Engineering Commons^™

Analytical Computation Of Proper Orthogonal Decomposition Modes And N-Width Approximations For The Heat Equation With Boundary Control, Tasha N. Fernandez

Masters Theses

Model reduction is a powerful and ubiquitous tool used to reduce the complexity of a dynamical system while preserving the input-output behavior. It has been applied throughout many different disciplines, including controls, fluid and structural dynamics. Model reduction via proper orthogonal decomposition (POD) is utilized for of control of partial differential equations. In this thesis, the analytical expressions of POD modes are derived for the heat equation. The autocorrelation function of the latter is viewed as the kernel of a self adjoint compact operator, and the POD modes and corresponding eigenvalues are computed by solving homogeneous integral equations of the …

Elastic And Magnetic Properties Of Tb6fe(Sb,Bi)2 Using Resonant Ultrasound Spectroscopy., David Michael Mccarthy

Masters Theses

Tb6FeSb2 and Tb6FeBi2 are novel rare earth compounds with little prior research. These compounds show high and variable curie temperatures for rare-earth compounds. This has lead to a literature review which includes the discussion of: elasticity, resonance, and magnetism. This review is used to discuss the theory and methodology which can relate these various properties to each other. Furthermore, synthesis, x-ray analysis, and RUS sample preparation of Tb6FeSb2 and Tb6FeBi2 were completed.

Resonant Ultrasound Spectroscopy (RUS) elastic studies were taken for Tb6FeSb2 and Tb6FeBi2 as a function temperature from 5-300K, in various magnetic fields ranging from 0-9T. Tb6FeSb2’s and Tb6FeBi2’s …

Nonlinear Acoustics Of Piston-Driven Gas-Column Oscillations, Andrew William Wilson

Masters Theses

The piston-driven oscillator is traditionally modeled by directly applying boundary conditions to the acoustic wave equations; with better models re-deriving the wave equations but retaining nonlinear and viscous effects. These better models are required as the acoustic solution exhibits singularity near the natural frequencies of the cavity, with an unbounded (and therefore unphysical) solution. Recently, a technique has been developed to model general pressure oscillations in propulsion systems and combustion devices. Here, it is shown that this technique applies equally well to the piston-driven gas-column oscillator; and that the piston experiment provides strong evidence for the validity of the general …

Theoretical Models For Wall Injected Duct Flows, Tony Saad

Doctoral Dissertations

This dissertation is concerned with the mathematical modeling of the flow in a porous cylinder with a focus on applications to solid rocket motors. After discussing the historical development and major contributions to the understanding of wall injected flows, we present an inviscid rotational model for solid and hybrid rockets with arbitrary headwall injection. Then, we address the problem of pressure integration and find that for a given divergence free velocity field, unless the vorticity transport equation is identically satisfied, one cannot find an analytic expression for the pressure by direct integration of the Navier-Stokes equations. This is followed by …