shells via FEM simulations. A reference model was simulated based on the measurements of an ordinary polypropylene flexible straw specimen, using two material models - linear elastic and elastically perfectly plastic. The effects of the interactions between frusta of the corrugated segment of a flexible straw were also studied by evaluating the difference in responses between an individual frustum and conjugated models of two or three frusta. It was found that by constraining the rotation of its bottom rim, an individual frustum can fairly reproduce the complex bistable behaviour of the shorter frustum within the corrugated part of a flexible straw. Furthermore, detailed parametric studies that focused on the effects of various geometric parameters were conducted and generalised formulas that predicted the critical force were derived. A comparison between the simulated results and the analytical model in predicting progressive inversion was made to distinguish the geometric boundaries that separate the one-off snap-through to the progressive inversion of frustum shells. Next, the behaviour of close-top frustum shells in response to vertical point loading at various locations on the top surface was evaluated. A hyperelastic material was used to fabricate the physical specimens. During the experiments, the corresponding deformed shapes were recorded by 3D scanning in addition to measurements of the displacement and reaction force. We observed a close resemblance between the experimental and FEM simulated results, which validated the FEM models. Two local peaks were observed before the structure was fully inverted into its secondary stable state and the overall critical force of the structure was defined by the higher one of the two. The relationship between their magnitudes and the loading locations was analysed and an optimal loading location which gave the minimum critical force was proposed and verified by additional simulations. Furthermore, generalised formulas in predicting critical force were also acquired based on parametric studies. The optimal loading location was found to be constant in spite of variations in height and thickness. The third part of this thesis discussed the effects of lateral point loading on both close-top and open-top frustum shells at various locations on the side surface and supplemented the second part. It is found that the removal of the top surface could cause the critical force to decrease if a point load was applied laterally. Moreover, we were able to fully invert the structure with a lower critical force through lateral loading in comparison to vertical loading.

O presente trabalho aborda um estudo sobre o fenômeno de biestabilidade em escoamentos transversais turbulentos sobre dois cilindros lisos paralelos, com razão de espaçamento, p/d, de 1,26, utilizando abordagem numérica e experimental. Nas comparações consideram-se o domínio computacional e a seção de testes experimental equivalentes. As análises comparam escoamentos turbulentos com números de Reynolds subcríticos, variando entre Re = 17000 e Re = 26000, além disto, uma análise laminar comparativa com Re = 167 é executada. Nas avaliações experimentais utilizam-se velocidades médias e flutuações de velocidade, adquiridas com a técnica de anemometria de fio quente, exploram-se também dados de flutuações de pressão obtidos com microfones condensadores posicionados na parede do canal aerodinâmico. Para comparação experimental e numérica executam-se leituras de pressões estáticas ao longo do canal aerodinâmico. Os sinais temporais das aquisições são analisados estatisticamente com médias e momentos, transformada de Fourier e transformada de ondaletas para caracterização e identificação do fenômeno biestável. Na avaliação numérica é executada a solução das equações de Navier-Stokes, utilizando a simulação LES (Large Eddy Simulation) com modelo Smagorinsky-Lilly dinâmico para sub-malha e a simulação URANS (Unsteady Reynolds Averaged Navier-Stokes) com o modelo de turbulência k ω – SAS (Scale Adaptive Simulation). Os resultados das duas abordagens são comparados utilizando as médias de valores, comportamento temporal e valores do número de Strouhal. O estudo de qualidade de malha, com o método GCI (Grid Convergence Index), é aplicado nas malhas utilizadas em URANS. Para a validação da simulação LES, aplica-se análise de quantidade de energia cinética resolvida comparando com resultados experimentais e uma metodologia para verificação da solução descrita na literatura, com a qual um comparativo entre duas simulações LES com diferentes malhas é executado. Nos resultados numérico e experimental observam-se a presença da biestabilidade e nota-se o comportamento não simultâneo da mesma ao longo dos cilindros. Este comportamento é observado nas análises numérica e experimental. A