Doctor of Philosophy (PhD), Ohio University, 2024, Mechanical and Systems Engineering (Engineering and Technology)

This dissertation presents the design and development of a novel hydrodynamic thrust bearing test rig featuring a new (patent pending) pressure-feedback control system for maintaining static bearing alignment. This research aims to provide an enhanced understanding of how the critical operational characteristics of fixed-geometry hydrodynamic thrust bearings including minimum oil film thickness (MOFT), hydrodynamic pressure distribution, and bearing temperature are affected by variability in bearing pad taper geometry under different speed, load, and oil conditions. Further, a new (patent pending) additively manufactured (AM) thrust bearing fabricated using direct metal laser sintering (DMLS) is experimentally evaluated to determine in-service viability. To support the experimental data obtained in the variable taper experiment, a Matlab simulation code is developed using the Reynolds equation to generate numerically predicted performance data for direct comparison. The AM thrust bearing is experimentally compared to a traditionally manufactured cast alloy bearing with identical surface geometry. For the variable taper study, trends in performance established by the numerical analysis show mutually agreeable results compared to experimental data. The average percent deviation of the experimentally gathered change in MOFT as load is increased with respect to the numerically predicted values is 24%. Comparison of experimental to numerical pressure distribution data shows an overall average percent deviation of 32%. For the AM vs. traditionally manufactured bearing experiment, the AM bearing showed an average increase in minimum oil film thickness of 53%, an average increase in trailing edge hydrodynamic pressure of 116%, while exhibiting an average decrease in bearing temperature of 1%.

Committee: Muhammad Ali (Advisor); Khairul Alam (Committee Member); Arthur Smith (Committee Member); Zaki Kuruppalil (Committee Member); Jay Wilhelm (Committee Member) Subjects: Mechanical Engineering

Doctor of Philosophy, University of Akron, 2020, Civil Engineering

The study aims to explore advanced tools for air crash analysis with universal meaning in air-crash analysis and uses the crash of Tu-154M large transport airplane in Smolensk, Russia on April 10, 2010, as an example. The crash was initiated by the impact of the left wing into a large birch tree according to the Russian investigation report. Nevertheless, some facts caused the attention and suspicion to this explanation. The research is devoted to investigate how far the wing has to be damaged for the airplane to lose balance, how a pilot can compensate the degraded aerodynamic performance of the aircraft, how to reconstruct the trajectory of a fall of major debris separated from the airplane in the air are critical in the air-crash analysis, what the most possible mechanism of airplane door is to end up one meter deep and perpendicular berried in the ground, and what the most possible outcome of the airplane wing impact into the birch tree. First of all, the aircraft in landing configuration with various wingtip damage on the left wing was under consideration while the no-damaged case was also studied as the baseline. Wind tunnel test results with a 1:100 scale model were correlated using CFD simulations. The variations of lift force, drag force, and asymmetric rolling moment with respect to the angle of attack and sideslip were investigated for different damage situations. The methods to compensate for the lift force and the asymmetric rolling moment were also investigated for the possibility of a safe landing. Secondly, estimating the trajectory of separated objects after disintegration caused by the impact will be useful in crashes analysis of airplane, especially in the circumstance when the impact condition cannot be determined. Since the motion of an airplane's fragments in the air is highly affected by the aerodynamic loads, computational fluid dynamics with an automated unstructured tetrahedral mesh approach using spring-based smoothing and remeshing a (open full item for complete abstract)

Committee: Wieslaw Binienda (Advisor); Qingdan Huang (Committee Member); Atef Saleeb (Committee Member); Xiaosheng Gao (Committee Member); Lingxing Yao (Committee Member) Subjects: Aerospace Engineering; Civil Engineering

Doctor of Philosophy, Case Western Reserve University, 2016, EECS - Electrical Engineering

