Browsing by Subject "Mechanics"

This dissertation proposes a family of computational frameworks for fracture modeling in coupled field problems. Fracture mechanics has been a topic of considerable interest for several decades due to the wide existence of fracture in different engineering structures and the important applications of fracture in multiple industries.

The present study first develops a continuum-discrete approach to model the fluid-driven fracture of granular media. This approach avoids remeshing by representing the particles as moving interfaces on a fixed background mesh. The effect of particle movement on the flow is characterized by a non-slip boundary condition. A boundary split scheme is proposed to ensure the coercivity of the method. The fluid-driven force on particles is represented by a boundary integral of the viscous drag force around the particles. The corresponding initial-boundary value problem is constructed for the invading fluid and is spatially discretized with the finite element method. A novel quadrature method is developed to handle partial elements that arise due to the mismatch between the mesh and the physical domain. The conditioning issue of partial elements is also addressed in the present study.

The present study also aims at developing a general and robust computational approach for the fracture modeling of conventional materials within coupled field problems. We follow the framework of a phase field regularization because of its strength in handling complex fracture patterns. The first application we consider is the fracture simulation of kidney stones during shock wave lithotripsy (SWL), an acoustic-solid-fracture coupling problem. The present study develops a novel computational framework for simulating SWL.

The propagation of acoustic pressure is modeled by a wave equation and the deformation of the phantom stone is modeled by the elasto-dynamics equations. The interactions between the acoustic wave and kidney stone is enforced via the continuity condition. The initialization and propagation of fracture within the stone is implicitly represented by the evolution of the phase field.

Traditional phase field is designed to model the brittle fracture of homogeneous materials. The present study develops a phase field framework to model fracture propagation in anisotropic and heterogeneous solids. The present model is distinguished from the traditional phase field approach by the fact that it converges to a cohesive type model instead of a Griffith model. A mathematically self-consistent strain energy density functional is proposed that is valid for any anisotropic linear elastic materials. Anisotropy in both the bulk moduli and the crack surface energy are characterized. The model employs multiple phase fields to capture the fracture behavior of the material with more than one preferential cleavage plane. The model develops a novel degradation function which relaxes the strong constraint between the regularization length l and the material properties. The convergence of the model with reducing l and the energy conservation properties of the framework are demonstrated through numerical examples. A robust adaptivity strategy is developed to increase the efficiency of the model. The present framework is applied to model fracture in heterogeneous and anisotropic materials. Coupled with a fine scale analysis, the present model is also used to model the fracture of functionally graded materials.

The dynamics of impacting components is of particular interest to engineers due to concerns about noise and wear, but is particularly difficult to study due to impact's non-linear nature. To begin transferring concepts studied purely analytically to the world of physical mechanisms, four experiments are outlined, and important non-linear concepts highlighted with these systems. A linear oscillator with a kicked impact, an impacting forced pendulum, two impacting forced pendulums, and a cam follower pair are studied experimentally, with complementary numerical results.

Some important ideas highlighted are limit cycles, basins of attraction with many wells, grazing, various forms of coexistence, super-persistent chaotic transients, and liftoff. These concepts are explored using a variety of non-linear tools such as time lag embedding and stochastic interrogation, and discussions of their intricacies when used in non-smooth systems yield important observations for the experimentalist studying impacting systems.

The focus is on experimental results with numerical validation, and spends much time discussing identification of these concepts from an experiment-first mindset, rather than the more traditional analytical-first approach. As such a large volume of experimentally important information on topics such as transducers and forcing mechanism construction are included in the appendices.

Fracture is a common phenomenon in engineering applications. Many types of fracture exist, including, but not limited to, brittle fracture, quasi-brittle fracture, cohesive fracture, and ductile fracture. Predicting fracture has been one of the most challenging research topics in computational mechanics. The variational treatment of fracture and its associated phase-field regularization have been employed with great success for modeling fracture in brittle materials. Extending the variational statement to describe other types of fracture and coupled field phenomena has proven less straightforward. Main challenges that remain include how to best construct a total potential that is both mathematically sound and physically admissible, and how to properly describe the coupling between fracture and other phenomena.