formação assimétrica das esteiras também é estudada e atribuída à interação entre os vórtices das esteiras, já que, inicialmente, os desprendimentos dos mesmos são simétricos. Na investigação do escoamento entre os cilindros a presença da perturbação da velocidade média é observada, mas a mesma não apresenta relação direta com a troca biestável. A alteração do patamar da velocidade média, neste caso, é resultado da influência da troca de modos que acontece nas esteiras. A biestabilidade também é observada na flutuação de pressão, de forma similar ao comportamento obtido com flutuações de velocidade nos estudos da literatura. No comparativo entre os dois métodos numéricos observa-se boa concordância nos resultados obtidos utilizando URANS com modelo k ω – SAS em relação aos observados com LES, sendo possível prever os principais comportamentos, mesmo com a aplicação da lei de parede na região entre cilindros na simulação URANS. / This paper reports a study on the bistable phenomenon in turbulent crossflow over two parallel smooth cylinders with spacing rate, p/d, 1.26 using numerical and experimental approaches. In the comparisons, the computational domain and experimental tests section are considered equivalents. Turbulent flows with subcritical Reynolds numbers ranging between Re = 17000 and Re = 26000 are compared and, in addition, a comparative laminar analysis with Re = 167. In the experimental evaluations the mean velocity and fluctuations velocities are used and acquired with the hot-wire anemometry technique, exploiting also pressure fluctuations data, obtained with condenser microphones positioned in the wall of the aerodynamic channel. For experimental and numerical comparisons, the static pressure over the aerodynamic channel using pressure taps is executed. The temporal signals from the acquisitions are analyzed statistically with mean and moments, Fourier transform and wavelet transform for characterization and identification of the bistable phenomenon. In the numerical evaluation performed, the Navier-Stokes equations are solved using LES simulation (Large Eddy Simulation) with Smagorinsky-Lilly dynamic model for sub-grid and URANS simulation (Unsteady Reynolds Averaged Navier-Stokes) with the turbulence model k ω – SAS (Scale Adaptive Simulation). The results of the two numerical approaches are compared using the mean values, temporal behavior and values of the Strouhal number. The mesh quality study is executed using the GCI (Grid Convergence Index) for the mesh used in URANS. To validate the LES simulation, the amount of solved kinetic energy is compared with experimental amounts. For verification of the LES solution a method described on literature is used, in which a comparison between two LES simulations with different meshes is performed. In the numerical and experimental results, the presence of bistability were observed and in addition the non-simultaneous behavior of the phenomenon over the cylinder was identified in both analyzes. The wakes asymmetric formation was also studied and attributed to the interaction between the vortices of the wakes, since initially the detachments are symmetrical. In the investigation of the flow between the cylinders, the presence of the average velocity disturbance is observed, but it does not have direct relation with the bistable switch. The change in the average velocity level, in this case, is the result of the switching modes influence from the change in the wakes. The bistability is observed also in pressure fluctuation, similar to the behavior obtained with velocity fluctuations in the literature. Comparing the two numerical methods were observed good agreement in the results obtained using URANS with model k ω - SAS in relation to those observed with LES, being possible to predict the main behaviors, even with the application of wall law in the region between cylinders for the URANS simulation.

Este trabalho apresentada um estudo experimental do fenômeno de biestabilidade que ocorre na geometria simplificada de dois tubos dispostos lado a lado submetidos a um escoamento cruzado turbulento. Na análise consideram-se a condição de tubos fixos e com um grau de liberdade (rotacional), submetidos a diferentes números de Reynolds. A técnica experimental consiste na medição de flutuações de velocidade do escoamento através da anemometria de fio quente em canal aerodinâmico, na avaliação dos esforços do escoamento sobre os tubos com o uso de uma célula de carga e na visualização dos efeitos do fenômeno biestável sobre os tubos livres para rotacionar. Os dados obtidos da medição no canal são tratados com o uso de ferramentas estatísticas, espectrais e de ondaletas. Os resultados das visualizações do escoamento são apresentados através de imagens obtidas das filmagens realizadas com uma câmera digital. A