Applied Mathematics Commons^™

Conical Orbital Mechanics: A Rework Of Classic Orbit Transfer Mechanics, Cian Anthony Branco

Mechanical & Aerospace Engineering Theses & Dissertations

Simple orbital maneuvers obeying Kepler’s Laws, when taken with respect to Newton’s framework, require considerable time and effort to interpret and understand. Instead of a purely mathematical approach relying on the governing relations, a graphical geometric conceptual representation provides a useful alternative to the physical realities of orbits. Conic sections utilized within the full scope of a modified cone (frustum) were employed to demonstrate and develop a geometric approach to elliptical orbit transformations. The geometric model in-question utilizes the rotation of a plane intersecting the orbital frustum at some angle β (and the change in this angle) in a novel …

Mathematical Modeling Of A Variable Mass Rocket’S Dynamics Using The Differential Transform Method, Ashwyn Sam

Honors Theses

In this paper, the mathematical modelling of a rocket with varying mass is investigated to construct a function that can describe the velocity and position of the rocket as a function of time. This research is geared more towards small scale rockets where the nonlinear drag term is of great interest to the underlying dynamics of the rocket. A simple force balance on the rocket using Newton’s second law of motion yields a Riccati differential equation for which the solution yields the velocity of the rocket at any given time. This solution can then be integrated with respect to time …

Target Control Of Networked Systems, Isaac S. Klickstein

Mechanical Engineering ETDs

The control of complex networks is an emerging field yet it has already garnered interest from across the scientific disciplines, from robotics to sociology. It has quickly been noticed that many of the classical techniques from controls engineering, while applicable, are not as illuminating as they were for single systems of relatively small dimension. Instead, properties borrowed from graph theory provide equivalent but more practical conditions to guarantee controllability, reachability, observability, and other typical properties of interest to the controls engineer when dealing with large networked systems. This manuscript covers three topics investigated in detail by the author: (i) the …

Investigating The Feasibility And Stability For Modeling Acoustic Wave Scattering Using A Time-Domain Boundary Integral Equation With Impedance Boundary Condition, Michelle E. Rodio

Mathematics & Statistics Theses & Dissertations

Reducing aircraft noise is a major objective in the field of computational aeroacoustics. When designing next generation quiet and environmentally friendly aircraft, it is important to be able to accurately and efficiently predict the acoustic scattering by an aircraft body from a given noise source. Acoustic liners are an effective tool for aircraft noise reduction and are characterized by a frequency-dependent impedance. Converted into the time-domain using Fourier transforms, an impedance boundary condition can be used to simulate the acoustic wave scattering by geometric bodies treated with acoustic liners

This work considers using either an impedance or an admittance (inverse …

Model-Based Network Reconstruction From Cascade Dynamics, Katherine Irena Chwistek

Graduate Research Theses & Dissertations

Network representation provides a natural framework for the study of real world complex systems. From social networks and animal groups to interneuronal communications and power grid systems, complex patterns of interaction can be captured and modeled using networks in a simple mathematical form. In many cases, however, a faithful network representation of the system is not readily available. For this reason, network reconstruction has become a growing topic of interest in recent years, the goal of which is to discover the hidden interaction patterns among individuals by fitting input-output data from multiple experiments to candidate network topologies.

During a cascade, …

Filtered-Dynamic-Inversion Control For Unknown Minimum-Phase Systems With Unknown Relative Degree, Sumit Suryakant Kamat

Theses and Dissertations--Mechanical and Aerospace Engineering

We present filtered-dynamic-inversion (FDI) control for unknown linear time-invariant systems that are multi-input multi-output and minimum phase with unknown-but-bounded relative degree. This FDI controller requires limited model information, specifically, knowledge of an upper bound on the relative degree and knowledge of the first nonzero Markov parameter. The FDI controller is a single-parameter high-parameter-stabilizing controller that is robust to uncertainty in the relative degree. We characterize the stability of the closed-loop system. We present numerical examples, where the FDI controller is implemented in feedback with mathematical and physical systems. The numerical examples demonstrate that the FDI controller for unknown relative degree …

