Applied Mathematics Commons^™

On The Existence Of Periodic And Eventually Periodic Solutions Of A Fluid Dynamic Forced Harmonic Oscillator, Charlie H. Cooke

Mathematics & Statistics Faculty Publications

For certain flow regimes, the nonlinear differential equation Y¨=F(Y)−G, Y≥0, G>0 and constant, models qualitatively the behaviour of a forced, fluid dynamic, harmonic oscillator which has been a popular department store attraction. The device consists of a ball oscillating suspended in the vertical jet from a household fan. From the postulated form of the model, we determine sets of attraction and exploit symmetry properties of the system to show that all solutions are either initially periodic, with the ball never striking the fan, or else eventually approach a periodic limit cycle, after a sufficient number of bounces away from …

Finite Element Thermal-Structural Analysis Of Cable-Stiffened Space Structures, Ajay Kumar Pandey

Mechanical & Aerospace Engineering Theses & Dissertations

Finite element thermal-structural analyses of cable-stiffened space structures are presented. A computational scheme for calculation of prestresses in the cable-stiffened structures is also described. The determination of thermal loads on orbiting space structures due to environmental heating is described briefly. Three finite element structural analysis techniques are presented for the analysis of prestressed structures. Linear, stress stiffening and large displacement analysis techniques are investigated.

The three techniques are employed for structural analysis of prestressed cable structures at different prestress levels. The three analyses produce similar results at small prestress. but at higher prestress differences between the results become significant. For …

Viscous Modeling And Computation Of Leading-And Trailing-Edge Vortex Cores Of Delta Wings, Balakrishnan Lakshmanan

Mechanical & Aerospace Engineering Theses & Dissertations

A Finite-Difference method is presented for calculating steady quasi-axisymmetric flow of an incompressible fluid at large Reynolds number. Approximations of the boundary-layer type are employed to reduce the Navier-Stokes equations to a pair of non-linear parabolic equations. Along with the governing equations, initial conditions are specified at some upstream cross section and boundary conditions are specified at the axis of symmetry and on the outer bounding surface.

The governing equations are replaced by a set of quasilinear finite-difference equations. The solution is obtained by a marching technique, which proceeds step-by-step in the axial direction. At each axial station, an iterative …

An Algorithm For The Electromagnetic Scattering Due To An Axially Symmetric Body With An Impedance Boundary Condition, F. Stenger, M. Hagmann, J. Scheing

Computer Science Faculty Publications

Let B be a body in R³, and let S denote the boundary of B. The surface S is described by S = {(x, y, z): (x² + Y²)^½= ƒ(z), -1≤ z ≤ I}, where ƒ analytic function that is real and positive on (-1, 1) and ƒ(±1) = 0. An algorithm is described for computing the scattered field due to a plane wave incident field, under Leontovich boundary conditions. The Galerkin method of solution used here leads to a block diagonal matrix involving 2M …

Sufficiency Of A Numerical Downstream Continuation, Charlie H. Cooke

Mathematics & Statistics Faculty Publications

(First paragraph) Customarily one does not impose n-th order boundary conditions on the solution of initial/boundary value problems whose characterizing partial differential equations are also n-th order. However, conjecture that such problems are not well-posed, or that a solution might not exist, is not always justified [l]. Perhaps a physically more natural example is provided by problems of computational fluid dynamics. Here boundary conditions which correctly should be applied at an infinite distance downstream from the region of interest are for computational convenience often applied at a finite location [2]. Results of numerical experimentation on viscous flows governed by …

Complementary Extremum Principles, J. Swetits, C. Rogers

Mathematics & Statistics Faculty Publications

Important complementary extremum principles are generated without recourse to general variational theory. The results are illustrated by an application to a class of boundary value problems in Magnetohydrodynamics.

Solar Magnetoatmospheric Waves-A Simplified Mathematical Treatment, John A. Adam

Mathematics & Statistics Faculty Publications

The inhomogeneous wave equation for a special class of magnetoatmospheric waves is formally solved, and the principle of stationary phase used to provide information on the group velocity properties of such waves. General results are presented concerning the associated mechanical energy flux. The basic problem considered is relevant to waves initiated by sudden events in the solar atmosphere.