MS, University of Cincinnati, 2019, Arts and Sciences: Mathematical Sciences

In this thesis, a numerical method for capturing topological changes as two moving interfaces intersect is presented. A moving interface is a co-dimension one set of points embedded within an N-dimensional space whose position evolves in time. In a Lagrangian framework, the interface can be approximated by a discrete set of points called marker particles that explicitly define the interface's position. The marker particle approach is straightforward to implement and is efficient but if two interfaces intersect, the interfaces will overlap and the approximation becomes invalid. The method proposed in this thesis addresses the difficulty of capturing topological changes when using marker particles through the use of local projections to and from an Eulerian frame of reference. This approach allows topological changes to be resolved naturally without arbitrary rules or ad-hoc reconstruction of the interface. This method is applied to benchmark problems that exhibit topological changes and numerical results suggest that this approach shows convergence.

Committee: Benjamin Vaughan Ph.D. (Committee Chair); Donald French Ph.D. (Committee Member); Stephan Pelikan Ph.D. (Committee Member) Subjects: Applied Mathematics

MS, University of Cincinnati, 2003, Engineering : Mechanical Engineering

The past decade has witnessed a great deal of progress in the area of computational fluid dynamics (CFD). Developments in computer technology hardware as well as in advanced numerical algorithms have made CFD a very important tool for attacking the complex problems in fluid mechanics and heat transfer which are governed by partial differential equations (PDEs). Though the cost of computer memory has been decreasing rapidly, memory can still be a limiting factor and so the quest for more economical and memory efficient methods continues till date. In this thesis we introduce and examine in detail the new Direct Matrix Inversion (DMI) method to solve some model PDEs. These model equations include the heat equation and Laplace's equation. The present method inverts the tri-diagonal or penta-diagonal coefficient matrices, representing the finite difference approximation of model equations directly in the symbolic form, which was considered impractical previously. Moreover, the inverse of the coefficient matrix requires storage space for very few elements and the majority of elements of the inverse matrix are then calculated using recursive formulas, thereby making the method very economical. In addition, for unsteady equations the coefficients of the inverse matrix are obtained in symbolic form just once and then used in the numerical solutions at different time levels. The present method has advantages in terms of memory requirement, accuracy and robustness. Numerical results for the two-dimensional incompressible Navier-Stokes equations are obtained to demonstrate the robustness and efficiency of the present method using the flow in a driven square cavity as the model problem. The computed results validate the analytical development of our new method.

Committee: Dr. Shaaban A. Abdallah (Advisor) Subjects: Engineering, Mechanical

Master of Science in Aerospace Systems Engineering (MSASE), Wright State University, 2024, Mechanical Engineering

The development of high order numerical schemes has been instrumental in advancing computational fluid dynamics (CFD), particularly for applications requiring high resolution of discontinuities and complex flow phenomena prevalent in high-speed flows. This thesis introduces the Pade-ENO scheme, a high-order method that integrates Essentially Non-Oscillatory (ENO) techniques with compact Pade stencils to achieve superior accuracy, up to 7th order, while maintaining stability in harsh environments. The scheme's performance is evaluated through benchmark tests, including the advection equation, Burgers' equation, and the Euler equations. For high Mach number flows, such as the sod shock tube the Pade-ENO method demonstrates its ability to resolve sharp gradients and discontinuities with no smoothing required. Numerical results highlight the scheme's robustness and its potential as a powerful tool for high-speed aerodynamic simulations, paving the way for future advancements in CFD modeling.

Committee: George Huang Ph.D., P.E. (Advisor); Jose Camberos Ph.D., P.E. (Committee Member); Nicholas Bisek Ph.D. (Committee Member); James Menart Ph.D. (Other) Subjects: Aerospace Engineering; Engineering; Fluid Dynamics; Mathematics; Mechanical Engineering

Master of Science in Engineering, University of Akron, 2023, Mechanical Engineering