The Potentials Of Faecal Sludge Treatment Using Local Conditioners In Tanzania: A Review, Doglas Benjamin1

Tanzania Journal of Engineering and Technology (TJET)

Worldwide, every day human beings generate millions of tons of Faecal Sludge (FS), which is rich in water, nutrients, energy, and organic compounds. Yet FS is not being managed in a way that permits us to derive value from its reuse, while at the same time, millions of farmers struggle with depleted soils and lack of water. In most of the developing countries, energy for cooking is mainly derived from cutting of trees, either as wood or charcoal. Resource recovery and reuse from FS can create livelihoods, enhance food security, support green economies, reduce waste and contribute to cost recovery …

General Nonlinear-Material Elasticity In Classical One-Dimensional Solid Mechanics, Ronald Joseph Giardina Jr

LSU New Orleans Theses and Dissertations

We will create a class of generalized ellipses and explore their ability to define a distance on a space and generate continuous, periodic functions. Connections between these continuous, periodic functions and the generalizations of trigonometric functions known in the literature shall be established along with connections between these generalized ellipses and some spectrahedral projections onto the plane, more specifically the well-known multifocal ellipses. The superellipse, or Lam\'{e} curve, will be a special case of the generalized ellipse. Applications of these generalized ellipses shall be explored with regards to some one-dimensional systems of classical mechanics. We will adopt the Ramberg-Osgood relation …

Investigation Of Fundamental Principles Of Rigid Body Impact Mechanics, Khalid Alluhydan

Mechanical Engineering Research Theses and Dissertations

In impact mechanics, the collision between two or more bodies is a common, yet a very challenging problem. Producing analytical solutions that can predict the post-collision motion of the colliding bodies require consistent modeling of the dynamics of the colliding bodies. This dissertation presents a new method for solving the two and multibody impact problems that can be used to predict the post-collision motion of the colliding bodies. Also, we solve the rigid body collision problem of planar kinematic chains with multiple contacts with external surfaces.

In the first part of this dissertation, we study planar collisions of Balls and …

Maximizing And Modeling Malonyl-Coa Production In Escherichia Coli, Tatiana Thompson Silveira Mello

LSU Master's Theses

In E. coli, fatty acid synthesis is catalyzed by the enzyme acetyl-CoA carboxylase (ACC), which converts acetyl-CoA into malonyl-CoA. Malonyl-CoA is a major building block for numerous of bioproducts. Multiple parameters regulate the homeostatic cellular concentration of malonyl-CoA, keeping it at a very low level. Understanding how these parameters affect the bacterial production of malonyl-CoA is fundamental to maximizing it and its bioproducts. To this end, competing pathways consuming malonyl-CoA can be eliminated, and optimal nutritional and environmental conditions can be provided to the fermentation broth. Most previous studies utilized genetic modifications, expensive consumables, and high-cost quantification methods, making …

Stability Analysis Of A More General Class Of Systems With Delay-Dependent Coefficients, Chi Jin, Keqin Gu, Islam Boussaada, Silviu-Iulian Niculescu

SIUE Faculty Research, Scholarship, and Creative Activity

This paper presents a systematic method to analyse the stability of systems with single delay in which the coefficient polynomials of the characteristic equation depend on the delay. Such systems often arise in, for example, life science and engineering systems. A method to analyze such systems was presented by Beretta and Kuang in a 2002 paper, but with some very restrictive assumptions. This work extends their results to the general case with the exception of some degenerate cases. It is found that a much richer behavior is possible when the restrictive assumptions are removed. The interval of interest for the …

Numerical Investigation Of Inclination On The Thermal Performance Of Porous Fin Heatsink Using Pseudospectral Collocation Method, George Oguntala, Gbeminiyi Sobamowo, Raed Abd-Alhameed, James Noras

Karbala International Journal of Modern Science

Numerical investigation of inclination effect on the thermal performance of a porous fin heat sink is presented. The developed thermal model is solved using pseudo-spectral collocation method (PSCM). Parametric studies are carried out using PSCM, and the thermal characterization of heat sink with the inclined porous fin of rectangular geometry is presented. Results show that heat sink of inclined porous fin exhibits higher thermal performance than heat sink of vertical porous fin operating under the same thermal conditions with the same geometrical configurations. Performance of inclined or tilted fin increases with decrease in length-thickness aspect ratio. However, increase in the …

