Showing papers on "Transverse plane published in 1972"

On one-dimensional finite-strain beam theory: the plane problem

Abstract: The paper formulates a one-dimensional large-strain beam theory for plane deformations of plane beams, with rigorous consistency of dynamics and kinematics via application of the principle of virtual work. This formulation is complemented by considerations on how to obtain constitutive equations, and applied to the problem of buckling of circular rings, including the effects of axial normal strain and transverse shearing strain.

Calculation and Experimental Proof of the Transverse Shift Induced by Total Internal Reflection of a Circularly Polarized Light Beam

Abstract: Wiegrefe, Fedorov, Costa de Beauregard, and Schilling have discussed the transverse energy flux existing in total reflection of an elliptically polarized light beam, the latter two proposing formulas for the transverse shift of the reflected beam. We have calculated the transverse shift by an energy-flux-conservation argument similar to Kristoffel's and to Renard's in their deduction of the longitudinal Goos-H\"anchen shift, thus obtaining a formula different from those of the previous authors. We have also tested experimentally the existence of the transverse shift, in the optimal case of circular polarization and quasilimit total reflection, by using two slightly different multiplying procedures. Our measurements definitely vindicate our own formula for the transverse shift against both Costa de Beauregard's and Schilling's. The relevance of our results in connection with noncollinearity of velocity and momentum of the spinning photon inside the evanescent wave is very briefly discussed.

Calculations on axial dechanneling

Abstract: An integral equation governing the change with depth of the distribution in transverse energy for an aligned beam is derived. The integral equation is approximated by a diffusion-like equation, in which the diffusion function depends on transverse energy. Thermal vibrations and scattering by electrons contribute to the diffusion. From the transverse energy distribution the yield vs. depth of close encounter processes is evaluated. Our primary aim in obtaining nurnerical solutions to the diffusion equation is to check the validity of simple analytical yield calculations in which diffusion is neglected.

Transverse Vibrations of Double‐Tapered Cantilever Beams

Abstract: The differential equation is developed from the Bernoulli‐Euler equation for the free vibrations of a double‐tapered cantilever beam. The beam tapers linearly in the horizontal and in the vertical planes simultaneously. From a computer solution of this equation, a table has been developed from which the fundamental frequency, second, third, fourth, and fifth harmonic can easily be obtained for various taper ratios. Charts are plotted for selected taper ratios in the vertical plane to show the effect of taper ratios on frequency.

Bonded wire i interconnection system

Abstract: An interconnection system suitable for transmission lines, in the form of electrical or optical conductors, or in the form of conduits for electrical waveguide transmission, reflected light or fluidic signals, wherein lengths of such transmission lines bridge between discrete point-to-point location on a substrate, the transmission lines being anchored by sealant and filler material at selected substrate locations and being cut generally transversely, or otherwise transversely formed, to provide exposed conductor or conduit end portions anchored at the selected locations. The transverse areas of the conductors or conduits defined by such transversely cut, or otherwise transversely formed, and exposed end portions provide energizable signal energy planes. More specifically, such discrete energizable planes in the form of transverse conductor surfaces, are of a size and shape conforming to the transverse conductor areas exposed by cutting or other forming operation. Such conductors may be either insulated electrical or optical conductors provided thereover with metal or a metallized coating to result in an electrical shielded, or an optically shielded and reflecting, interconnection system. The transmission lines in the form of conduits provide discrete, end-anchored conduits for conveying signal energy excitations in the form of fluidic pressure, reflected optical energy or electrical waveguide transmissions. The ends of the conduits are anchored in the substrate and define generally transverse end openings of the conduits. The transverse areas of such openings provide energizable signal energy planes through which the conveyed signal excitations are transmitted. The size and shape of the energizable signal energy planes conform to the conduit transverse end areas exposed by cutting.