investigação experimental consiste de ensaios de cilindros rígidos elasticamente montados e pivotados na base e posteriormente liberados para oscilar e/ou rotacionar em um eixo central aos dois tubos, submetidos ao escoamento perpendicular permanente de ar no canal Nos resultados experimentais observam-se a presença da biestabilidade e nota-se o comportamento não simultâneo deste fenômeno ao longo dos cilindros. A formação assimétrica das esteiras também é estudada e atribuída à interação entre os vórtices das esteiras, já que, inicialmente, o desprendimento dos vórtices atrás dos cilindros é simétrico. Na avaliação dos esforços por extensiometria, as etapas de condicionamento e aquisição do sinal foram elaboradas e os resultados de deformação mecânica apresentaram similaridade com o fenômeno observado na anemometria experimental. Para um número de Reynolds de 27635 encontrou-se uma força de 26,1 mN com um torque desenvolvido na célula de carga de 84,95Nmm. A técnica de visualização do fenômeno empregada corrobora a interpretação dos resultados obtidos através da técnica de anemometria de fio quente e extensiometria em canal aerodinâmico. / This paper presents an experimental study of the bistability phenomenon that occurs in the simplified geometry of two tubes arranged side by side submitted to a turbulent cross flow. In the analysis we consider the condition of fixed tubes and with a degree of freedom (rotational), submitted to different Reynolds numbers. The experimental technique consists in the measurement of velocity fluctuations through the aerodynamic channel with the hot wire anemometry technique, the evaluation of the stresses of the flow on the tubes with the use of a load cell and the visualization of the effects of the bistable phenomenon on the tubes free to rotate. The data obtained from the measurement in the channel are treated with the use of statistical, spectral and wavelet tools. The results of the flow visualizations are presented through images obtained with a high speed digital camera. The experimental investigation consists of tests of rigid cylinders mounted elastically and pivoted at the base and later released to oscillate and / or to rotate in a central axis to the two tubes, submitted to the flow of air in the channel In the experimental results we observe the presence of bistability and note the non-simultaneous behavior of the phenomenon along the cylinders. The asymmetric formation of the wakes is also studied and attributed to the interaction between the vortices from wakes behind the cylinders, since, initially, the wake detachments is symmetrical. In the evaluation of the forces by means of the extensiometry technique, the steps of conditioning and acquisition of the signal were elaborated and the results of mechanical deformation presented similarity with the phenomenon observed in the experimental anemometry. For a Reynolds number of 27635 a force of 26.1 mN was found with a torque developed in the load cell of 84.95 Nmm. The technique used for the visualization of the phenomenon corroborates the interpretation of the results obtained through hot wire anemometry and extensiometry in aerodynamic channel.

Este trabalho apresentada um estudo experimental do fenômeno de biestabilidade que ocorre na geometria simplificada de dois tubos dispostos lado a lado submetidos a um escoamento cruzado turbulento. Na análise consideram-se a condição de tubos fixos e com um grau de liberdade (rotacional), submetidos a diferentes números de Reynolds. A técnica experimental consiste na medição de flutuações de velocidade do escoamento através da anemometria de fio quente em canal aerodinâmico, na avaliação dos esforços do escoamento sobre os tubos com o uso de uma célula de carga e na visualização dos efeitos do fenômeno biestável sobre os tubos livres para rotacionar. Os dados obtidos da medição no canal são tratados com o uso de ferramentas estatísticas, espectrais e de ondaletas. Os resultados das visualizações do escoamento são apresentados através de imagens obtidas das filmagens realizadas com uma câmera digital. A investigação experimental consiste de ensaios de cilindros rígidos elasticamente montados e pivotados na base e posteriormente liberados para oscilar e/ou rotacionar em um eixo central aos dois tubos, submetidos ao escoamento perpendicular permanente de ar no canal Nos resultados experimentais observam-se a presença da biestabilidade e nota-se o comportamento não simultâneo deste fenômeno ao longo dos cilindros. A formação assimétrica das esteiras também é estudada e atribuída à interação entre os vórtices das esteiras, já que, inicialmente, o desprendimento dos vórtices atrás dos cilindros é simétrico. Na avaliação dos esforços por extensiometria, as etapas de condicionamento e aquisição do sinal foram elaboradas e os resultados