Conventional thermoelectric modules (TEMs) are composed of n-type and p-type thermoelectric (TE) legs connected electrically in series and thermally in parallel. The development of TE technology based on the traditional TEM structure has been limited by its low efficiency and high cost. Most of ongoing research nowadays focuses on developing new TE materials that have higher intrinsic efficiency. This research analyzes the TE problem from an electrical engineering angle. The conventional electrically serial structure considers TE legs as voltage power sources. In contrast, this research takes advantage of TE legs as current power sources, leading to an alternative TEM structure, where all TE legs are made from single type of TE material and connected in parallel both electrically and thermally. Experimental, analytical and numerical analysis have been carried out to evaluate the performance of unit modules with the newly proposed electrically parallel structure. It indicates that the modules' figure-of-merit and energy conversion efficiency can be increased within a certain device area limit, the fabrication cost can be decreased, the power density and mechanical durability can be increased, while the temperature gradient is kept in the cross-plane direction. It can also increase the device lifetime, because on the one hand, there is no mismatch between the thermal expansion rate among TE legs. On the other hand, for serial structure, even a single break of the connection can lead to the failure of the device. However, for the electrically parallel structure, a small break of the junction will not affect the performance significantly. Meanwhile, the proposed electrically parallel structure can also benefit the back-end step-up DC-DC converter design. It can produce a higher output voltage (so a higher output power and efficiency) to the load, and possibly work under a slower switching frequency to decrease the switching energy loss. In addition, th (open full item for complete abstract)

Committee: Xiong Yu (Advisor); Christian Zorman (Committee Member); Philip Feng (Committee Member); Hongping Zhao (Committee Member); Chung-Chiun Liu (Committee Member); Alp Sehirlioglu (Committee Member) Subjects: Electrical Engineering; Energy

Doctor of Philosophy, University of Akron, 2014, Civil Engineering

Numerical simulation plays an irreplaceable role in reducing time and cost for the development of aerospace and automotive structures, such as composite fan cases, car roof and body panels etc. However, a practical and computationally-efficient methodology for predicting the performance of large braided composite structures with the response and failure details of constituent level under both static and impact loading has yet to be developed. This study focused on the development of efficient and sophisticated numerical analysis modeling techniques suitable for two-dimensional triaxially braided composite (TDTBC) materials and structures under high speed impact. A new finite element analysis (FEA) based mesomechanical modeling approach for TDTBC was developed independently and demonstrated both stand alone and in the combined multi-scale hybrid FEA as well. This new mesoscale modeling approach is capable of considering the detailed braiding geometry and architecture as well as the mechanical behavior of fiber tows, matrix, and the fiber tow interface, making it feasible to study the details of localized behavior and global response that happen in the complex constituents. Furthermore, it also accounts for the strain-rate effects on both elastic and inelastic behavior and the failure/damage mechanism in the matrix material, which had been long observed in experiments but were neglected for simplicity by researchers. It is capable of simulating inter-laminar and intra-laminar damage and delamination of braided composites subjected to dynamic loading. With high fidelity in both TDTBC architecture and mechanical properties, it is well suited to analyze high speed impact events with improved simulation capability in both accuracy and efficiency. Special attention was paid to the applicability of the method to relatively large scale components or structures. In addition, a novel hybrid multi-scale finite element analysis method, entitled Combined Multiscale (open full item for complete abstract)

Committee: Wieslaw Binienda Dr. (Advisor); Ernian Pan Dr. (Committee Member); Guo-Xiang Wang Dr. (Committee Member); Robert Goldberg Dr. (Committee Member); Qindan Huang Dr. (Committee Member); Kevin Kreider Dr. (Committee Member) Subjects: Aerospace Engineering; Aerospace Materials; Automotive Engineering; Engineering; Mechanical Engineering