The research in this thesis focuses on the development of a numerical model to simulate the explosive boiling phenomenon that occurs during the laser ablation of boron. The onset of explosive boiling during a laser pulse depends on the laser's fluence interacting with the target. At low fluences, the ablated material is primarily removed by normal vaporization defined by Hertz-Knudsen evaporation. However, as the fluence increases, explosive boiling phase changes begin to dominate the Hertz-Knudsen evaporation, resulting in more material removal and deeper craters. Explosive boiling has been studied for many materials like aluminum and carbon, but not many studies have focused on the explosive boiling of boron. The model was developed using a forward-in-time and centered-in-space (FTCS) scheme with finite volumes using MATLAB to run each simulation. These results were compared to previously published experimental and theoretical results for carbon and tungsten to ensure accuracy. Once the results from this model were compared with these published results, the crater development of boron targets exposed to 1064 nm wavelength light was investigated to compare to experimental results. In addition, a boron target exposed to 355 nm wavelength light was simulated to investigate the laser wavelength's effect on material removal and crater formation. In addition to the different materials and wavelengths investigated, several models are developed and used. To compare to previous carbon ablation results, a two-dimensional axisymmetric model was used. These carbon results modelled Hertz-Knudsen evaporation with two-dimensional heat transfer, so explosive boiling was not included. A one-dimensional model was developed for the boron cases that included explosive boiling, and these cases were simulated along the laser centerline. To bridge the gap between the axisymmetric and one-dimensional models, a one-dimensional multi-zone model (open full item for complete abstract)

Committee: Alex Povitsky (Advisor); Nicholas Garafolo (Committee Member); Yalin Dong (Committee Member) Subjects: Mechanical Engineering

Doctor of Philosophy, The Ohio State University, 2023, Mechanical Engineering

A 32.5% water-urea mixture, commercially known as AdBlue®, is stored onboard diesel vehicles as a liquid within storage tanks and is used for exhaust aftertreatment. In cold weather conditions, the mixture may freeze and expand over the span of several hours or days, resulting in the damage of the enclosing tank. However, computational modelling of the solidification/melting process in tanks of such “large” size and over such “long” durations is a challenging task, partly due to the simultaneous presence of all three phases (solid, liquid and gas). Furthermore, as natural convection plays an important role during the freezing process, it cannot be ignored. Capturing the dynamics of natural convection requires the use of extremely small time-step sizes, in relation to the overall freezing time scales, which significantly affects the computational speed of these simulations. This fact is demonstrated in the preliminary assessment phase of this study, where the in-built models of the commercial CFD solver ANSYS FluentTM are utilized to study the freezing process in a simple, small, partially filled 2D tank. Results show that though the models are able to provide great physical details of the solidification process, they result in impractically long simulation run times (~year). This led to the main objective of this work: the development, validation, and demonstration of an efficient 3D computational model that can be used to model the solidification process in large, partially-filled tanks containing either water or Adblue®. The first part of this work developed a new “reduced” model that accounts for the heat transfer due to natural convection during solidification/melting but, ignores the movement of the gas-(solid/liquid) interface due to expansion of ice. This new reduced natural convection model bypasses solving for flow and reduces the energy equation to a pure conduction equation by modeling convective heat fluxes using an equivalent conductive heat flux via (open full item for complete abstract)

Committee: Sandip Mazumder (Advisor); Seung Hyun Kim (Committee Member); Datta Gaitonde (Committee Member); Marcello Canova (Committee Member) Subjects: Fluid Dynamics; Mechanical Engineering

Master of Arts (MA), Bowling Green State University, 2022, Mathematics/Scientific Computation

Numerical solutions to differential equations are a growing portion of the mathematical and scientific worlds. We first discuss the background on the understanding and construction of the two main families of numerical methods, being Runge-Kutta methods and linear multistep methods, their properties as deemed by stability and error estimates, and why the ideas of stability and error estimates are both shaky and weaker than we want them to. We then cover the main idea behind numerical smoothing, the changes made to make this concept easier and stronger as a tool, and why these changes and idea as a whole are deemed superior to that of numerical stability. We then show some results that have already been found and proven regarding smoothing and the Runge-Kutta family. After this, we discuss the visual representation of smoothing and stability on various third-order linear multistep models and give some early views into how this idea extends to other numerical methods.

Committee: Tong Sun Ph.D. (Advisor); Gordon Wade Ph.D. (Committee Member); So-Hsiang Chou Ph.D. (Committee Member) Subjects: Applied Mathematics; Mathematics

Master of Science, The Ohio State University, 2020, Mechanical Engineering

The increasing complexity of the Powertrain model with the emerging trends in the hybrid and connected vehicles industry demands new approaches. As an Optimal Control Problem for the Energy Management of these class of vehicles becomes more complicated and larger in size due to addition of several mixed integer (continuous and discrete) states and controls variables in a dynamical system, the currently used offline global optimization techniques such as Dynamic Programming may not find a practical application due to a significantly high computational effort or in some cases, even failing to provide any solution at all. Thus, it becomes important to investigate a substitute optimization-based algorithm that can offer a good scalability in terms of numerical efficiency and computational effort as the Optimization Control Problem (OCP) becomes larger in size. In this thesis, we attempt to explore and solve different sizes of Optimal Energy Management Problems concerned with a Parallel P2 Hybrid Electric Vehicle using DP as well as a new algorithm called Pseudospectral Collocation method or PSC (using CasADi). Due to PSC's promising performance and a possible interface with MATLAB/Simulink as shown in the last chapter, this thesis essentially aims to stimulate researchers' interest even further to explore and solve much complicated and larger Hybrid/Electric Vehicle EMS problems using the proposed methodology.

