The eigenvalue problem associated with the determination of the natural frequencies, mode shapes and impulse response of a linear vibrating system is a classical and very important engineering problem. This dissertation presents a new technique for obtaining useful approximate, and in some cases, exact, solutions for such problems. The fundamental concepts on which the technique is based are: 1) The use of inertia (mass) as a perturbation parameter for developing series solutions for the response of a system to harmonic excitation. 2) The expansion of these series solutions as continued fractions. The series solutions are obtained by applying the classical perturbation technique, which assumes the solution for the governing differential equation (say, for the case of one independent and one dependent variable) can be expressed as w = w₀ + μ w₁ + μ² w₂ + μ³ w₃ + . . . . . where w is the dependent variable, and the wᵢ are unknown functions. µ is an inertia parameter that appears in the coefficients of the acceleration terms of the governing differential equation. The series for w is substituted in the governing differential equation, and the associated initial and boundary conditions. Since µ is arbitrary, the coefficients of like powers of µ are equated to zero. The result is an infinite set of differential equations, and boundary and initial conditions, each of which is (hopefully) easier to solve than the original problem. w₀ becomes the massless, or static, solution, in which the system responds instantaneously to, and in phase with, the applied excitation. The equation governing w₁ is the same as that for w₀ , except that some function of w₀ appears as a loading function, and, in general, the equation governing wᵢ will involve some function of wᵢ₋₁ as a loading function. There are two ways in which the problem can become a so-called singular perturbation problem. First, if the order of the equations governing wᵢ is not as high as that of the original equation, it may not be possible to accommodate all the initial and boundary conditions. However, initial conditions are not necessary for determining the eigenvalues of a linear vibrating system. The second way in which a singular perturbation may arise is the limiting of the range of validity of the series solution to small values of some combination an independent variable and the perturbation parameter. The range of validity of the series solution can be extended by truncating the series after some term and converting the truncated series to the quotient of two polynomials by means of continued fractions. The zeros of the denominator polynomial will correspond to resonant conditions. Lumped systems without damping are completely amenable to this method of solution, and a two-degree-of-freedom system with damping is solved. Approximate solutions for an axially loaded rod, a Timoshenko beam, and an Euler beam of variable cross-section illustrate the application of the method of analysis to continuous systems. / Doctor of Philosophy

The maximum target material spray velocity emanating from the rear of a penetrated thin target is studied utilizing the one-dimensional shock-wave theory. A set of experiments is designed to evaluate the analytical results. The targets are 0.0025-cm-thick 1100 aluminum foil and 0.041-cm-thick 1100 Hl4 aluminum plate. The projectiles are made of tungsten and disk shaped. Their diameter is 0.56 em and their thickness is either 0.076 or 0.038 cm. The projectile and target dimensions assure that the one-dimensional assumptions in the theory are valid.. The impact velocity range is from 0.089 to 0.295 cm/µsec. A method is developed to launch unskewed and intact very dense disk-shaped projectiles to high velocity. By using very dense tungsten projectiles the maximum aluminum target material spray velocity is as predicted by the theory well in excess of the projectile impact velocity. A ratio is defined as the maximum target material spray velocity to projectile impact velocity. The experimental ratio points are seen to agree with the predicted values for the impact velocity range covered. Photographic data are presented and analyzed for the fragmentation of material on the leading edge of the target material spray cloud. As the impact velocity is increased the complete fragmentation of material on the leading edge is shown in the photographic data. / Master of Science

This project was undertaken to determine the effects of continued close confinement on the normal physiological characteristics of the gray squirrel. A total of 46 squirrels divided into three groups: normal, confined-stressed, and confined-shocked were sampled within a period of 10 months from September 15, 1965 to June 30, 1966. The confined-shocked squirrels exhibited acute hypoglycemia, hypolacticemia, and hypothermia indicating a general breakdown in the overall homeostatic processes. The adrenal glands from the confined-shocked individuals were approximately 6-8 mg heavier than either the normal or confined-stressed animals. Packed-cell-volumes averaged from 31-36% higher than normal in both the confined-stressed and confined-shocked animals indicating a polycythemic condition which developed due to the increased stress of confinement. Normal adult liver glycogen levels were approximately 17.2 mg/g of liver tissue higher than immature squirrels. Death from shock could have been caused by the acute reduction of plasma glucose, plasma lactic acid, or body temperature or any combination of these three physiological characteristics. High PCV may have been an additive factor to the shock syndrome evident in this study. However, further intensive study must be conducted before we can contribute the observed shock losses to any specific physiological mechanism. / Master of Science

