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Approximate solutions for the shape of the geomagnetic hollow and the effect of a uniform external pressure from the interplanetary plasma
A theoretical and experimental study is made to investigate the effect on plate vibrations of varying the stiffness of corner elastic point supports. A theoretical model is developed using a Rayleigh-Ritz analysis which approximates the plate mode shapes as products of free-free beam modes. The elastic point supports are modelled both as massless translational springs, and springs with tip masses. The tip masses are included to better represent the experimental supports. An experiment is constructed using the bending stiffness of horizontal beams to support a square plate at its four corners. The stiffness of these supports can be varied over such a range that the plate fundamental frequency is lowered to 40% of the rigid support frequency. The variation with support stiffness of the frequencies of the first eight plate modes is measured, and compared with the theoretical results. The plate mode shapes for rigid supports are analyzed using holographic interferometry. There is excellent agreement between the theoretical and experimental results, except for high plate modes where the theoretical model is demonstrated to be inadequate.
A theoretical and experimental study is made to investigate the effect on plate vibrations of varying the stiffness of corner elastic point supports. An experiment is conducted in which the bending stiffness of horizontal beams is used to support a square plate at its four corners. The stiffness of these supports can be varied over such a range that the plate fundamental frequency is lowered to 40% of the rigid support frequency. The variation with support stiffness of the frequencies of the first eight plate modes is measured and is compared with results from a theoretical model in which a Rayleigh-Ritz analysis is used which approximates the plate mode shapes as products of free-free beam modes. The elastic point supports are modeled both as massless translational springs and springs with tip masses, which are included to better represent the experimental supports.
Natural frequencies, as a function of power were determined using a finite element model. Operating conditions investigated were operation with a resistive electrical load and operation synchronized to an electrical utility grid. The influence of certain drive train components on frequencies and mode shapes is shown. An approximate method for obtaining drive train natural frequencies is presented.
Contrary to popular belief, very large meteorites can be sufficiently slowed by aerodynamic drag to survive impact with the earth's surface provided that they enter the atmosphere at very low angles. This is a stringent requirement and survival probabilities for large, unguided objects are low; but they are not zero. Based on high-velocity impact experiments and published tabulations of the parameters of shallow angle entry trajectories, we estimate the probability of survival for an iron meteorite approximately the size and shape of the legendary Chinguetti meteorite (100 x 40 x 20-40 m) to be between 0.1 and 1 percent. Together with a limiting estimate of the flux of such bodies encountering the earth, this leads to an expected survival rate of one per (0.1-1.0) billion years on the earth's land surface.
Numerical solutions are presented for the fundamental natural frequency and mode shape of a rectangular plate loaded by in-plane hydrostatic forces for a wide variety of aspect ratios, boundary conditions, and load magnitudes. All six possible combinations of simply supported and clamped edges are considered. The limiting conditions of unloaded vibration and buckling are discussed in detail, with emphasis on the preferred mode shape. Design curves and approximate formulae are presented which provide a simple means of determining the fundamental frequency parameter.
The equipment used in the Nighttime Daytime Optical Survey of Lightning experiment, carried out on the second and fourth Space Shuttle missions, is described. Attention is then given to one of the more spectacular lightning photographs, that of a Y-shaped discharge taken by Thomas K. Mattingly II on the night of June 29, 1982, over southern Brazil. Since the orientation of the camera with respect to the earth is not known, the scale of the photograph cannot be determined accurately. If the camera had been looking directly down from the vehicle at its altitude of 300 km, the Y-shaped pattern would be approximately 60 km long and 40 km wide. If, as is thought probable, the camera was not looking directly down, the pattern would have somewhat greater dimensions. The photographs show that illumination from lightning discharges can cover a rather wide area.
An exploratory wind tunnel investigation was performed to observe the flow field effects produced by vertically deployed apex fences on a planar 74 degree delta wing. The delta shaped fences, each comprising approximately 3.375 percent of the wing area, were affixed along the first 25 percent of the wing leading edge in symmetric as well as asymmetric (i.e., fence on one side only) arrangements. The vortex flow field was visualized at angles of attack from 0 to 20 degrees using helium bubble and oil flow techniques; upper surface pressures were also measured along spanwise rows. The results were used to construct a preliminary description of the vortex patterns and induced pressures associated with vertical apex fence deployment. The objective was to obtain an initial evaluation of the potential of apex fences as vortex devices for subsonic lift modulation as well as lateral directional control of delta wing aircraft.
Simple, rugged gauge used to measure speed of flow and temperature of steam or other gas flowing through pipes of arbitrary diameter, from 1 to 28 in. or larger. Specially designed, instrumented whistle - has no moving parts, small, nonobstruction, operates at high temperature and pressure, and cleans itself. Does not operate at zero flow, but at moderate flows (tens of meters per second) generates intense sound for use in measurements. Consists of slanted ring groove of depth D and pressure taps in wall of pipe carrying flow to be measured. Resonant wavelength of sound generated by ring groove depends primarily on size and shape of groove and approximately equal to 4D.