Committee: Qadeer Ahmed Dr. (Advisor); Giorgio Rizzoni Dr. (Committee Member) Subjects: Automotive Engineering; Mechanical Engineering

Master of Science, University of Akron, 2018, Applied Mathematics

A mathematical model is developed to describe the light field in vertical line seaweed cultivation to determine the degree to which the seaweed shades itself and limits the amount of light available for photosynthesis. A probabilistic description of the spatial distribution of kelp is formulated using simplifying assumptions about frond geometry and orientation. An integro-partial differential equation called the radiative transfer equation is used to describe the light field as a function of position and angle. A finite difference solution is implemented, providing robustness and accuracy at the cost of large CPU and memory requirements, and a less computationally intensive asymptotic approximation is explored for the case of low scattering. Conditions for applicability of the asymptotic approximation are discussed, and depth-dependent light availability is compared to the predictions of simpler light models. The 3D model of this thesis is found to predict significantly lower light levels than the simpler 1D models, especially in regions of high kelp density where a precise description of self-shading is most important.

Committee: Kevin Kreider Ph.D (Advisor); Curtis Clemons Ph.D (Advisor); Gerald Young Ph.D (Advisor) Subjects: Applied Mathematics; Aquaculture; Aquatic Sciences; Ocean Engineering; Optics

Master of Science, University of Toledo, 2017, Mathematics

In this paper we study convergence rates using quotient convergence factors and root convergence factors as described by Ortega and Rheinboldt for Hestenes' Gram- Schmidt conjugate direction method without derivatives. We do study this computa- tionally and analytically by comparing this conjugate direction method for minimizing a non quadratic function f with Newton's method for solving rf = 0. This method of Hestenes is dierent from that of Smith, Powell, and Zangwill in its mathematical development. All of these ideas have already been developed and based upon 1952 paper of Hestenes and Siefel, the 1980 book Conjugate Direction Methods in Opti- mization by Hestenes and the 1975 paper by Dennemeyer and Mookini. The primary purpose of this work is to provide details analytically and computationally of what has been done before.

Committee: Ivie Stein Ph.D. (Advisor) Subjects: Mathematics

Doctor of Philosophy, The Ohio State University, 1973, Graduate School

Committee: Not Provided (Other) Subjects: Education

Doctor of Philosophy, The Ohio State University, 2015, Electrical and Computer Engineering

In this dissertation, the Theory of Characteristic Modes is used as a framework for the design, optimization, and benchmarking of electrically small radiating systems. The foundation of this work is in the theory of Characteristic Modes, an eigenvalue equation of the Method of Moments impedance matrix [Z], that leads to derive the fundamental radiation modes of arbitrary-shaped bodies. After an overview of small antenna theory, we derive a new method for computing the Q factor of arbitrary-shaped radiating bodies using CMs using only the Method of Moments impedance matrix [Z]. Following this derivation, we present a new method for computing the fundamental limits on Q (and thus bandwidth) for arbitrary-shaped antennas. As a by-product of this method, we extract the optimal current distribution as a function of antenna shape for design guidelines. We further extend this theory to find the Q limits of arbitrary-shaped antennas and antenna-platform systems, subject to specific radiation pattern requirements. In the second part of the thesis, we use the Theory of Characteristic Modes to optimize the location and excitation of single and multiple in-situ ESAs mounted on finite, sub-wavelength platforms as relates to unmanned aerial vehicles (UAVs). By properly analyzing the CMs of the supporting platform, we show that a complex, multivariate optimization problems can by radically simplified using CMs. Based on this capability, we present a new, systematic design methodology for location optimization of small antennas on-board finite platforms. The approach is shown to drastically reduce the time, computational cost, and complexity of a multi-element in-situ antenna design, as well as providing significant performance improvements in comparison to a typical single-antenna implementations.