Doctor of Philosophy, University of Akron, 2009, Electrical Engineering

Over the last decades, there has been an ever increasing interest in nano-focusing oflight and subwavelength resolution overcoming the classical diffraction limit. Examples of that are scanning near-field optical microscopy (SNOM) and “perfect lenses” with negative-index materials. Development of scanning techniques, better performing probes for SNOM and engineering of effective material parameters depends on numerical modeling more than ever before. More accurate models and precise simulations are required to obtain quantitative rather than just qualitative results. This dissertation discusses numerical challenges of nano-scale structure simulations with enhanced and strongly localized electric field distributions. In particular, the thesis focuses on the simulation of scattering-type apertureless SNOM in the mid-infrared and field distributions in plasmon-enhanced Raman spectroscopy in the visible range. Although the ideas of field enhancement are similar (sharp, optionally plasmon-coated, object causing a strong localized enhancement in the vicinity of an AFM tip), applicable models and the nature of computational and engineering challenges are different. For the plasmon-enhanced SNOM, the quasi-static and the full-wave FEM analyses are compared and a qualitative agreement is shown. The optical response of the AFM tip is shown to correlate with the amplitude of the local field distribution. This allows one to use dark field microscopy for tip testing. Several tip designs proposed in the literature were analyzed using the quasi-static approximation; parametric analysis and optimization were performed for selected tips. Numerical challenges due to the multi-scale nature of the problem and multiple scattering in scattering-type SNOM are exemplified in 3D simulations of a realistic cantilevered AFM tip in the mid-infrared. The finite element method (FEM) with adaptive meshing is shown to be a useful tool, but the computation resources of a st (open full item for complete abstract)

Committee: Igor Tsukerman PhD (Advisor) Subjects: Electrical Engineering; Electromagnetism; Optics

Master of Science, Miami University, 2024, Mechanical and Manufacturing Engineering

Lattice structures are celebrated for their lightweight characteristics and superior mechanical performance. In this research, a strut reinforcement technique was employed to enhance the energy absorption capacities of 3D re-entrant auxetic (Aux), hexagonal (Hex), and hybrid Auxetic-Hexagonal (AuxHex) lattice structures. The investigation involved finite element analysis to delve into the mechanical and energy absorption properties of these novel designs during quasi-static compression testing. The results from the uniaxial compression tests of the reinforced designs were then compared with those from traditional 3D hexagonal and re-entrant auxetic lattice structures. To accurately simulate the mechanical behavior of the 3D printed lattice structures, the mechanical properties of the PA2200 matrix material—manufactured via additive manufacturing—were utilized. The outcomes indicated by the stress-strain and energy absorption curves suggest that these newly proposed designs are optimal for applications requiring high energy absorption at large strains. Thus, these findings pave the way for developing novel designs in 3D hexagonal and re-entrant auxetic lattice structures, which are poised to offer enhanced mechanical strength and exceptional specific energy absorption properties. Expanding on these insights, future research could explore further variations in lattice geometry and reinforcement methods to optimize the performance of these structures under different loading conditions.

Committee: Muhammad Jahan (Advisor); Carter Hamilton (Committee Member); Jinjuan She (Committee Member); Jeff Ma (Advisor) Subjects: Biomechanics; Experiments; Materials Science; Mechanical Engineering; Mechanics

MS, University of Cincinnati, 2024, Engineering and Applied Science: Mechanical Engineering

Within this thesis document we focus on the application of Nonlinear Model Predictive Control (NMPC) onto an epidemic compartmental model. The compartmental model is a partial differential equation (PDE) based Susceptible Latent Infected Recovered (SLIR) epidemic model. This model serves as the basis of the NMPC. In order to generate the necessary parameters for initializing and training the use of constrained optimization, a single-objective Genetic Algorithm (GA), and LSTM (Long-Short-Term-Memory) deep learning were explored. The spatial domains considered for the SLIR epidemic model includes Hamilton County, Ohio as well as the entire state of Ohio, USA. With respect to Hamilton County, Ohio three different time periods were evaluated in which varied levels of infection relating to COVID-19 were observed. At the state wide level only one time period was consider. The NMPC considers two control schemes. The first being control applied uniformly across the spatial domain of interest. While the second focuses on applying the control in a spatially targeted manner to specific geographical areas based on observed higher levels of infection. The NMPC also employs a cost function comprising the infection spread density and the associated cost of applied control measures. The latter of which in turn representing socioeconomic effects. Overall, the NMPC framework developed here is intended to aid in the evaluation of optimal Non-Pharmaceutical Interventions (NPI) towards spread mitigation of infectious diseases.