Returned radar power estimates are used in an iterative procedure which generates successive approximations to the target shape in order to determine the shape of a 3-D surface. A simulation is shown which involves the reconstruction of an edge of a flat plate. Although this is a somewhat artificial example, it addresses the real problem of recovering edges of space objects lost in shadow or against a dark background. The results indicate that a microwave/optical sensor fusion system is possible, given sufficient computing power and accurate radar cross section measuring systems.
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A general solution, based on the classical buckling criterion, is given for the problem of buckling of low arches under a lateral loading acting toward the center of curvature. For a sinusoidal arch under sinusoidal loading, the critical load can be expressed exactly as a simple function of the beam dimension parameters. For other arch shapes and load distributions, approximate values of the critical load can be obtained by summing a few terms of a rapidly converging Fourier series. The effects of initial end thrust and axial and lateral elastic support are discussed. The buckling load based on energy criterion of Karman and Tsien is also calculated. Results for both the classical and the energy criteria are compared with experimental results.
A numerical and experimental investigation of the bending behavior of six eight-ply graphite-epoxy circular cylinders is presented. Bending is induced by applying a known end-rotation to each end of the cylinders, analogous to a beam in bending. The cylinders have a nominal radius of 6 inches, a length-to-radius ratio of 2 and 5, and a radius-to-thickness ratio of approximately 160. A (+/- 45/0/90)S quasi-isotropic layup and two orthotropic layups, (+/- 45/0 sub 2)S and (+/- 45/90 sub 2)S, are studied. A geometrically nonlinear special-purpose analysis, based on Donnell's nonlinear shell equations, is developed to study the prebuckling responses and gain insight into the effects of non-ideal boundary conditions and initial geometric imperfections. A geometrically nonlinear finite element analysis is utilized to compare with the prebuckling solutions of the special-purpose analysis and to study the buckling and post buckling responses of both geometrically perfect and imperfect cylinders. The imperfect cylinder geometries are represented by an analytical approximation of the measured shape imperfections. Extensive experimental data are obtained from quasi-static tests of the cylinders using a test fixture specifically designed for the present investigation. A description of the test fixture is included. The experimental data are compared to predictions for both perfect and imperfect cylinder geometries. Prebuckling results are presented in the form of displacement and strain profiles. Buckling end-rotations, moments, and strains are reported, and predicted mode shapes are presented. Observed and predicted moment vs. end-rotation relations, deflection patterns, and strain profiles are illustrated for the post buckling responses. It is found that a geometrically nonlinear boundary layer behavior characterizes the prebuckling responses. The boundary layer behavior is sensitive to laminate orthotropy, cylinder geometry, initial geometric imperfections, applied end-rotation, and non-ideal boundary conditions. Buckling end-rotations, strains, and moments are influenced by laminate orthotropy and initial geometric imperfections. Measured buckling results correlate well with predictions for the geometrically imperfect specimens. The postbuckling analyses predict equilibrium paths with a number of scallop-shaped branches that correspond to unique deflection patterns. The observed postbuckling deflection patterns and measured strain profiles show striking similarities to the predictions in some cases. Ultimate failure of the cylinders is attributed to an interlaminar shear failure mode along the nodal lines of the postbuckling deflection patterns.
We have discovered a novel two-phase synthesis of CuInSe2 at 25 deg C from Cu2Se and (C5H5)3In in 4-methylpyridine (4-MePy). An analogous reaction to produce CuInS2 must be run at 140 deg C in refluxing 4-MePy in the presence of 2-mercaptopyridine. Microscopy of CuInSe2 produced at 25 deg C shows it to be platelet-shaped crystallites with an approximate particle size of 10 microns, less than 2 percent C and H, with a small amount of unidentified crystalline impurity. Our results demonstrate that it is possible to produce from solution a material that is ordinarily synthesized in bulk or films at much higher temperatures or using extraneous reagents and/or electrons.
Results are presented from a steady state numerical model of the low-latitude boundary layer (LLBL) on closed field lines and its coupling to the dayside auroral ionosphere. In the model the boundary layer approximation is used, the result being that inertial forces are taken into account only in the main flow direction (-x) where they are balanced by pressure forces, j x B forces, and viscous forces. Motion in the transverse directions (y and z) is treated kinematically, the force balances in these two directions being purely static. Computationally, the model is two dimensional, describing the motion of plasma and frozen-in magnetic field in the equatorial (xy) plane but allowing for lowest-order polynomial variation of some quantities with the coordinate (z) perpendicular to that plane. The plasma expands and compresses isentropically; the magnetic field is calculated self-consistently, which leads to approximately parabolic field line shape in planes parallel to the magnetopause (the xz plane), with maximum field curvature near the magnetopause edge of the LLBL. Coupling to the ionosphere via region 1 field-aligned currents is included. The effects of the ionosphere are represented by two parallel resistive plates at fixed height above and below the equatorial plane. The model can be used to investigate the influence of various physical parameters, for example, viscous and magnetic Reynolds numbers, and of boundary conditions at the magnetopause and in the magnetosphere on the LLBL development in the -x direction. Special attention is given to viscous effects which, under suitable circumstances, lead to a region 1 current that first increases and then reduces with increasing longitude away from local noon. Asymptotic matching of the antisunward motion of the cool LLBL plasma to sunward convection of hot plasma in the magnetosphere is illustrated along with the entrainment of magnetospheric plasma by the antisunward LLBL flow.