Committee: John Volakis Dr. (Advisor); Kubilay Sertel Dr. (Advisor); Robert Burkholder Dr. (Committee Member) Subjects: Electrical Engineering

MS, University of Cincinnati, 2014, Engineering and Applied Science: Mechanical Engineering

This thesis report a work on an implementation of a Cell-based Smoothed Finite Element method (CS-FEM) using quadrilateral element (Q4) in the framework of the commercial software package ABAQUS®. The CS-FEM is one of the Smoothed Finite Element Method (S-FEM) models introduced by Dr. G.R. Liu and his colleagues in recent years. Because smoothing domains used by CS-FEM are within the element, it is known as the model closest to the standard FEM. User-defined Element subroutine (UEL) feature was proposed to be used to implant the CS-FEM model into ABAQUS. In this paper, a couple of UELs are constructed respectively for 2-dimentional (2D) problems using Q4 elements. To implant CS-FEM into ABAQUS, a custom input file and corresponding user subroutine are developed. Then the implementation is verified using a number of linear elastic problems that has analytical solutions. In this article, details on data input file and the user element subroutine construction are provided, which contribute the key ingredients of this implementation. Several numerical examples utilizing the subroutines are presented to demonstrate the features and accuracy of the developed ABAQUS CS-FEM Q4 user element, by comparison with the analytical and the ABAQUS solutions.

Committee: Guirong Liu Ph.D. (Committee Chair); Yijun Liu Ph.D. (Committee Member); David Thompson Ph.D. (Committee Member) Subjects: Mechanical Engineering

PhD, University of Cincinnati, 2014, Engineering and Applied Science: Computer Science and Engineering

Circuit simulation is an integral parts of the VLSI design process. Complex models have been developed to mimic the various phenomena that occur at the physical level; sophisticated numerical methods have also been simultaneously designed to handle the complexity of the mathematical models. As a result, large realistic models can be simulated accurately and efficiently. The SPICE simulation tool, with an extensive model library and extremely optimized numerical methods, is the current industry standard for circuit simulation. Recently though, due to the rapid reduction in feature sizes, values assumed for some of the parameters within the model during the design phase cannot be reproduced exactly during the fabrication phase. These aleatoric uncertainties in the model parameters induce non-determinism in the rest of the system variables. This has transformed the traditional circuit simulation problem into one of Statistical Performance Estimation (SPE). Statistical distributions are used to represent parameters and Monte Carlo (MC) type methods are used for analysis. While this approach is robust and easy to implement, it suffers from long analysis times due to its repetitive nature and, more importantly, the curse of dimensionality. The focus of this dissertation is to develop MC alternate methods for SPE: at the top level, we have developed two different methodologies using (a) interval arithmetic and (b) polynomial chaos expansions, with which we have developed intrusive methods to generate a system of equations that amenable to efficient SPE. The first approach uses interval valued variables to represent the uncertainties. Interval arithmetic follows special computation rules which allows for guaranteed enclosures to be produced. Since the computations are inherently pessimistic and prone to interval blowup, some transformations are necessary to contain these effects. We present a graph theoretic method to transform the DAE modeling the circuit into a (open full item for complete abstract)

Committee: Fred Beyette Ph.D. (Committee Chair); Harold Carter Ph.D. (Committee Member); Wen Ben Jone Ph.D. (Committee Member); Joy Moore Ph.D. (Committee Member); Carla Purdy Ph.D. (Committee Member); Ranganadha Vemuri Ph.D. (Committee Member) Subjects: Engineering

Master of Science in Mathematics, Youngstown State University, 2011, Department of Mathematics and Statistics

The purpose of this paper is to develop a root finding method for non-linear functions. The problem, f(x)=0 where x is in R, is common in many areas of mathematics and can be traced back as far as 1700 B.C. A cuneiform table in the Yale Babylonian Collection dating from that period gives a base-60 number equivalent to 1.414222 as an approximation to the square root of 2, a result accurate to within .00001 (the square root of 2 is approximately 1.414214). We wanted to develop a hybrid method that quickly produces a small interval containing the solution and then switch to a method with faster convergence. We have created a method to solve functions whose exact roots are not easy to find using common techniques learned in algebra and calculus courses. We have compiled test functions, some of our own and some from other works on the same topic. We have also compared our method with that of several other methods consisting of Secant Method, False Position, a modified version of Modified False Position, Inverse Quadratic Interpolation, Bisection and a few other hybrid methods. Our method begins with the modified version of Modified False Position, which will be discussed in more detail later, then switches to Muller's method once a certain tolerance is reached. In certain instances, our method switches back to the modified version of Modified False Position. We found our method outperformed these methods in most cases and was competitive to the other hybrid methods, and in many cases, it outperformed them as well.