de deformação mecânica apresentaram similaridade com o fenômeno observado na anemometria experimental. Para um número de Reynolds de 27635 encontrou-se uma força de 26,1 mN com um torque desenvolvido na célula de carga de 84,95Nmm. A técnica de visualização do fenômeno empregada corrobora a interpretação dos resultados obtidos através da técnica de anemometria de fio quente e extensiometria em canal aerodinâmico. / This paper presents an experimental study of the bistability phenomenon that occurs in the simplified geometry of two tubes arranged side by side submitted to a turbulent cross flow. In the analysis we consider the condition of fixed tubes and with a degree of freedom (rotational), submitted to different Reynolds numbers. The experimental technique consists in the measurement of velocity fluctuations through the aerodynamic channel with the hot wire anemometry technique, the evaluation of the stresses of the flow on the tubes with the use of a load cell and the visualization of the effects of the bistable phenomenon on the tubes free to rotate. The data obtained from the measurement in the channel are treated with the use of statistical, spectral and wavelet tools. The results of the flow visualizations are presented through images obtained with a high speed digital camera. The experimental investigation consists of tests of rigid cylinders mounted elastically and pivoted at the base and later released to oscillate and / or to rotate in a central axis to the two tubes, submitted to the flow of air in the channel In the experimental results we observe the presence of bistability and note the non-simultaneous behavior of the phenomenon along the cylinders. The asymmetric formation of the wakes is also studied and attributed to the interaction between the vortices from wakes behind the cylinders, since, initially, the wake detachments is symmetrical. In the evaluation of the forces by means of the extensiometry technique, the steps of conditioning and acquisition of the signal were elaborated and the results of mechanical deformation presented similarity with the phenomenon observed in the experimental anemometry. For a Reynolds number of 27635 a force of 26.1 mN was found with a torque developed in the load cell of 84.95 Nmm. The technique used for the visualization of the phenomenon corroborates the interpretation of the results obtained through hot wire anemometry and extensiometry in aerodynamic channel.

O presente trabalho aborda um estudo sobre o fenômeno de biestabilidade em escoamentos transversais turbulentos sobre dois cilindros lisos paralelos, com razão de espaçamento, p/d, de 1,26, utilizando abordagem numérica e experimental. Nas comparações consideram-se o domínio computacional e a seção de testes experimental equivalentes. As análises comparam escoamentos turbulentos com números de Reynolds subcríticos, variando entre Re = 17000 e Re = 26000, além disto, uma análise laminar comparativa com Re = 167 é executada. Nas avaliações experimentais utilizam-se velocidades médias e flutuações de velocidade, adquiridas com a técnica de anemometria de fio quente, exploram-se também dados de flutuações de pressão obtidos com microfones condensadores posicionados na parede do canal aerodinâmico. Para comparação experimental e numérica executam-se leituras de pressões estáticas ao longo do canal aerodinâmico. Os sinais temporais das aquisições são analisados estatisticamente com médias e momentos, transformada de Fourier e transformada de ondaletas para caracterização e identificação do fenômeno biestável. Na avaliação numérica é executada a solução das equações de Navier-Stokes, utilizando a simulação LES (Large Eddy Simulation) com modelo Smagorinsky-Lilly dinâmico para sub-malha e a simulação URANS (Unsteady Reynolds Averaged Navier-Stokes) com o modelo de turbulência k ω – SAS (Scale Adaptive Simulation). Os resultados das duas abordagens são comparados utilizando as médias de valores, comportamento temporal e valores do número de Strouhal. O estudo de qualidade de malha, com o método GCI (Grid Convergence Index), é aplicado nas malhas utilizadas em URANS. Para a validação da simulação LES, aplica-se análise de quantidade de energia cinética resolvida comparando com resultados experimentais e uma metodologia para verificação da solução descrita na literatura, com a qual um comparativo entre duas simulações LES com diferentes malhas é executado. Nos resultados numérico e experimental observam-se a presença da biestabilidade e nota-se o comportamento não simultâneo da mesma ao longo dos cilindros. Este comportamento é observado nas análises numérica e experimental. A formação assimétrica das esteiras também é estudada e atribuída à interação entre os vórtices das esteiras, já que, inicialmente, os desprendimentos dos mesmos são simétricos. Na investigação