The research presented in this dissertation aims at addressing the aforementioned challenges. A variational framework is proposed to describe fracture in general dissipative solids. In essence, the variational statement is extended to account for large deformation kinematics, inelastic deformation, dissipation mechanisms, dynamic effects, and thermal effects. The proposed variational framework is shown to be consistent with conservations and laws of thermodynamics, and it provides guidance and imposes restrictions on the construction of models for coupled field problems. Within the proposed variational framework, several models are instantiated to address practical engineering problems. A brittle and quasi-brittle fracture model is used to investigate fracture evolution in polycrystalline materials; a cohesive fracture model is applied to revisit soil desiccation; a novel ductile fracture model is proposed and successfully applied to simulate some challenging benchmark problems; and a creep fracture model is developed to simulate the spallation of oxide scale on high temperature heat exchangers.

Biosensing is a critical area of research that involves detecting and measuring biological molecules. Among the various types of biosensors, acoustic biosensors are attractive for their simplicity, robustness, and low cost, particularly in point-of-care (POC) applications. However, the quality factor (Q-factor) of acoustic biosensors is often low, limiting their sensitivity and accuracy in terms of in-liquid gravimetric detection for biosensing applications. In this dissertation, we present a novel approach that eliminates nearly all dissipation and damping from sample liquids, rendering a significant improvement in Q-factor for in-liquid gravimetric detection. We constructed rigid microfluidic channels to confine liquids and the associated acoustic energy, thereby eliminating acoustic radiation damping. We also used the channels' side walls to create pressure waves, confining the liquids within and suppressing acoustic damping due to the viscous layer. The quartz crystal microbalance (QCM) was selected as the model system for implementing the new paradigm due to its widespread usage in various applications, simplicity, cost-effectiveness, and relevance of its principles to other types of acoustic biosensors. We hypothesized that the ratio of the wavelength of the pressure wave to the width of the channels is a crucial determining factor for optimal performance. We then tested the hypothesis by building the microfluidic QCM (the µ-QCM) to improve the Q-factor of conventional QCM. The combination of experiments, simulations, and theoretical studies demonstrated a 10-fold improvement in the Q-factor. The new system offers many other advantages, including direct data interpretation, minimized sample volume requirement, and easier temperature control for in-liquid gravimetric detection. Additionally, the same principles can be applied to other acoustic biosensors, benefiting the entire field.

A variety of intriguing surface patterns have been observed on developing natural systems, ranging from corrugated surface of white blood cells at nanometer scales to wrinkled dog skins at millimeter scales. To mimetically harness functionalities of natural morphologies, artificial transformative skin systems by using soft active materials have been rationally designed to generate versatile patterns for a variety of engineering applications. The study of the mechanics and design of these dynamic surface patterns on soft active materials are both physically interesting and technologically important.

This dissertation starts with studying abundant surface patterns in Nature by constructing a unified phase diagram of surface instabilities on soft materials with minimum numbers of physical parameters. Guided by this integrated phase diagram, an electroactive system is designed to investigate a variety of electrically-induced surface instabilities of elastomers, including electro-creasing, electro-cratering, electro-wrinkling and electro-cavitation. Combing experimental, theoretical and computational methods, the initiation, evolution and transition of these instabilities are analyzed. To apply these dynamic surface instabilities to serving engineering and biology, new techniques of Dynamic Electrostatic Lithography and electroactive anti-biofouling are demonstrated.

Many physical systems are modeled using partial dierential equations (PDEs) with uncertain or random inputs. For such systems, naively propagating a xed number of samples of the input probability law (or an approximation thereof) through the PDE is often inadequate to accurately quantify the risk associated with critical system responses. In addition, to manage the risk associated with system response and devise risk-averse controls for such PDEs, one must obtain the numerical solution of a risk-averse PDE-constrained optimization problem, which requires substantial computational eorts resulting from the discretization of the underlying PDE in both the physical and stochastic dimensions.

Bayesian Inverse problem, where unknown system parameters need to be inferred from some noisy data of the system response, is another important class of problems that suffer from excessive computational cost due to the discretization of the underlying PDE. To accurately characterize the inverse solution and quantify its uncertainty, tremendous computational eorts are typically required to sample from the posterior distribution of the system parameters given the data. Surrogate approximation of the PDE model is an important technique to expedite the inference process and tractably solve such problems.