Three-Dimensional Wall Jet Originating from a Circular Orifice,

Abstract: An incompressible three-dimensional turbulent wall jet originating from a circular orifice located adjacent to a plane wall is studied both theoretically and experimentally. An approximate similarity analysis predicts that the two transverse length scales, l 0 and L0, and the inverse of the mean velocity scale grow linearly with distance downstream x from the orifice. Experimental measurements of mean velocity and longitudinal turbulence intensity profiles were made both in air and water with hot-wire and hot-film anemometers respectively. The behaviour predicted by the similarity analysis was verified. It was found that the rate of growth of the length scale normal to the plane wall, dl 0/dx, was somewhat less than that found for a two-dimensional wall jet, whereas the rate of growth of the length scale in the lateral direction, dL0/dx, was about seven times greater than dl 0/dx.

Calculation of Plane‐Wave Propagation in Anisotropic Elastic‐Plastic Solids

Abstract: Wave‐propagation effects induced in isotropic materials by either explosive or impact loading uniformly over a planar surface are much simpler than those produced in anisotropic solids in which significant transverse particle motion may occur. Such behavior in linearly elastic anisotropic solids has been investigated previously, and in the present work the analysis has been extended to include elastic‐plastic behavior. A general mathematical description of both elastically and plastically anisotropic materials is presented, and then several specific applications are considered in detail. For the case of an elastically isotropic solid that is plastically anisotropic with a single slip plane and direction, it is found that for certain orientations two plastic waves can be propagated, one of which is quasilongitudinal and the other is quasitransverse. For more general orientations there may be two quasitransverse waves and a single quasilongitudinal disturbance. These results approximate the behavior of a single‐crystal material of hexagonal symmetry, such as beryllium, for which effects of elastic anisotropy are small and slip occurs predominantly on the basal plane. Since there is a single spatial coordinate involved in planar wave propagation, the general equations describing elastic‐plastic wave propagation can be written in one‐dimensional finite‐difference form and solved numerically for arbitrary crystal structure and orientation. A number of specific examples are considered and compared with analytical solutions.

Propagation Mode and Scattering Loss of a Two-Dimensional Dielectric Waveguide with Gradual Distribution of Refractive Index

Abstract: An analytical discussion of the mode property and the scattering loss of a two-dimensional dielectric waveguide with gradual refractive-index distribution in the transverse direction is presented. To describe scattering loss, a transverse correlation as well as an axial correlation of the irregular variation of the refractive index have been used. The field distribution, the group delay, and the maximum film thickness of a single-mode waveguide scarcely depends on the shape of the distribution. The maximum value of the film thickness in the single-mode transmission region optimizes the scattering loss and the energy confinement. The scattering loss of a waveguide with a gradual index distribution is smaller than that of a three-layer waveguide when the transverse correlation is small, but it is not much altered when the transverse correlation is large.

Wave Surfaces Due to Impact on Anisotropic Plates

Abstract: The stress waves induced in anisotropic plates by transverse, short- duration impact forces are examined in this report The anisotropy is related to the layup angles of the fibers of a fiber composite laminated plate. Using a modification of Mindlin's approximate theory of plates, it is shown that both extensional and bending waves are generated by transverse impact. The magnitudes of the wave velocities in different directions are calculated for graphite fiber-epoxy matrix plates for various layup angles. Finally, the shapes of the wave fronts or wave surfaces due to point impact are also presented for the cases mentioned.

Lawn edging structure

Abstract: A plastic extruded lawn edging comprising a T-section including vertical wall and a wide transverse upper head portion which extends inwardly of the wall toward the flower bed and outwardly toward the grass and provides a shade area to prevent the growth of vegetation. In one embodiment a C-shaped connector interconnects the ends of adjacent sections. Another embodiment utilizes a connector which bridges the wall portion of adjacent sections and is slidably fitted between the head of the T and an angled anchor flange at the bottom of the walls.