Committee: Manish Kumar Ph.D. (Committee Chair); Shelley Ehrlich M.D. (Committee Member); Subramanian Ramakrishnan Ph.D. (Committee Member); David Thompson Ph.D. (Committee Member) Subjects: Mechanical Engineering

MS, University of Cincinnati, 2024, Engineering and Applied Science: Mechanical Engineering

The COVID-19 pandemic highlighted the need for improved and precise prediction of the spatiotemporal trends of epidemic transmission. An optimized epidemic model is crucial for effectively forecasting flow of infection. By optimizing the model parameters, they can provide valuable insights into the dynamics of infection transmission and this degree of tuning helps health officials and policymakers to make data-driven decisions regarding disease control strategies, allocation of resources, and planning for healthcare. Therefore, it highlights the need of implementing reliable optimizing strategies in case of epidemic models. Similarly, the basic and effective reproductive numbers (R0, Re) are quantitative metrics widely used for estimating the rate at which the infection propagates. The limitations of existing techniques for estimating R0 and Re points the need for novel approaches to accurately estimate them using the available data. This initial part of this study presents the development of a custom GA which is capable of efficiently searching for the parameters of an epidemic model in any specified geographical region and time period. Following this, a novel computational framework for predicting the reproduction numbers from true infection data has been presented. The computational framework is derived from a reaction-diffusion based PDE epidemic model which involves fundamental mathematical derivations for obtaining their values. The PDE model is optimized using the proposed GA and the model output using the optimized parameters is found to be in correspondence with the ground truth COVID-19 data of Hamilton county, Ohio. Subsequently, the established framework for calculating the reproduction numbers was applied on the optimized model and their predictions are found to correlate with the true incidence data. In addition, these predictions are compared with a commonly used retrospective method (Wallinga-Teunis) and are found to be in harmony thereby est (open full item for complete abstract)

Committee: Manish Kumar Ph.D. (Committee Chair); Subramanian Ramakrishnan Ph.D. (Committee Member); Shelley Ehrlich M.D. (Committee Member); Derek Wolf Ph.D. (Committee Member) Subjects: Mechanical Engineering

PhD, University of Cincinnati, 2024, Arts and Sciences: Mathematical Sciences

This dissertation presents a comprehensive study of a novel enriched Discontinuous Galerkin (xDG) method, designed specifically for solving highly oscillatory differential equations, with a primary focus on its application to High-Intensity Focused Ultrasound (HIFU). HIFU is a medical procedure that employs ultrasound waves, ranging between 0.1 to 20 MHz, to target and ablate abnormal tissues within the body, serving as a motivating application for this research. Central to this study is a comparative analysis between the proposed enriched Symmetric Interior Penalty Galerkin (xSIPG) method and its predecessors, highlighting the advancements in solving crucial differential equations, notably the Helmholtz and Bioheat equations. These equations are pivotal for understanding the propagation of ultrasound waves and their interaction with human tissues. A significant achievement of this research is the optimization of penalty parameters within the xDG framework, which plays an essential role in the accuracy and computational efficiency of the methods. The results indicate xSIPG's significant improvement in modeling efficiency for HIFU simulations, potentially enhancing computational performance by up to three orders of magnitude compared to conventional FEM. Moreover, this study establishes the limitations of previous xDG methods in fully capturing the complexities of the HIFU model, a challenge addressed by the xSIPG approach. This advancement not only highlights the methodological leap facilitated by the xSIPG method but also reinforces the potential of applying xDG techniques to simulate HIFU.

Committee: Benjamin Vaughan Ph.D. (Committee Chair); Deniz Bilman Ph.D. (Committee Member); Sookkyung Lim Ph.D. (Committee Member) Subjects: Mathematics

MS, University of Cincinnati, 2021, Engineering and Applied Science: Aerospace Engineering