In this thesis, we develop a goal-oriented, adaptive sampling and local reduced basis approximation for PDEs with random inputs. The method, which we denote by local RB, determines a set of samples and an associated (implicit) Voronoi partition of the parameter domain on which we build local reduced basis approximations of the PDE solution. The local basis in a Voronoi cell is composed of the solutions at a xed number of closest samples as well as the gradient information in that cell. Thanks to the local nature of the method, computational cost of the approximation does not increase as more samples are included in the local RB model. We select the local RB samples in an adaptive and greedy manner using an a posteriori error indicator based on the residual of the approximation.

Additionally, we modify our adaptive sampling process using an error indicator that is specifically targeted for the approximation of coherent risk measures evaluated at quantities of interest depending on PDE solutions. This allow us to tailor our method to efficiently quantify the risk associated with the system responses. We then combine our local RB method with an inexact trust region method to eciently solve risk-averse optimization problems with PDE constraints. We propose a numerical framework for systematically constructing surrogate models for the trust-region subproblem and the objective function using local RB approximations.

Finally, we extend our local RB method to eciently approximate the Gibbs posterior distribution for inverse problems under uncertainty. The local RB method is employed to construct a cheap surrogate model for the loss function in the Gibbs posterior formula. To improve the accuracy of the surrogate approximation, we adopt a Sequential Monte Carlo framework to guide the progressive and adaptive construction of the local RB surrogate. The resulted method provides subjective and ecient inference of unknown system parameters under general distribution and noise assumptions.

We provide theoretical error bounds for our proposed local RB method and its extensions, and numerically demonstrate the performance of our methods through various examples.

Interfaces play a dominant role in governing the response of many biological systems and they pose many challenges to traditional finite element. For sharp-interface model, traditional finite element methods necessitate the finite element mesh to align with surfaces of discontinuities. Diffuse-interface model replaces the sharp interface with continuous variations of an order parameter resulting in significant computational effort. To overcome these difficulties, we focus on developing a computationally efficient spline-based finite element method for interface problems.

A key challenge while employing B-spline basis functions in finite-element methods is the robust imposition of Dirichlet boundary conditions. We begin by examining weak enforcement of such conditions for B-spline basis functions, with application to both second- and fourth-order problems based on Nitsche's approach. The use of spline-based finite elements is further examined along with a Nitsche technique for enforcing constraints on an embedded interface. We show that how the choice of weights and stabilization parameters in the Nitsche consistency terms has a great influence on the accuracy and robustness of the method. In the presence of curved interface, to obtain optimal rates of convergence we employ a hierarchical local refinement approach to improve the geometrical representation of interface.

In multiple dimensions, a spline basis is obtained as a tensor product of the one-dimensional basis. This necessitates a rectangular grid that cannot be refined locally in regions of embedded interfaces. To address this issue, we develop an adaptive spline-based finite element method that employs hierarchical refinement and coarsening techniques. The process of refinement and coarsening guarantees linear independence and remains the regularity of the basis functions. We further propose an efficient data transfer algorithm during both refinement and coarsening which yields to accurate results.

The adaptive approach is applied to vesicle modeling which allows three-dimensional simulation to proceed efficiently. In this work, we employ a continuum approach to model the evolution of microdomains on the surface of Giant Unilamellar Vesicles. The chemical energy is described by a Cahn-Hilliard type density functional that characterizes the line energy between domains of different species. The generalized Canham-Helfrich-Evans model provides a description of the mechanical energy of the vesicle membrane. This coupled model is cast in a diffuse-interface form using the phase-field framework. The effect of coupling is seen through several numerical examples of domain formation coupled to vesicle shape changes.

This thesis assesses the role of several types of designed initial imperfection on the buckling behavior of 3D printed cylindrical shells through experimental method. The buckling loads and paths are given by the axial compression tests while the lateral force-displacement relationships are given by the lateral poking tests at first. Then the influences of designed imperfections on them are discussed. The test results show that the effect of designed initial imperfections in this thesis might be overridden by other unpredictable imperfections. Poking tests can provide some information on the buckling loads and paths that is difficult to obtain through compression tests. The designed buckling mode shapes imperfections may generate bigger influences than the designed imperfections as shown in this thesis.