A reinterpretation of the life history of warm core ring 82-b is constructed from drifter trajectories, hydrographic profiles, and satellite-derived sea surface temperature fields. An analysis of the observations strongly suggests this ring is fundamentally a dipole structure for much of its existence. The dipole has unequal strength vortices, with the cyclone being the weaker component. Quantification of the dipole indicates the anticyclonic is oval shaped and rotates at approximately 7.7 deg per day, while the cyclone revolves around the anticyclone at about 14.5 deg per day, yielding an orbit period of approximately 25 days for the cyclone. The elusive part of the dipole explanation is in interpreting its surface signature as a function of time, as the cyclone appears to disappear when in proximity to the steep continental slope. Vortex modeling suggests that when the weaker cyclonic eddy is placed close to a boundary, the cyclone is drawn into a filament as it is advected through the gap between the anticyclone and the boundary. This means the cyclone is either in a filamentation state or undergoing the straining associated with filamentation approximately three fourths of this time, which is in complete agreement with the satellite imagery. In addition, the 82-B dipole configuration is sufficiently robust to survive continuous interaction with the continental slope and the onset of a Gulf Stream interaction. Although only warm core ring 82-B is analyzed in detail (and found to be a vortex pair), dipole configurations are found in the warm core ring 81-F time series as well.
The Ames airborne tracking sunphotometer was operated at the National Oceanic and Atmospheric Administration (NOAA) Mauna Loa Observatory (MLO) in 1991 and 1992 along with the NOAA Climate Monitoring and Diagnostics Laboratory (CMDL) automated tracking sunphotometer and lidar. June 1991 measurements provided calibrations, optical-depth spectra, and intercomparisons under relatively clean conditions; later measurements provided spectra and comparisons for the Pinatubo cloud plus calibration checks. June 1991 results are similar to previous MLO springtime measurements, with midvisible particle optical depth at the near-background level of 0.012 +/- 0.006 and no significant wavelength dependence in the measured range (lambda = 0.38 to 1.06 micrometers). The arrival of the Pinatubo cloud in July 1991 increased midvisible particle optical depth by more than an order of magnitude and changed the spectral shape of to an approximate power law with an exponent of about -1.4. By clearly September 1991, the spectrum was broadly peaked near 0.5 micrometers, and by July 1992, it was peaked near 0.8 micrometers. Our optical-depth spectra include corrections for diffuse light. NOAA- and Ames Research Center (ARC)-measured spectra are in good agreement. Columnar size distributions inverted from the spectra show that the initial (July 1991) post-Pinatubo cloud was relatively rich in small particles (r less than 0.25 micrometers), which were progressively depleted in the August-September 1991 and July 1992 periods. Conversely, both of the later periods had more of the optically efficient medium-sized particles (0.25 less than r less than 1 micrometers) than did the fresh July 1991 cloud. These changes are consistent with particle growth by condensation and coagulation. Photometer-inferred column backscatter values agree with those measured by the CMDL lidar on nearby nights. Combining lidar-measured backscatter profiles with photometer-derived backscatter-to-area ratios gives peak particle areas that could cause rapid heterogeneous loss of ozone, given sufficiently low particle acidity and suitable solar zenith angles (achieved at mid- to high latitudes). Top-of-troposphere radiative forcings for the September 1991 and July 1992 optical depths and size distributions over MLO are about -5 and -3 W/sq m, respectively (hence comparable in magnitude but opposite in sign to the radiative forcing caused by the increase in manmade greenhouse gases since the industrial revolution). Heating rates in the Pinatubo layer over MLO are 0.55 +/- 0.13 and 0.41 +/- 0.14 K/d for September 1991 and July 1992, respectively.
Thermostructural analysis was performed on a heated titanium honeycomb-core sandwich panel. The sandwich panel was supported at its four edges with spar-like substructures that acted as heat sinks, which are generally not considered in the classical analysis. One side of the panel was heated to high temperature to simulate aerodynamic heating during hypersonic flight. Two types of surface heating were considered: (1) flat-temperature profile, which ignores the effect of edge heat sinks, and (2) dome-shaped-temperature profile, which approximates the actual surface temperature distribution associated with the existence of edge heat sinks. The finite-element method was used to calculate the deformation field and thermal stress distributions in the face sheets and core of the sandwich panel. The detailed thermal stress distributions in the sandwich panel are presented, and critical stress regions are identified. The study shows how the magnitudes of those critical stresses and their locations change with different heating and edge conditions. This technical report presents comprehensive, three-dimensional graphical displays of thermal stress distributions in every part of a titanium honeycomb-core sandwich panel subjected to hypersonic heating on one side. The plots offer quick visualization of the structural response of the panel and are very useful for hot structures designers to identify the critical stress regions.