As global warming becomes a cause of serious concern worldwide, stricter and stricter emission regulations are being imposed on gas turbine engines. Flameless combustion is a novel combustion technique that offers a significant reduction in NOx and CO emissions. The presence of a flameless flame is indicated by uniform temperature distribution in the combustor, which leads to simultaneous reductions in NOx and CO emissions. Nick Overman conducted tests on a swirl stabilized flameless burner in the GDPL lab at the University of Cincinnati. A well-distributed flameless flame was observed for an overall equivalence ratio of 0.36. But as the equivalence ratio was increased, the flame in the combustor switched to a diffusion flame, and non-uniform temperature distribution was observed, which led to an increase in NOx emissions. The work in this thesis aims to improve the operational range of flameless combustion by modifying the swirl stabilized setup used by Nick Overman to include a cavity upstream of the swirler. ANSYS Fluent is used to numerically investigate the performance of such a cavity-swirler setup. The k-epsilon realizable and Laminar Finite Rate model is used to model turbulence and combustion, respectively. Multiple cavity designs which lead to a final successful design are described in detail in this thesis. The final successful design consists of 8 fuel injectors surrounded by 24 air injectors introducing fresh reactants to the cavity. Modifications were then made to this design to include 8 injectors in the second stage of the swirler. The cavity injectors aligned at an angle to the cavity also possess a swirl angle to impart a tangential component of velocity to the reactants being introduced in the cavity. The performance of two designs, the Swirler Reduced air and Swirler Fuel cases, are investigated at different equivalence ratios. Parameters such as temperature, OH distribution, NOx, CO, CO2, H2O, and combustion efficiency are used to compare the tw (open full item for complete abstract)

Committee: Ephraim Gutmark Ph.D. (Committee Chair); Prashant Khare Ph.D. (Committee Member); Rodrigo Villalva Gomez Ph.D. (Committee Member) Subjects: Aerospace Materials

Doctor of Philosophy, The Ohio State University, 2021, Mathematics

This thesis contains two parts. In the first part, we discuss certain class of KP solitons in connections with singular projective curves, which are labeled by certain types of numerical semigroups. In particular, we show that some class of the (singular and complex) KP solitons of the $l$-th generalized KdV hierarchy with $l\ge 2$ is related to the rational space curves associated with the numerical semigroup $\langle l,lm+1,\ldots, lm+k\rangle$ where $m\ge 1$ and $1\le k\le l-1$. We also calculate the Schur polynomial expansions of the $\tau$-functions for those KP solitons. Moreover, we construct smooth curves by deforming the singular curves associated with the soliton solutions, then we check that quasi-periodic solutions of $l$-th generalized KdV hierarchy indeed degenerate to soliton solutions we begin with when we degenerate the underlying algebraic curve and the line bundle over it properly. For these KP solitons, we also construct the space curves from commutative rings of differential operators in the sense of the well-known Burchnall-Chaundy theory. This part is mainly based on a published paper \cite{Kodama-Xie2021KP}. In the second part, we discuss solutions of the full Kostant-Toda (f-KT) lattice and their connections with the flag varieties. Firstly, we carry out Kowalevski-Painlev\'e analysis for f-KT equation. In particular, we associate each solution of the indicial equations with a Weyl group element, provide explicit formulas for eigenvalues of Kowalevski matrix and at last parameterize all the Laurent series solutions by $\mathcal{G} \slash \mathcal{B} \times \mathbb{C}^n$ where $\mathcal{G} \slash \mathcal{B}$ is the flag variety and $\mathbb{C}^n$ represents the spectral parameters. Secondly, we use iso-spectral deformation theory to study f-KT in the Hessenberg form, and give explicit form of the wave functions and entries in the Lax matrix expressed by $\tau$-functions with which we study $\ell$-banded Kostant-Toda hierarchy. W (open full item for complete abstract)

Committee: Yuji Kodama (Advisor); David Anderson (Committee Member); Herb Clemens (Committee Member); James Cogdell (Committee Member) Subjects: Mathematics

Bachelor of Science, Wittenberg University, 2020, Math

The objective of this thesis is to understand the systematic analytic treatment of the model presented in Anna Ghazaryan and Vahagn Manukian's journal article, “Coherent Structures in a Population Model for Mussel-Algae Interaction," which concentrates on the formation of mussel beds on soft sediments, like those found on cobble beaches. The study will investigate how the tidal flow of the water is the main structure that creates the mussel-algae interaction observed on soft sediments. With this investigation, the idea of fast-time and slow-time systems is explicated according to Geometric Singular Perturbation Theory, how Invariant Manifold Theory proves the existence of our solutions, the process of non-dimensionalization, and the re-scaling of the model. It will apply concepts found in nonlinear dynamics to discover equilibria and nullclines of the system. Finally, the study will discuss what the findings mean in context of the population model and the implications of tidal flow on other ecological relationships.