This dissertation addresses interface problems simulated with the finite element method (FEM) with mesh adaptivity. More specifically, we concentrate on the strategies that adaptively modify the mesh and the associated data transfer issues.

In finite element simulations there often arises the need to change the mesh and continue the simulation on a new mesh. Analysts encounter such an issue when they adaptively refine the mesh to reduce the computational cost, smooth distorted elements to improve system conditioning, or introduce new surfaces and change the domain in simulations of fracture problems. In such circumstances, the transfer of data from the old mesh to the new one is of crucial importance, especially for nonlinear problems. We are concerned in this work with contact problems with adaptive re-meshing and fracture problems modeled with the eXtended finite element method (X-FEM). For the former ones, the transfer of surface data is built upon the technique of parallel transport, and the error of such a transfer strategy is investigated through classic benchmark tests. A transfer scheme based on a least squares problem is also proposed to transfer the bulk data when nearly incompressible hyperelastic materials are employed. For the latter type of problems, we facilitate the transfer of internal variables by making partial elements utilize the same quadrature points from the uncut parent elements and meanwhile adjusting the quadrature weights via the solution of moment fitting equations. The proposed scheme helps avoid the complicated remapping procedure of internal variables between two different sets of quadrature points. A number of numerical examples are presented to demonstrate the robustness and accuracy of our proposed approaches.

Another renowned technique to simulate fracture problems is based upon the phase-field formulation, where a set of coupled mechanics and phase-field equations are solved via FEM without modeling crack geometries. However, losing the ability to model distinct surfaces in the phase-field formulation has drawbacks, such as difficulties simulating contact on crack surfaces and poorly-conditioned stiffness matrices. On the other hand, using the pure X-FEM in fracture simulations mandates the calculation of the direction and increment of crack surfaces at each step, introducing intricacies of tracing crack evolution. Thus, we propose combining phase-field and X-FEM approaches to utilize their individual benefits based on a novel medial-axis algorithm. Consequently, we can still capture complex crack geometries while having crack surfaces explicitly modeled by modifying the mesh with the X-FEM.

From batteries to bones, rocks to concrete, porous materials are ubiquitous in the natural and engineered environment, yet remain elusive in their characterization. One of the fundamental challenges of studying porous materials comes down to a fundamental question of linking the microscale to the mesoscale. This work addresses two primary linkages for analysis--the chemical response and the mechanical response of the material. Minkowski functionals served as the primary vessel for understanding how material microstructural geometry ties to macroscale energetics. In the case of chemical systems, Minkowski functionals proved to be powerful predictive tools in both reaction steady states and reaction dynamics. These exponential linkage to morphometers serves as a basis for understanding how the interfacial geometry of system affects the non-mixed chemical behavior of said system over time.As a study on novel simulation frameworks for modeling discrete chemical behavior at the microstructural scale, this work also introduces a unique means for modeling interface chemistry--surface CRNs. Surface CRNs are asynchronous cellular automata models similar to Markov chain models. This class of simulator efficiently translates complex chemical behavior into relatively easy-to-follow reaction rules. This class of simulator has proven to be surprisingly accurate despite its simplicity, creating a strong basis for understanding chemical behavior at a discrete level. While one half of this work focused on the ability of Minkowski functionals to predict chemical behavior, the other half of this work focuses on their ability to link to the mechanics of a microstructure. To address the mechanics problem, Minkowski functionals were extracted from 3D x-ray tomographic scans and assessed mechanically via 3D printed and digitally modeled strength assessments. Ultimately, a deep learning model was trained that could accurately predict and recreate the mechanical response profile of a digitally simulated porous microstructure from just four Minkowski functionals. This extended further to 3D printed samples, allowing for the mechanical behavior of physical samples to be predicted just from its geometric descriptors.