Committee: Jozsi Jalics PhD (Advisor); Richard Burden PhD (Committee Member); J. D. Faires PhD (Committee Member) Subjects: Applied Mathematics; Mathematics

PhD, University of Cincinnati, 2000, Engineering : Aerospace Engineering

The successful application of CFD and turbulence modeling methods to an aerospike nozzle system first involves the successful simulation of its key flow components. This report addresses the task using the Chien low-Re k-? and the Yakhot et al. high-Re RNG k-? turbulence models. An improved implicit axis of symmetry boundary condition is also developed to increase stability and lower artificial dissipation. Grid adaptation through the SAGE post-processing package is used throughout the study. The RNG model, after low-Re modifications, and the Chien low-Re k-? model are applied to the supersonic axisymmetric base flow problem. Both models predict a peak recirculation velocity almost twice as large as experiment. The RNG model predicts a flatter base pressure and lower recirculation velocity more consistent with experimental data using less grid points than a comparable Chien model solution. The turbulent quantities predicted by both models are typical of other numerical results and generally under predict peak values obtained in experiment suggesting that too little turbulent eddy viscosity is produced. After several test cases, the full 3-D aerospike nozzle is simulated using both the Chien and modified RNG low-Re models. The Chien model outperforms the RNG model in all circumstances. The surface pressure predicted by the Chien model along the nozzle center-plane is very near experiment while mid-plane results are not as close but useful for design purposes. The lack of a thick boundary layer along the nozzle surface in RNG simulations is the cause of poor surface pressure comparisons. Although initial base flow comparisons between the model predictions and experiment are poor, the profiles are relatively flat. To accelerate the progress to a steady-state solution, a process involving the artificial lowering of the base pressure and subsequent iteration to a new steady state is undertaken. After several of these steps, the resulting steady-state base pressure is ver (open full item for complete abstract)

Committee: Karman Ghia (Advisor) Subjects: Engineering, Aerospace

Doctor of Philosophy, The Ohio State University, 2009, Electrical and Computer Engineering

The finite difference time domain (FDTD) and finite element numerical methods are two popular time domain computational methods in electromagnetics, but the two numerical methods have certain tradeoffs. FDTD is a fast explicit method with second order accuracy, but the method's accuracy is reduced when analyzing structures that are not conforming to a Cartesian grid. The finite element method on the other hand excels at examining domains with non-conforming structures, but its method of solution usually requires a matrix inverse operation, which is computationally expensive. Fortunately, research in hybrid methods have shown that the FDTD method for isotropic materials can be viewed upon as a subset of finite elements, and from this viewpoint, the FDTD and finite element method in the time domain can be hybridized together to the advantages of both methods while mitigating the disadvantages.With the recent rise in the study of metamaterials, which contain anisotropic media, having a hybridized method to study anisotropic media is a desirable tool as, for example, the effects of these materials combined with antennas are being examined. However, the hybridization approach combining the FDTD and finite element method for isotropic media does not extend to anisotropic media since the anisotropic FDTD equation cannot be recovered from the finite element formulation in this fashion. In this dissertation, a hybridized FDTD/finite element method for anisotropic materials will be developed. In the derivation of the hybridized method, a new finite element method will be formulated which incorporates the constitutive relation in a finite element point of view. This new finite element method will also be used to construct new anisotropic FDTD stencils in a systematic manner for certain interface and boundary conditions that the traditional anisotropic FDTD update fails to handle. Numerical tests will be performed to demonstrate the accuracy of the both the hybridized anisotrop (open full item for complete abstract)

Committee: Robert Lee PhD (Advisor); Fernando Teixeira PhD (Committee Member); Prabhakar H. Pathak PhD (Committee Member) Subjects: Electrical Engineering; Electromagnetism