do escoamento entre os cilindros a presença da perturbação da velocidade média é observada, mas a mesma não apresenta relação direta com a troca biestável. A alteração do patamar da velocidade média, neste caso, é resultado da influência da troca de modos que acontece nas esteiras. A biestabilidade também é observada na flutuação de pressão, de forma similar ao comportamento obtido com flutuações de velocidade nos estudos da literatura. No comparativo entre os dois métodos numéricos observa-se boa concordância nos resultados obtidos utilizando URANS com modelo k ω – SAS em relação aos observados com LES, sendo possível prever os principais comportamentos, mesmo com a aplicação da lei de parede na região entre cilindros na simulação URANS. / This paper reports a study on the bistable phenomenon in turbulent crossflow over two parallel smooth cylinders with spacing rate, p/d, 1.26 using numerical and experimental approaches. In the comparisons, the computational domain and experimental tests section are considered equivalents. Turbulent flows with subcritical Reynolds numbers ranging between Re = 17000 and Re = 26000 are compared and, in addition, a comparative laminar analysis with Re = 167. In the experimental evaluations the mean velocity and fluctuations velocities are used and acquired with the hot-wire anemometry technique, exploiting also pressure fluctuations data, obtained with condenser microphones positioned in the wall of the aerodynamic channel. For experimental and numerical comparisons, the static pressure over the aerodynamic channel using pressure taps is executed. The temporal signals from the acquisitions are analyzed statistically with mean and moments, Fourier transform and wavelet transform for characterization and identification of the bistable phenomenon. In the numerical evaluation performed, the Navier-Stokes equations are solved using LES simulation (Large Eddy Simulation) with Smagorinsky-Lilly dynamic model for sub-grid and URANS simulation (Unsteady Reynolds Averaged Navier-Stokes) with the turbulence model k ω – SAS (Scale Adaptive Simulation). The results of the two numerical approaches are compared using the mean values, temporal behavior and values of the Strouhal number. The mesh quality study is executed using the GCI (Grid Convergence Index) for the mesh used in URANS. To validate the LES simulation, the amount of solved kinetic energy is compared with experimental amounts. For verification of the LES solution a method described on literature is used, in which a comparison between two LES simulations with different meshes is performed. In the numerical and experimental results, the presence of bistability were observed and in addition the non-simultaneous behavior of the phenomenon over the cylinder was identified in both analyzes. The wakes asymmetric formation was also studied and attributed to the interaction between the vortices of the wakes, since initially the detachments are symmetrical. In the investigation of the flow between the cylinders, the presence of the average velocity disturbance is observed, but it does not have direct relation with the bistable switch. The change in the average velocity level, in this case, is the result of the switching modes influence from the change in the wakes. The bistability is observed also in pressure fluctuation, similar to the behavior obtained with velocity fluctuations in the literature. Comparing the two numerical methods were observed good agreement in the results obtained using URANS with model k ω - SAS in relation to those observed with LES, being possible to predict the main behaviors, even with the application of wall law in the region between cylinders for the URANS simulation.

Mathematical models displaying travelling waves appear in a variety of domains. These waves are often faced with different kinds of perturbations. In some cases, these perturbations result in propagation failure, also known as wave-blocking. Wave-blocking has been studied in the case of several specific models, often with the help of numerical tools. In this thesis, we will display a technique that uses symmetry and a center manifold reduction to find a criterion which defines regions in parameter space where a wave will be blocked. We focus on waves with low velocity and small symmetry-breaking perturbations, which is where the blocking initiates; the organising center. The range of the tools used makes the technique easily generalizable to higher dimensions. In order to demonstrate this technique, we apply it to the bistable equation. This allows us to do calculations explicitly. As a result, we show that wave-blocking occurs inside a wedge originating from the organising center and derive an expression for this wedge to leading order. We verify our results with some numerical simulations.