Stair Climbing Hand Truck, James Mcpherson

All Undergraduate Projects

Abstract

Getting a heavy object up a flight of stairs usually requires a team of two or more people. Even with a team of people, the task is often still difficult, dangerous, and possibly insurmountable by one person. This problem is especially prevalent in for those who are moving into apartment complexes. Most apartment complexes have many buildings with two or more floors of living quarters, and elevators are often missing. This project sought to offer a solution to this problem. The solution in question; a motorized hand-truck with 2, trigonal planar pinwheels in place of the stock wheels. The …

Non-Marginal Decisions: A Novel Bayesian Multiple Testing Procedure, Noirrit Kiran Chandra, Sourabh Bhattacharya

Journal Articles

In this paper, we consider the problem of multiple testing where the hypotheses are dependent. In most of the existing literature, either Bayesian or non-Bayesian, the decision rules mainly focus on the validity of the test procedure rather than actually utilizing the dependency to increase efficiency. Moreover, the decisions regarding different hypotheses are marginal in the sense that they do not depend upon each other directly. However, in realistic situations, the hypotheses are usually dependent, and hence it is desirable that the decisions regarding the dependent hypotheses are taken jointly. In this article, we develop a novel Bayesian multiple testing …

Creating A Computational Tool To Simulate Vibration Control For Piezoelectric Devices, Ahmet Ozkan Ozer, Emma J. Moore

Posters-at-the-Capitol

Piezoelectric materials have the unique ability to convert electrical energy to mechanical vibrations and vice versa. This project takes a stab to develop a reliable computational tool to simulate the vibration control of a novel “partial differential equation” model for a piezoelectric device, which is designed by integrating electric conducting piezoelectric layers constraining a viscoelastic layer to provide an active and lightweight intelligent structure. Controlling unwanted vibrations on piezoelectric devices (or harvesting energy from ambient vibrations) through piezoelectric layers has been the major focus in cutting-edge engineering applications such as ultrasonic welders and inchworms. The corresponding mathematical models for piezoelectric …

Risk Assessment Of Dropped Cylindrical Objects In Offshore Operations, Adelina Steven

LSU New Orleans Theses and Dissertations

Dropped object are defined as any object that fall under its own weight from a previously static position or fell due to an applied force from equipment or a moving object. It is among the top ten causes of injuries and fatality in oil and gas industry. To solve this problem, several in-house tools and guidelines is developed over time to assess the risk of dropped objects on the sub-sea structures. This thesis focuses on compiling and comparing those methods in hope to improve the recommended practices available in the market. A simple modification is done on the in-house tools …

Rotordynamic Analysis Of Theoretical Models And Experimental Systems, Cameron R. Naugle

Master's Theses

This thesis is intended to provide fundamental information for the construction and

analysis of rotordynamic theoretical models, and their comparison the experimental

systems. Finite Element Method (FEM) is used to construct models using Timoshenko

beam elements with viscous and hysteretic internal damping. Eigenvalues

and eigenvectors of state space equations are used to perform stability analysis, produce

critical speed maps, and visualize mode shapes. Frequency domain analysis

of theoretical models is used to provide Bode diagrams and in experimental data

full spectrum cascade plots. Experimental and theoretical model analyses are used

to optimize the control algorithm for an Active Magnetic Bearing …

Some Insights Into The Migration Of Double Imaginary Roots Under Small Deviation Of Two Parameters, Dina Alina Irofti, Keqin Gu, Islam Boussaada, Silviu-Iulian Niculescu

SIUE Faculty Research, Scholarship, and Creative Activity

This paper studies the migration of double imaginary roots of the systems’ characteristic equation when two parameters are subjected to small deviations. The proposed approach covers a wide range of models. Under the least degeneracy assumptions, we found that the local stability crossing curve has a cusp at the point that corresponds to the double root, and it divides the neighborhood of this point into an S-sector and a G-sector. When the parameters move into the G-sector, one of the roots moves to the right halfplane, and the other moves to the left half-plane. When the parameters move into the …

