Ordinary Differential Equations and Applied Dynamics Commons^™

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 …

Teaching Numerical Methods In The Context Of Galaxy Mergers, Maria Kourjanskaia

Physics

Methods of teaching numerical methods to solve ordinary differential equations in the context of galaxy mergers were explored. The research published in a paper by Toomre and Toomre in 1972 describing the formation of galactic tails and bridges from close tidal interactions was adapted into a project targeting undergraduate physics students. Typically undergraduate physics students only take one Computational Physics class in which various techniques and algorithms are taught. Although it is important to study computational physics techniques, it is just as important to apply this knowledge to a problem that is representative of what computational physics researchers are investigating …

Smarticles: A Method For Identifying And Correcting Instability And Error Caused By Explicit Integration Techniques In Physically Based Simulations, Susan Aileen Marano

Master's Theses

Using an explicit integration method in physically based animations has many advantages including conceptual and computational simplicity, however, it re- quires small time steps to ensure low numerical instability. Simulations with large numbers of individually interacting components such as cloth, hair, and fluid models, are limited by the sections of particles most susceptible to error. This results in the need for smaller time steps than required for the majority of the system. These sections can be diverse and dynamic, quickly changing in size and location based on forces in the system. Identifying and handling these trou- blesome sections could allow …

Evolution Of Perturbations In Flow Field Mechanics, Samantha R. Bell, David Forliti, Nils Sedano, Kriss Vanderhyde

STAR Program Research Presentations

This project explores the stability analysis of a given flow field. Specifically, where the peak disturbance occurs in a flow as this is the disturbance that is most likely to occur. In rocket combustion, it is important to understand where the maximum disturbance occurs so that the mixing of fuel can be stabilized. The instabilities are the results of frequencies in the area surrounding the flow field. The linear stability governing equations are employed to better understand the disturbance. The governing equations for continuity and momentum in the x and y directions are used to form an equation for the …