This dissertation focuses on acceleration techniques for Uncertainty Quantification (UQ). The manuscript is divided into five chapters. Chapter 1 provides an introduction and a brief summary of Chapters 2, 3, and 4. Chapter 2 introduces a model reduction strategy that is used in the context of elasticity imaging to infer the presence of an inclusion embedded in a soft matrix, mimicking tumors in soft tissues. The method relies on Polynomial Chaos (PC) expansions to build a dictionary of surrogates models, where each surrogate is constructed using a different geometrical configuration of the potential inclusion. A model selection approach is used to discriminate against the different models and eventually select the most appropriate to estimate the likelihood that an inclusion is present in the domain. In Chapter 3, we use a Domain Decomposition (DD) approach to compute the Karhunen-Loeve (KL) modes of a random process through the use of local KL expansions at the subdomain level. Furthermore, we analyze the relationship between the local random variables associated to the local KL expansions and the global random variables associated to the global KL expansions. In Chapter 4, we take advantage of these local random variables and use DD techniques to reduce the computational cost of solving a Stochastic Elliptic Equation (SEE) via a Monte Carlo sampling method. The approach takes advantage of a lower stochastic dimension at the subdomain level to construct a PC expansion of a reduced linear system that is later used to compute samples of the solution. Thus, the approach consists of two main stages: 1) a preprocessing stage in which PC expansions of a condensed problem are computed and 2) a Monte Carlo sampling stage where samples of the solution are computed in order to solve the SEE. Finally, in Chapter 5 some brief concluding remarks are provided.

The main objectives of this research are: (i) to elaborate a unified nonlinear viscoelastic model for rubber-like materials, in finite strain, accounting for material softening under deformation, and for damage induced anisotropy, (ii) to conceive, implement and test, simple, robust and efficient frictional rolling and sliding contact algorithms, in steady-state, as alternatives to existing, general purpose, contact solving strategies, (iii) to develop and verify high fidelity and computationally efficient modeling tools for isotropic and anisotropic viscoelastic objects in steady-state motion, (iv) to investigate, numerically and through experimentation, the influence of various material parameters, including material nonlinearities such at the Payne effect and the Mullins effect, as well as geometric parameters and contact surface conditions, on viscoelastic rolling resistance, and (iv) to explore, analytically and through experimentation, the conditions under which favorable mechanical synergies occur between material components and develop novel composites with improved structural performances.

A new constitutive model that unifies the behavioral characterizations of rubber-like materials in a broad range of loading regimes is proposed. The model reflects two fundamental aspects of rubber behavior in finite strain: (i) the Mullins effect, and (ii) hyper-viscoelasticity with multiple time scales, including at high strain rates. Suitable means of identifying the system's parameters from simple uniaxial extension tests are explored. A directional approach extending the model to handle softening induced anisotropy is also discussed.

Novel, simple, and yet robust and efficient algorithms for solving steady-state, frictional, rolling/sliding contact problems, in two and three dimensions are presented. These are alternatives to powerful, well established, but in particular instances, possibly `cumbersome' general-purpose numerical techniques, such as finite-element approaches based on constrained optimization. The proposed algorithms are applied to the rolling resistance of cylinders and spheres.

Two and three-dimensional boundary element formulations of isotropic, transversely isotropic, and fully orthotropic, compressible and incompressible, viscoelastic layers of finite thickness are presented, in a moving frame of reference. The proposed formulations are based on two-dimensional Fourier series expansions of relevant mechanical fields in the continuum of the layers and support any linear viscoelastic material model characterized by general frequency-domain master-curves. These modeling techniques result in a compliance matrix for the upper boundary of the layers, including the effects of steady-state motion. Such characterizations may be used as components in various problem settings to generate sequences of high fidelity solutions for varying parameters. These are applied, in combination with appropriate contact solvers, to the rolling resistance of rigid cylinders and spheres.

The problem of a viscoelastic sphere moving across a rigid surface is significantly more complicated than that of a rigid indenter on a viscoelastic plane. The additional difficulties raised by the former may explain why previous work on this topic is so sparse. A new boundary element formulation for the multi-layered viscoelastic coating of a rigid sphere is developed. The model relies on the assumption of a relatively small contact surface in order to decouple equilibrium equations in the frequency domain. It is applied in combination with an adapted rolling contact solving strategy to the rolling resistance of a coated sphere.

New modeling approaches yielding rolling resistance estimates for rigid spheres (and cylinders) on viscoelastic layers of finite thicknesses are also introduced, as lower-cost alternatives to more comprehensive solution-finding strategies, including those proposed in this work. Application examples illustrate the capabilities of the different approaches over their respective ranges of validity.