The Millers Cove area is underlain by rock ranging in age from Middle Cambrian Elbrook Dolomite to Early Mississippian Price Sandstone. Carbonate deposition was dominant into the Ordovician with elastic sedimentation dominant throuhout the rest of the Paleozoic. Cove Mountain is formed by the overturned northeast plunging Cove Mountain anticline and Dragons Tooth syncline. To the southwest the anticline passes beneath the Pulaski fault. The extension of the anticline to the northeast is unknown but it may be continuous with the Broad Run anticline. The Dragons Tooth syncline is continuous to the northeast with the North Mountain syncline but to the southwest passes beneath the Pulaski fault. The southwest plunging Brush Mountain-Little Mountain syncline may be continuous with the northeast plunging Broad Run Mountain syncline. The Miller fault has 10,000 feet of stratigraphic displacement where it passes under the Pulaski fault but it loses displacement and apparently terminates to the northeast. Thus, the Miller fault block is paraautochthonous. The Pulaski fault which separates the Miller fault block from the Catawba syncline is an overthrust of 10 mile horizontal displacement and 10,000 foot stratigraphic displacement. The first of two different deforming forces produced folds whose axes trend N. 35° E. The second was associated with thrust faulting and caused refolding along trends of N. 60° E. Accompanying faulting was the rotation of the southwestern end of the Miller fault block, the depression of the Brush Mountain-Little Mountain syncline beneath the weight of the Pulaski and Miller fault blocks, and the bowing of the Catawba syncline and Sinking Creek anticline under the buttressing action of Cove Mountain. / Master of Science

An investigation was undertaken to develop a procedure for preparing molybdena-alumina catalysts for olefin disproportionation and to develop equipment and procedures for exploratory testing of the catalysts. A reproducible procedure for preparing molybdena-alumina catalysts was developed. This procedure consisted of impregnating Harshaw Al-0104-T, 1/8 inch alumina catalyst pellets with 10 to 30 percent aqueous ammonium molybdate solutions at 210 °F. The impregnated pellets were placed in the reactor, dried for three hours at 250 to 300 °F and were activated at 1000 °F for five hours. Dry nitrogen was passed over the catalysts during drying and activation. A reaction system was designed, constructed, and operated to perform exploratory tests on the catalysts. The reactor was constructed from 3/8 inch stainless steel tubing and packed with approximately 5.8 grams of catalyst for each test. The reactor was operated at pressures of 30 to 170 pounds per square inch, gage, at temperatures of 250 to 550 °F and at a weight hourly space velocity of 1.1 gram of feed per hour per gram of catalyst. The reaction products were analyzed by gas chromatography. The catalysts prepared during this investigation gave disproportionation of propylene to ethylene and 2-butene. Ethylene and 2-butene were formed in approximately equimolar quantities. Maximum conversion was found to occur in the temperature range from 300 to 400 °F. Conversion up to 30 percent was obtained using the catalysts prepared during this investigation. Limited data indicated conversion to be independent of pressure in the range of 30 to 170 pounds per square inch, gage. The catalysts were found to deactivate with time-on-stream. Due to the limited data taken, no quantitative conclusions were reached as to the rate of deactivation. / M.S.