<div>Lattices composed of bistable elements are of great significance across various fields of science and engineering due to their ability to support a class of solitary waves, called transition waves. Common with all solitary waves, transition waves carry highly concentrated energy with minimal degradation and thus have many useful engineering applications, such as extreme waveguides, bandgap transmission, vibration absorption, and energy harvesting. The rich dynamics arising from the strong nonlinearities of the constitutive bistable microstructures still have much to be unveiled for the practical implementation of the transition waves in real-world engineering structures. Especially, the quasi-particle characteristics of the transition waves can potentially address the performance limits posed by the unit cell size in linear metamaterials.</div><div><br></div><div>In this thesis, we first present an input-independent generation of transition waves in the lattices of asymmetric bistable unit cells when snap-through transitions occur at any site within the lattice. The resulting responses are invariant across the lattice except near the boundaries. These characteristics imply useful applications in broadband energy harvesting, exploiting the highly concentrated energy of the transition waves. We further observe that the inherent lattice discreteness induces dominantly monochromatic oscillatory tail following the main transition wave. This radiated energy of the tail can always be efficiently harvested through resonant transduction regardless of the input excitations. This type of bistable lattice transforms any input disturbance into an output form that can be conveniently transduced; thus, energy harvesting becomes an inherent metamaterial property of the bistable lattice.</div><div><br></div><div>To enhance the responses further for improved energy harvesting capability, we introduce engineered defects in the form of a mass impurity, inhomogeneous inter-site stiffness, and their combinations, achieving localization of energy at desired sites. Remarkably, we also observe a long-lived breather-like mode for the first time in this type of lattice. To enhance the tail motions globally across the lattice, we investigate the responses in a set of bistable lattices with the same mass and elastic densities but with different lattice spacing distances (or lattice discreteness). From the available tail energy, we observe a significant increase in the harvesting capability with the increased lattice discreteness.</div><div><br></div><div>Next, the effect of functional grading on the onsite and inter-site stiffnesses are investigated to augment the control of the transition waves in the bistable lattices. The unidirectionality still remains in the direction of decreasing stiffness, while a boomerang-like wave reversal occurs in the direction of increasing stiffness. Both the compression and rarefaction transition waves are allowed to propagate, enabling continuous transmission of the transition waves without complex resetting mechanisms, thus expanding the bistable lattices' functionality for practical applications.</div><div><br></div><div>The observed input-independent dynamics of the one-dimensional bistable lattices can be extended to higher-dimensional metastructures by allowing macrostructural flexibility. Metabeams composed of spring-joined bistable elements are subjected to in-plane sinusoidal input at the microstructural level, and the out-of-plane responses at the macrosctructural level are measured. As long as transition waves are triggered within the metabeam, the most dominant output frequency occurs near the natural frequency of the macroscopic structure regardless of the input excitations initiating the transition waves, yielding energy transfer between uncorrelated frequencies.</div><div><br></div><div>Finally, high-fidelity in-house numerical solvers are developed for the massively parallelized computation of the problems involving generic bistable architectures, addressing the problem size limit. The improved numerical solution accuracy and computational performance, compared to those of commercial solvers, provide great potential to discover new dynamics by drastically expanding the accessible analysis regimes.</div><div><br></div><div>The experiments, simulations, and theoretical contributions in this thesis illustrate the possibilities afforded by strongly nonlinear phenomena to tailor the dynamics of materials systems. Importantly, the presented results show mechanisms to affect global dynamic properties unconstrained by the unit cell size, thereby offering new routes to extreme dynamics beyond current metamaterial architectures.</div>

The purpose of this research is to present a class of Self-Retracting Fully-compliant Bistable Micromechanisms (SRFBM). Fully-compliant mechanisms are needed to overcome the inherent limitations of microfabricated pin joints, especially in bistable mechanisms. The elimination of the clearances associated with pin joints will allow more efficient bistable mechanisms with smaller travel. Small travel, in a linear path facilitates integration with efficient on-chip actuators. Tensural pivots are developed and used to deal with the compressive loading to which the mechanism is subject. SRFBM are modeled using the Pseudo-Rigid-Body Model and finite element analysis. Suitable configurations of the SRFBM concept have been identified and fabricated using the MUMPs process. Complete systems, including external actuators and electrical contacts are 1140 μm by 625 μm (individual SRFBM are less than 300 μm by 300 μm). These systems have been tested, demonstrating on-chip actuation of bistable mechanisms. Power requirements for these systems are approximately 150 mW. Testing with manual force testers has also been completed and correlates well with finite element modeling. Actuation force is approximately 500 μN for forward actuation. Return actuation can be achieved either by external actuators or by thermal self-retraction of the mechanism. Thermal self-retraction is more efficient, but can result in damage to the mechanism. Fatigue testing has been completed on a single device, subjecting it to approximately 2 million duty cycles without failure. Based on the SRFBM concept a number of improvements and adaptations are presented, including systems with further power and displacement reductions and a G-switch for LIGA fabrication.