Committee: Adam Parker (Advisor); Alyssa Hoofnagle (Committee Member); Jeremiah Williams (Committee Member) Subjects: Applied Mathematics; Aquatic Sciences; Ecology; Mathematics

Master of Science, University of Toledo, 2020, Mechanical Engineering

For many problems, especially nonlinear systems, the reliability assessment must be done in the time domain. Monte-Carlo simulation (MCS) can accurately assess the reliability of the system. However, its computational cost is highly expensive for the complex dynamic system. Importance Sampling (IS) method is a more efficient method than standard MCS for the reliability assessment of a system. It has been applied to dynamic systems when the excitation is defined by a Power Spectral Density (PSD) function. The central idea of the IS method is about generating sample time histories using a sampling PSD and introducing the likelihood ratio to each replication to give the unbiased estimator of the probability of failure. Another more efficient method than MCS for the reliability assessment of the dynamic system is the Separable Monte-Carlo (SMC) method. However, this method has been applied to linear dynamic systems as following. It starts with the step of drawing frequencies from PSD of excitation, calculation of system responses to each frequency, and storing them in a database. Then the stored frequencies and the respective responses are chosen randomly with the replacement for each replication to find the system response to the linear combination of the respective sinusoidal functions. Therefore, SMC can assess the reliability of the system with a proper database. The size of the database would depend on the shape of the PSD function and the complexity of the system. This research proposed a new method by combining IS with SMC to assess the reliability of linear dynamic systems. In this method, the database of the proposed method formed by using a sampling PSD is used to estimate the reliability of the system for the true spectrum The proposed method is more efficient than both IS or SMC methods individually in terms of both computational time and accuracy. The proposed method is demonstrated using a 10-bar truss.

Committee: Mohammad Elahinia (Committee Chair); Mahdi Norouzi (Committee Co-Chair); Shawn P. Capser (Committee Member) Subjects: Mechanical Engineering

MS, University of Cincinnati, 2018, Engineering and Applied Science: Aerospace Engineering

Since its inception, Particle Image Velocimetry (PIV) has been increasingly used to measure the velocity of the flow field, especially in aerospace applications. One of the major assumptions of PIV is that velocity of the flow field is same as the velocity of tracers in it. The ability of PIV to measure velocity depends upon the potential of tracers to track the flow surrounding them. Shock-Boundary Layer Interactions (SBLIs) have been studied extensively over the years using experimental and computational methods due to their importance in almost every supersonic flow. PIV has been doing a great job in analyzing SBLIs over the past few years but it has its limitations especially when there are high temporal and spatial accelerations. On the other hand, numerical simulations that better predict shock interactions have a hard time analyzing the turbulence properties of SBLIs. This implies that only by using both computational and experimental results together physics of SBLIs can be better understood. The current study was divided into two parts. First, development and validation of a post-processing code to be able to accommodate the solid particles. For this, Visual3 has been chosen because it lets a user control even smallest of its processes. Visual3 code has been modified to track particles using accurate physics within a flow. Forces acting on a particle in a flow were analyzed and compared using data obtained from Modified-Visual3 (MV3). Based on this data, dominant forces on a particle in high-speed flow are determined. Results obtained from Modified-Visual3 are compared with Melling(1997) data to validate the code. A specific case is solved mathematically to compare with Modified-Visual3 and Melling's data. A second validation was done using an example of a generalized oblique shock to understand the behavior of the particle passing through the shock. Finally, particle relaxation times for different particle specifications were calculated to understand (open full item for complete abstract)

Committee: Paul Orkwis Ph.D. (Committee Chair); Prashant Khare (Committee Member); Mark Turner Sc.D. (Committee Member) Subjects: Aerospace Materials

PHD, Kent State University, 2018, College of Arts and Sciences / Department of Mathematical Sciences

The solution of the linear system of algebraic equations that arise from the finite element discretization of the advection-diffusion equation is considered here. In this dissertation, we study three hybrid Schwarz domain decomposition algorithms to solve this non-symmetric problem. We use the GMRES and BiCGStab methods to solve the resulting preconditioned system. In each iteration step, we solve a coarse finite element problem and a number of local problems depending on the algorithm. Local problems are solved in non-overlapping subdomains and ring-shaped overlapping subdomains into which the original domain is subdivided. These three algorithms combine the advantages of additive and multiplicative methods. We show that these algorithms are scalable in the sense that the rate of convergence is independent of the mesh size and the number of subdomains. The performance of these algorithms in two dimensions is illustrated by numerical experiments.