Experimental resonant frequencies and mode shapes from vibration tests with a 1/5-scale model of the Titan III-A launch vehicle are presented, Measurements of longitudinally excited vibration modes of the model structure supported in a suspension system offering negligible restraint to longitudinal motion for five different propellant loadings are shown. The data indicate the quantitative and qualitative effect on the overall model vibration response due to different amounts of simulated liquid propellant in the tanks. The experimental data show the response of the model to be complex due primarily to structural coupling of modes. Two mathematical models are used to calculate the model vibration response; one represents a simple lumped-mass analysis and the other a more refined interpretation which considers axisymmetric shell, fluid, and mass components of the structure. Longitudinal vibration mode shapes and frequencies computed from the component model show better correlation with measured basic longitudinal structural. modes than those obtained using the lumped-mass representation. / M.S.

A taxonomic study has been made of two closely related races of Etheostoma flabellare flabellare Rafinesque, one from the Roanoke River of Virginia and the other from the Neuse River of North Carolina. They are compared in twenty-three characters (scalation, ray counts, and color marks). For eight characters, the Roanoke sample has been divided into its component groups (the Blackwater and Pigg river samples). These are compared to each other and to the Neuse sample. Four new characteristics are described. The shape of the line behind the eye is rated as rectangular or 8-shaped. The shape of the spots on the caudal fin is rated as solid or hollow. Three major color patterns are described; one of which is a juvenile pattern and the others are characteristic of males and females. In respect to belly scalation, three categories have been established which are dependent upon the extent of development of the scale row along the ventral mid-line. These are as follows: totally scaled, partially scaled, and naked. The Roanoke and Neuse fantail darters differ most in seven characters. These are as follows: total and pored scales lateral line, scales across belly, belly scalation, shape and number of spots caudal fin, and the persistence of juvenile color patterns in the adult Neuse female. Paedomorphosis, in the Neuse fantail, accounts for most of the major differences between the populations. / M.S.

While solutions to the nonlinear von Karman equations for large deflections of thin plates have been presented for annular plates under certain axisymmetric/loading conditions, little work has been done with unsymmetrical large deflections. In this investigation a systematic mathematical iteration technique is used to obtain a solution to the von Karman equations for an annulus fixed at the outer edge and which has a central rigid plug that is rotated about its diameter out of the plane of the plate. The linear, small-deflection solution to this problem presented by H. Reissner is used as the first approximation for large deflections. By using Reissner's solution for the lateral displacement to evaluate the nonlinear terms in one of the von Karman equations, a linear fourth order partial differential equation for the stress function is obtained. The particular solution to the stress function equation leads to multi·valued in-plane displacements, which are eliminated by proper selection of the homogeneous solution, The boundary conditions for the stress function equation are written in terms of the in-plane displacements, and wherever trigonometric functions of the small angle of rotation of the rigid inclusion appear, they are expressed in a power series of the angle and terms of higher order than the second power are neglected. By using the resulting stress function and the Reissner solution for lateral displacement to evaluate the nonlinear terms in the second von Karman equation, a linear, fourth order partial differential equation for the second approximation to the large deflection lateral displacement is obtained. Again the boundary conditions are expressed in a power series of the rotation angle and terms of higher order than the third power are neglected. The solution for the lateral displacement is a function of the first and third powers of the angle of rotation, where the part containing the first power is the Reissuer solution and the part containing the third power is a correction term reflecting a reduction in lateral displacement caused by the in-plane stresses. Thus by neglecting the third power of the small angle of rotation, the large-deflection solution reduces to the linear, small deflection solution. Any further iterations are not performed because the algebra involved becomes excessive; however, the iteration procedure can be repeated to obtain higher approximations. By taking appropriate derivatives of the stress function and the lateral displacement, expressions for the bending and membrane stresses as functions of the position in the plate and the angle of rotation are obtained. Numerical results are presented in graphical form for typical plates. Experimental data was obtained with an 18 inch outer diameter, 7.2 inch inner diameter, 0.0634 inch thick plate made of 7075-T6 aluminum. The results of the iteration solution are found to agree very well with the experimental data for lateral displacements up to one and one-half times the thickness of the plate, but the iteration solution begins to overestimate the nonlinear effect for larger displacements. As a limiting case to the title problem, an iteration solution for large deflections of a clamped circular plate loaded by a central concentrated moment is given. / Ph. D.