Doctor of Philosophy, The Ohio State University, 2007, Electrical Engineering

This dissertation presents a domain decomposition method as an effective and efficient preconditioner for frequency domain FEM solution of geometrically complex and electrically large electromagnetic problems. The method reduces memory requirements by decomposing the original problem domain into several non-overlapping and possibly repeatable sub-domains. At the heart of this research are the Robin-to-Robin map, the “cement” finite element coupling of non-conforming grids and the concept of duality paring. The Robin's transmission condition is employed on interfaces between adjacent sub-domains to enforce continuity of electromagnetic fields and to ensure the sub-domain problems are well-posed. Through the introduction of cement variables, the meshes at the interface could be non-conformal which significantly relaxes the meshing procedures. By following the spirit of duality paring a symmetric system is obtained to better reflect physical nature of the problem. These concepts in conjunction with the so-called finite element tearing and interconnecting algorithm form the basic modules of the present domain decomposition method. To enhance the convergence of DDM solver, the Krylov solvers instead of classical stationary solvers are employed and studied. In order to account the radiation condition exactly thus eliminating spurious reflection, a boundary element formulation is hybridized with the present DD method, also through the aforementioned novel concepts. One of the special cases of present hybridization is the well known hybrid finite element and boundary element method. It will be shown that the proposed hybrid offers simultaneously: (1) symmetry, (2) modularity, (3) non-conformity between FEM and BEM domains, (4) free of internal resonance, and (5) natural and effective preconditioning scheme that guarantees spectral radius less or equal to one. Lastly this dissertation presents a DDM solution scheme for analyzing electromagnetic problems involving multiple se (open full item for complete abstract)

Committee: Jin-Fa Lee (Advisor) Subjects:

Doctor of Philosophy, The Ohio State University, 2004, Mathematics

Most of the time, when pricing financial instruments, it is impossible to find closed form solutions for their values. Finding numerical solutions for the governing pricing equations becomes therefore an appealing approach to pricing, especially since powerful desktop computers are now available. In this paper we demonstrate how two of the main numerical methods known today—the finite differences method and the Monte Carlo simulation — can be used for pricing discretely measured lookback basket options. We also take a look at one of the most competitive markets today, The Individual Variable Annuity marketplace, at some of the currently sold death benefits and how they are related to the lookback put options.

Committee: Bostwick Wyman (Advisor) Subjects: Mathematics

Doctor of Philosophy (PhD), Ohio University, 2007, Physics (Arts and Sciences)

A time-dependent two-dimensional Monte Carlo/Fokker-Planck (MC/FP) code, which uses a Monte Carlo technique for Compton scattering and radiative transport, and a Fokker-Planck technique for electron evolution, has been fully parallelized with the Message Passing Interface (MPI) to take advantage of computers with multiple processors and decrease running time. This code has been successfully applied to the following astrophysically relevant scenario: it was coupled with the line transfer program XSTAR to simulate multiple Compton reflections within photon bubbles, making predictions for their X-ray spectral features. Predictions include a spectral feature at ~9 keV and hard power-law tails similar to those observed in X-ray binaries in the very high state. This dissertation also includes the results of an observational project to determine the redshifts of six BL Lac objects, (i.e., galaxies dominated by radiation from the jets emerging from their central black holes) with the 2.4 m Hiltner telescope at the MDM observatory on Kitt Peak, Arizona. The redshifts of these objects have been constrained in agreement with previous estimates in most cases; however, in one case (W Comae) the constraints and previous estimates were not in agreement.

Committee: Boettcher Markus (Advisor) Subjects: Physics, Astronomy and Astrophysics

Master of Science in Mechanical Engineering, Cleveland State University, 2010, Fenn College of Engineering

Flow induced vibrations of pipes with internal fluid flow is studied in this work. Finite Element Analysis methodology is used to determine the critical fluid velocity that induces the threshold of pipe instability. The partial differential equation of motion governing the lateral vibrations of the pipe is employed to develop the stiffness and inertia matrices corresponding to two of the terms of the equations of motion. The equation of motion further includes a mixed-derivative term that was treated as a source for a dissipative function. The corresponding matrix with this dissipative function was developed and recognized as the potentially destabilizing factor for the lateral vibrations of the fluid carrying pipe. Two types of boundary conditions, namely simply-supported and cantilevered were considered for the pipe. The appropriate mass, stiffness, and dissipative matrices were developed at an elemental level for the fluid carrying pipe. These matrices were then assembled to form the overall mass, stiffness, and dissipative matrices of the entire system. Employing the finite element model developed in this work two series of parametric studies were conducted. First, a pipe with a constant wall thickness of 1 mm was analyzed. Then, the parametric studies were extended to a pipe with variable wall thickness. In this case, the wall thickness of the pipe was modeled to taper down from 2.54 mm to 0.01 mm. This study shows that the critical velocity of a pipe carrying fluid can be increased by a factor of six as the result of tapering the wall thickness.

Committee: Majid Rashidi PhD (Committee Chair); Rama S Gorla PhD (Committee Member); Asuquo B Ebiana PhD (Committee Member) Subjects: Design; Fluid Dynamics; Mechanical Engineering