Committee: Jing Li (Advisor); Lothar Reichel (Committee Member); Chuck Gartland (Committee Member); Arden Ruttan (Committee Member); Ye Zhao (Committee Member) Subjects: Applied Mathematics

Doctor of Philosophy (Ph.D.), Bowling Green State University, 2018, Mathematics

In an effort to improve the error analysis of numerical methods for time-dependent PDEs and obtain reasonable error estimates, Sun developed the concept of numerical smoothness in [29] and [30]. In this dissertation, we prepare the framework for applying numerical smoothness to the error analysis for parabolic equations. The Discontinuous Galerkin (DG) method for solving parabolic equations is considered to be a successful scheme, but the error analysis for the method is limited. To provide the framework, we focus on a class of primal DG methods, namely variations of interior penalty methods. The numerical smoothness technique is used to perform an error analysis for a method in this class known as the Symmetric Interior Penalty Galerkin (SIPG) method. We take our model problem to be the one dimensional heat equation with Dirichlet boundary conditions. Therefore, this work represents a first step in applying Sun's numerical smoothness technique to the error analysis of parabolic equations. Two examples are provided to show how our numerical smoothness indicators can be used. Concluding remarks discuss how this early stage may be expanded to more complex parabolic equations and other numerical schemes.

Committee: Tong Sun Ph.D. (Advisor); John Farver Ph.D. (Other); So-Hsiang Chou Ph.D. (Committee Member); Steven Seubert Ph.D. (Committee Member) Subjects: Mathematics

BS, Kent State University, 2017, College of Arts and Sciences / Department of Computer Science

I present a numerical method for approximating the solution of Singularly Perturbed Nonlinear Initial Value Problems. Then I show how my method gives errors less than those of the conventional approaches.

Committee: Relja Vulanovic (Advisor); Leslie Heaphy (Committee Member); Gro Hovhannisyan (Committee Member); Angela Guercio (Committee Member) Subjects: Mathematics

Master of Science, The Ohio State University, 2017, Mechanical Engineering

Shipping containers are exposed to complex dynamic loading conditions during transport via truck, rail, and air. The loading conditions are further complicated by contact gap nonlinearities between the cart and ground, cart holders and suspended parts, and between neighboring suspended parts. This study focuses on developing a modeling strategy to simulate a container cart with parts undergoing random vibration tests based on standard road profiles. Initially, the linear system response to a random excitation profile of the cart structure is examined in frequency domain and correlated with experimental measurements. The linear system predictions lacked the required modeling fidelity to capture the nonlinear dynamic behavior observed during the testing as the container is loaded. Thus, the nonlinear response is then simulated in time domain using the explicit integration method with contact-driven boundary conditions using a commercially available finite element software. The total run time is determined to be prohibitively long for the time domain formulation, say over 5 seconds with a time step size of 0.3 microsec. Finally, a dynamic substructuring strategy is employed and implemented using super elements in the commercial finite element code. This particular method captured the dynamic amplification of the cart, maintained the contact nonlinearities, and reduced the computational burden. Further, a minimal order lumped model of the dynamic system is developed to understand the physics of the problem. Both lumped and finite element models consistently captured the nonlinear random vibration phenomenon and predicted the overall acceleration levels within 20% of measurements.

Committee: Rajendra Singh (Advisor); Jason Dreyer (Committee Member); Scott Noll (Committee Member) Subjects: Engineering; Mechanical Engineering; Packaging

Doctor of Philosophy, The Ohio State University, 1984, Graduate School

Committee: Not Provided (Other) Subjects: Business Administration

Doctor of Philosophy, The Ohio State University, 1966, Graduate School

Committee: Not Provided (Other) Subjects: Engineering