The computational tools proposed in this dissertation are verified by comparison to dynamic finite element simulations and to existing solutions in limiting cases. The dependencies of rolling resistance on problem parameters are explored. It is for instance shown that, on orthotropic layers, the dissipated power varies with the direction of motion, which suggests new ways of optimizing the level of damping in various engineering applications of very high impact. Interesting lateral viscoelastic effects resulting from material asymmetry are unveiled. These phenomena could be harnessed to achieve smooth and `invisible' guides across three-dimensional viscoelastic surfaces, and hence suggest new ways of controlling trajectories, with a broad range of potential applications.

A new experimental apparatus is designed and assembled to measure viscoelastic rolling resistance. Experiments are conducted by rolling steel balls between sheets of rubber. Principal sources of measurement error, specific to the device, are discussed. Rolling resistance predictions are obtained using the computational tools presented in this dissertation, and compared to the measurements. Interesting conclusions are drawn regarding the fundamental influence of the Payne effect on viscoelastic rolling friction.

The work presented in this dissertations finally touches on the mechanical behavior of casing-infill composite tubes, as potential new lightweight structural elements. The axial behavior of composite circular tubes is addressed analytically. The influence of material parameters and geometry on structural performances are revealed and presented in original graphical forms. It is for instance shown that significantly improved overall stiffness and capacity at yield can be obtained using a moderately soft and highly auxetic infill, which further highlights the need to develop new lightweight auxetic materials, without compromising their stiffness. It is furthermore concluded that limited mechanical synergies can be expected in metal-polymer composite tubes, within the linear range of the materials involved. This prediction is confirmed by a bending experiment conducted on an Aluminum-Urethane composite tube. The experiment however reveals unexpected and quite promising mechanical synergies under large deformations. This novel composite has a potential influence on the design and performance of lightweight protecting structures against shocks and accelerations due to impacts, which justifies that it be characterized further.

Nucleic acids are subjected to many different mechanical loadings inside. These loadings could cause large deformations and conformational changes to these molecules. This is why the mechanical properties of nucleic acids are so important to their functions. Here we use a newly designed and built high-performance AFM force spectrometer, supplemented with molecular dynamics simulations and NMR spectroscopy to investigate the relationship between mechanical properties and structure of different nucleic acids.

To test the mechanical properties of nucleic acids, we successfully designed and purpose-built a single molecule puller, an instrument to physically stretch single molecules, at a fraction of the cost of a commercial AFM instrument. This instrument has similar force noise to hybrid instruments, while also exhibiting significantly lower drift, on the order of five times lower. This instrument allows the measurement of subtle transitions as a molecule is stretched. With the addition of a lock-in amplifier, we possibly could obtain better force resolution, the order of femtonewtons.

We find that helical structure does indeed have an effect on the mechanical properties of double-stranded DNA. As the A-form double helix has a shorter, wider structure compared to the B-form helix, its force spectra exhibit a shorter initial length before the overstretching force plateau, compared to B-form DNA. Contrarily, the Z-form double helix has a narrower, more extended helical structure than B-form DNA, and we see this fact manifest in the force spectra of Z-DNA, which has a longer initial length before the overstretching force plateau. Also, interestingly, we find that neither A, nor Z-DNA force spectra display the second melting force plateau. Indicating this plateau is not necessarily cause by melting of strands apart, but rather a feature of B-DNA.

To better understand the forces that stabilized these different structures, specifically base stacking, we also mechanically characterize different single-stranded helical polynucleotides using AFM based force spectroscopy. We expand on previous studies by confirming that single helical polynucleotides undergo a force transition at a force of ~20 pN as they are uncoiled, and also demonstrating, that when stretched beyond this force transition, the molecules behave differently depending on base sequence and backbone sugar. Specifically, the force spectra of poly-adenylic acid possess a linear force region, which persists to ~300 pN, after the force plateau. We also observe that poly-deoxyadenylic acid is comparatively stiffer than other polynucleotides after undergoing two force transitions. By supplementing our force spectroscopic data with MD simulations and NMR spectroscopy, we find that base stacking in adenine is quite strong, persisting above 100 pN. We find that initial helical structure, which is defined by base stacking and backbone sugar, guides the stretching pathway of the polynucleotides. This finding can possibly be extrapolated to the elasticity of double-stranded DNA.