Communication Based Control For Dc Microgrids, Mahmoud S. Saleh, Yusef Esa, Ahmed Mohamed

Publications and Research

Centralized communication-based control is one of the main methods that can be implemented to achieve autonomous advanced energy management capabilities in DC microgrids. However, its major limitation is the fact that communication bandwidth and computation resources are limited in practical applications. This can be often improved by avoiding redundant communications and complex computations. In this paper, an autonomous communication-based hybrid state/event driven control scheme is proposed. This control scheme is hierarchical and heuristic, such that on the primary control level, it encompasses state-driven local controllers, and on the secondary control level, an event-driven MG centralized controller (MGCC) is used. This …

Resistance Temperature Detectors In A Cryostat Refrigeration System, Kirsten Marie Manahan, Alice Callen

STAR Program Research Presentations

The Large Synoptic Survey Telescope (LSST) is a ground-based telescope that will survey the Southern sky every few nights. Located in the telescope will be a 3.2 gigapixel digital camera. To ensure proper instrumentation of the camera, there must be a monitored stable temperature. As part of my research, I assembled resistance temperature detectors and tested them to verify their reliability in measuring temperature in the camera’s cryostat refrigeration cooling system. Resistance temperature detectors function by the principle of thermal resistivity, in which their electrical resistances vary as temperature varies. Through testing, I was able to determine whether these particular …

Strong Stability Of A Class Of Difference Equations Of Continuous Time And Structured Singular Value Problem, Qian Ma, Keqin Gu, Narges Choubedar

SIUE Faculty Research, Scholarship, and Creative Activity

This article studies the strong stability of scalar difference equations of continuous time in which the delays are sums of a number of independent parameters tau_i, i = 1, 2, . . . ,K. The characteristic quasipolynomial of such an equation is a multilinear function of exp(-tau_i s). It is known that the characteristic quasipolynomial of any difference equation set in the form of one-delayper- scalar-channel (ODPSC) model is also in such a multilinear form. However, it is shown in this article that some multilinear forms of quasipolynomials are not characteristic quasipolynomials of any ODPSC difference equation set. The equivalence …

Strong Stability Of A Class Of Difference Equations Of Continuous Time And Structured Singular Value Problem, Qian Ma, Keqin Gu, Narges Choubedar

SIUE Faculty Research, Scholarship, and Creative Activity

This article studies the strong stability of scalar difference equations of continuous time in which the delays are sums of a number of independent parameters τi, i = 1, 2, . . . , K. The characteristic quasipolynomial of such an equation is a multilinear function of e−τis. It is known that the characteristic quasipolynomial of any difference equation set in the form of one-delay-per-scalar-channel (ODPSC) model is also in such a multilinear form. However, it is shown in this article that some multilinear forms of quasipolynomials are not characteristic quasipolynomials of any ODPSC difference equation set. The equivalence between …

Investigation Of Toppling Ball Flight In American Football With A Mechanical Field-Goal Kicker, Chase M Pfeifer, Timothy J. Gay, Jeff A. Hawks, Shane Farritor, Judith M. Burnfield

Department of Mechanical and Materials Engineering: Faculty Publications

A mechanical field-goal kicking machine was used to investigate toppling ball flight in American football place-kicking, eliminating a number of uncontrollable impact variables present with a human kicker. Ball flight trajectories were recorded using a triangulation-based projectile tracking system to account for the football’s 3-dimensional position during flight as well as initial launch conditions. The football flights were described using kinematic equations relating to projectile motion including stagnant air drag and were compared to measured trajectories as well as projectile motion equations that exclude stagnant air drag. Measured football flight range deviations from the non-drag equations of projectile motion corresponded …