The Bays Formation is of late Middle Ordovician (upper Wilderness) age and ls a predominantly clastic formation that crops out in 16 belts in the southeastern side of the Appalachian Valley from near Roanoke, Virginia, to northwestern Georgia. The various lithotopes in the Bays include conglomerates containing limestone cobbles and quartz pebbles more than 1 inch across, sandstones, siltstones, mudstones, shales, and impure limestones. In most strike belts much of the formation is calcareous. The characteristic color of the Bays is "red”, but olive-gray, greenish-gray, and yellowish-gray are also common. Mud cracks are common in fine-grained Bays strata, particularly in the basal portion. The maximum known thickness of the Bays is about 1095 feet, in Monroe County, Tennessee. The Bays Formation in its maximum stratigraphic development is equivalent to the succession that includes the Bowen, Witten, Moccasin, and Eggleston formations of middle belts in the Appalachian Valley. The Bays at its type locality in the Bays Mountain synclinorium in northeastern Tennessee is underlain by the Sevier Formation and overlain by the Martinsburg Formation Several bentonites occur in the upper part of the Boys-Moccasin sequence and augment stratigraphic control. The presence of ghosts of glass bubbles and Y-shaped shards in tuffaceous rocks associated with the bentonites indicates a volcanic origin for the bentonitic material. The bentonltes (K-bentonites of some writers) are composed chiefly of illite, mixed-layer chlorite-montmor-illonite. Generally, clastic rocks in the Bays gradually decrease in grain size from southeast to northwest. The amount of calcium carbonate in Bays strata increases from southeast to northwest. This decrease in grain size and increase in calcium carbonate in the rocks toward the northwest also occurs in the Bowen, Witten, Moccasin, and Eggleston formations of middle belts in the Appalachian Valley. The increase in grain size of Bays sediments toward the southeast suggests that the source area of Bays sediments was in that direction. Sedimentary structures indicating current direction suggest that Bays sediments came from the south, southeast, and east. Rock southeast, and fragments in Bays strata include limestone, sandstone, siltstone, chert, orthoquartzite, metaquartzite, amphibolite, fine-grained metamorphics such as slate and phyiltte, and vein quartz. Nonopaque heavy minerals in Bays Strata include zircon, tourmaline, apatite, hornblende, zoisite, garnet, epidote, and corundum. These clasts and minerals indicate that Bays sediments were derived from older sedimentary rocks, low-grade and high-grade metamorphic rocks, and silicic igneous intrusive rocks. These data suggest that Bays sediments were derived from a rising crystalline land mass (or masses) to the southeast, possibly in the vicinity of the present Piedmont and adjacent Blue Ridge. A belt of Cambrian and older Ordovician sedimentary rocks, probably along the northwest side of the rising crystalline complex, was also exposed during at least part of Bays time and contributed to Bays sediments. It is believed that the great volume of Bays sediments necessitates a land mass source area larger than a volcanic island arc. It is beleived that local troughs on the Bays sea floor subsided faster than adjacent areas, and accommodated greater thicknesses of sediments. A few of these troughs may have also attracted slightly coarser sediments that bypassed less rapidly subsiding parts of the depositional basin. The rising of the land mass required to supply the large volume of coarse and fine Bays sediments and the volcanism that was important in the latter part of Bays time indicate considerable tectonic activity. The differential subsidence of the Bays depositional basin also suggests that Bays time was characterized by important tectonic activity in the southern Appalachian region. / Ph. D.

The purpose of this study was to derive industrial arts subject matter, suitable for use at the secondary school level, from the technology of microelectronics. This subject matter was to reflect the technology of the microelectronic industry and also be compatible with the objectives of industrial arts education. The study involved three major steps. The first step was the arrangement of information about the technology of microelectronics into groups of information denoted by conventional electric terms. In the second step, industrial arts subject matter was selected from the groups of information by using Olson’s “curricular components” as “categories of subject matter''. The third step involved the placing of the selected subject matter under the technical, avocational, and consumer functions of industrial arts. The sources of information about the technology of microelectronics were 312 periodicals dealing with the electronic industry for the years 1963, 1964, and 1965. The derived subject matter was presented in both narrative and topical outline forms. / Master of Science