Asymptotic Modal Analysis (AMA) is a computationally efficient and accurate method for studying the response of dynamical systems experiencing banded, random harmonic excitation at high frequencies when the number of responding modes is large. In this work, AMA has been extended to systems of coupled continuous components as well as nonlinear systems. Several prototypical cases are considered to advance the technique from the current state-of-the-art. The nonlinear problem is considered in two steps. First, a method for solving problems involving nonlinear continuous multi-mode components, called Iterative Modal Analysis (IMA), is outlined. Secondly, the behavior of a plate carrying a nonlinear spring-mass system is studied, showing how nonlinear effects on system natural frequencies may be accounted for in AMA. The final chapters of this work consider the coupling of continuous systems. For example, two parallel plates coupled at a point are studied. The principal novel element of the two-plate investigation reduces transfer function sums of the coupled system to an analytic form in the AMA approximation. Secondly, a stack of three parallel plates where adjacent plates are coupled at a point are examined. The three-plate investigation refines the reduction of transfer function sums, studies spatial intensification in greater detail, and offers insight into the diminishing response amplitudes in networks of continuous components excited at one location. These chapters open the door for future work in networks of vibrating components responding to banded, high-frequency, random harmonic excitation in the linear and nonlinear regimes.

The rolling isolation system (RIS) studied in this dissertation functions on the principle of a rolling pendulum; an isolated object rests on a steel frame that is supported at its corners by ball-bearings that roll between shallow steel bowls, dynamically decoupling the floor motion from the response of the object. The primary focus of this dissertation is to develop predictive models that can capture experimentally-observed phenomena and to advance the state-of-the-art by proposing new isolation technologies to surmount current performance limitations. To wit, a double RIS increases the system's displacement capacity, and semi-active and passive damped RISs suppress the system's displacement response.

This dissertation illustrates the performance of various high-performance isolation strategies using experimentally-validated predictive models. Effective modeling of RISs is complicated by the nonholonomic and chaotic nature of these systems which to date has not received much attention. Motivated by this observation, the first part of this dissertation addresses the high-fidelity modeling of a single, undamped RIS, and later this theory is augmented to account for the double (or stacked) configuration and the supplemental damping via rubber-coated bowl surfaces. The system's potential energy function (i.e. conical bowl shape) and energy dissipation model are calibrated to free-response experiments. Forced-response experiments successfully validate the models by comparing measured and predicted peak displacement and acceleration responses over a range of operating conditions.

Following the experimental analyses, numerical simulations demonstrate the potential benefits of the proposed technologies. This dissertation presents a method to optimize damping force trajectories subject to constraints imposed by the physical implementation of a particular controllable damper. Potential improvements in terms of acceleration response are shown to be achievable with the semi-active RIS. Finally, extensive time-history analyses establish how the undamped and damped RISs perform when located inside biaxial, hysteretic, multi-story structures under recorded earthquake ground motions. General design recommendations, supported by critical-disturbance spectra and peak-response distributions, are prescribed so as to ensure the uninterrupted operation of vital equipment.

Electrowetting-on-dielectric (EWD) digital microfluidics is a droplet-based fluid handling technology capable of radically accelerating the pace of genome engineering research. EWD-based laboratory-on-chip (LoC) platforms demonstrate excellent performance in automating labor-intensive laboratory protocols at ever smaller scales. Until now, there has not been an effective means of gene transfer demonstrated in EWD microfluidic platforms. This thesis describes the theoretical and experimental approaches developed in the demonstration of an EWD-enabled electrotransfer device. Standard microfabrication methods were employed in the integration of electroporation (EP) and EWD device architectures. These devices enabled the droplet-based bulk transformation of E. coli with plasmid and oligo DNA. Peak on-chip transformation efficiencies for the EP/EWD device rivaled that of comparable benchtop protocols. Additionally, ultrasound induced in-droplet microstreaming was developed as a means of improving on-chip electroporation. The advent of electroporation in an EWD platform offers synthetic biologists a reconfigurable, programmable, and scalable fluid handling platform capable of automating next-generation genome engineering methods. This capability will drive the discovery and production of exotic biomaterials by providing the instrumentation necessary for rapidly generating ultra-rich genomic diversity at arbitrary volumetric scales.