Optimization And Control Of An Array Of Wave Energy Converters, Jianyang Lyu

Dissertations, Master's Theses and Master's Reports

This study explored optimal configuration of both the array layout and the dimension of each WEC in the array. The array contains heaving buoys with full interaction and exact hydrodynamics. Optimization of dimension was done on each WEC in the array with a given optimal layout, and a higher q-factor was achieved. Both impedance matching optimal control and derivative control were employed, which provides both theoretical maximum energy and a more realistic case. Then the work was expanded to optimization of both the array layout and the dimension of each WEC in the array. An average of 39.21% higher q-factor …

Data-Driven Predictive Framework For Modeling Complex Multi-Physics Engineering Applications, Arturo Schiaffino Bustamante

Open Access Theses & Dissertations

Computational models are often encountered in multiple engineering application, such as structural design, material science, heat transfer and fluid dynamics. These simulations offer the engineers the capability of understanding complex physical situations before putting them to practice, either through experimentation or prototyping. The current advances in computational sciences, hardware architecture, software development and big data technology, have allowed the construction of sturdy predicting frameworks for analyzing a wide array of natural phenomena across different disciplines, either through the implementation of statistical methods, such as big data, and uncertainty quantification, or through high performance computing of a numerical model. The objective …

Heterogeneous Anisotropy Index And Scaling In Multiphase Random Polycrystals, Muhammad Ridwan Murshed

Theses and Dissertations

Under consideration is the finite-size scaling of elastic properties in single and two-phase random polycrystals with individual grains belonging to any crystal class (from cubic to triclinic). These polycrystals are generated by Voronoi tessellations with varying grain sizes and volume fractions. By employing variational principles in elasticity, we introduce the notion of a 'Heterogeneous Anisotropy Index' and investigate its role in the scaling of elastic properties at finite mesoscales. The index turns out to be a function of 43 variables, 21 independent components for each phase and the volume fraction of either phase. Furthermore, the relationship between Heterogeneous Anisotropy Index …

Rogue Rotary - Modular Robotic Rotary Joint Design, Sean Wesley Murphy, Tyler David Riessen, Jacob Mark Triplett

Mechanical Engineering

This paper describes the design process from ideation to test validation for a singular robotic joint to be configured into a myriad of system level of robots.

On The Ramberg-Osgood Stress-Strain Model And Large Deformations Of Cantilever Beams, Ronald J. Giardina Jr

LSU New Orleans Theses and Dissertations

In this thesis the Ramberg-Osgood nonlinear model for describing the behavior of many different materials is investigated. A brief overview of the model as it is currently used in the literature is undertaken and several misunderstandings and possible pitfalls in its application is pointed out, especially as it pertains to more recent approaches to finding solutions involving the model. There is an investigation of the displacement of a cantilever beam under a combined loading consisting of a distributed load across the entire length of the beam and a point load at its end and new solutions to this problem are …

Evaluation And Enhancement Of Clean Energy Systems: Analytical, Computational And Experimental Study Of Solar And Nuclear Cycles, Nima Fathi

Mechanical Engineering ETDs

Clean (and specifically renewable) energy is steadily improving its global share. However, finite availability of fossil fuels and the growing effects of climate change make it an urgent priority to convince the industry and governments to incentivize investment in the renewable energy field and to make it more attractive by decreasing the capital cost. Until recently, uncertainties in funding limited renewable energy development, especially in the US. That limitation has been one of the barriers to progress. Another limitation of many renewable energy systems is the variability in their output, which makes them unsuitable for baseline power production. Therefore, fossil …

Mathematical Description And Mechanistic Reasoning: A Pathway Toward Stem Integration, Paul J. Weinberg

Journal of Pre-College Engineering Education Research (J-PEER)

Because reasoning about mechanism is critical to disciplined inquiry in science, technology, engineering, and mathematics (STEM) domains, this study focuses on ways to support the development of this form of reasoning. This study attends to how mechanistic reasoning is constituted through mathematical description. This study draws upon Smith’s (2007) characterization of mathematical description of scientific phenomena as ‘‘bootstrapping,’’ where negotiating the relationship between target phenomena and represented relations is fundamental to learning. In addition, the development of mathematical representation presents a viable pathway towards STEM integration. In this study, participants responded to an assessment of mechanistic reasoning while cognitive interviews …