The excess noise field of subsonic jets

Abstract: The sound field generated by the interaction of spatial instabilities on the shear layer shed from a duct with the nozzle lip is studied. It is shown that the intensity varies with direction θ from the exhaust and with the subsonic exhaust speed U according to I ∼ U6(1 − cosθ)2 and I ∼ U6 sin2 θ for the axisymmetric and first azimuthal (sinuous) modes respectively. The first of these results is interpreted in terms of monopole and dipole sources at the exit plane, representing the acoustic effect of fluctuating mass flow and axial thrust across the exit plane, and the second in terms of a transverse dipole at the exit plane, corresponding to fluctuations in cross-stream thrust. A correlated thrust fluctuation of 1% is shown to overwhelm the jet mixing noise in the forward arc, θ > 90° while the acoustic efficiency of the interaction process is never less than 10−6 M3 even under the cleanest possible exit conditions. Forward flight of the duct a t Mach number Mα is shown to increase the forward-arc intensity by the factor (1 + Mα cos θ)−4. It is suggested that much of the discrepancy between the noise fields of real engines and the predictions of Lighthill's theory of jet mixing noise – the so-called ‘excess noise’ problem – can be explained in terms of this interaction mechanism.

Quantized Longitudinal and Transverse Shifts Associated with Total Internal Reflection

Abstract: A recent experiment has shown us that the Goos-H\"anchen shift is quantized, the eigen-functions being the transverse electric and magnetic modes. We give here a straightforward theory of this phenomenon, together with the prediction that our new transverse shift is also quantized, with the circularly polarized modes inside the evanescent wave as eigenfunctions. An experimental test of the latter point is being considered.

The Transverse Poisson's Ratio of Composites

Abstract: An expression is developed that makes possible the prediction of Poisson's ratio for unidirectional composites with reference to any pair of orthogonal axes that are normal to the direction of the reinforcing fibers. This prediction appears to be a reasonable one in that it follows the trends of the finite element analysis and the bounding estimates, and has the correct limiting value for zero fiber content. It can only be expected to apply to composites containing stiff, circular, isotropic fibers bonded to a soft matrix material.

Transverse-flux tubular motors

Abstract: The paper describes a new range of tubular induction motors. Compared with the usual forms of tubular motors, in which the magnetic flux lies largely in planes that are parallel to the direction of motion, the new machines have flux paths lying transverse to this direction. Two winding arrangements are described; the first of these uses skewed coils that completely surround the secondary conductor, the second uses a double helical system. The excitation produced by these windings is in the form of a circumferentially modulated axially travelling wave, and an appropriate multilayer analysis using cylindrical geometry is presented. Experimental and theoretical results are given that show that the transverse-flux machine can provide more thrust than the conventional machine when the core-flux density is the limiting design factor.

Lindhard's multiple scattering description justifies axial and planar dechannelling data

Abstract: The dechannelled fraction vs. penetration depths X(z) has been measured for 0.3 to 1.5 MeV protons impinging along the {110} plane of Si and Ge. The experimental results show an exponential trend of X(z) vs. the penetration depth and a very small dependence on the crystal temperature. The theoretical model previously proposed to describe the axial dechannelling in terms of changes in the ion transverse energy has been extended to the planar case. Due to the difference in symmetries between planes and axes, the change of transverse energy gives rise to a diffusion equation. The analytical form of the diffusion coefficient has been obtained taking into account the Lindhard's description of nuclear and electronic reduced multiple scatterings. A comparison between the planar and the axial case brings into light the different role played by nuclear and electronic scatterings in dechannelling.

A theory of flux peaking effect in channeling

Abstract: The redistribution of the channeled ion flux in the transverse plane has been examined. General formulae describing the flux peaking effect are obtained. Main factors on which the effect depends are investigated. An analysis is made of back-scattering experiments. The study has been made for the axial and planar channeling.

Mud flap assembly and bracket therefor

Abstract: A mud flap mounting assembly and a mounting bracket therefor wherein the mounting bracket is formed of a narrow elongated plate of elongated cross-section, one end of the plate being twisted through an angle of approximately 90* with respect to the other end about the longitudinal axis of the plate, and also being bent through an angle of approximately 90* with respect to the other end about an axis transverse to the longitudinal axis of the plate. The mud flap can then be mounted directly to one end of the plate and the other end can be mounted directly to a vehicle or can be removably mounted in a socket on the vehicle for ease of removal of the bracket.

Scattering of a transverse elastic wave by an elastic sphere in a solid medium

Abstract: Cross sections are computed for the scattering of a plane transverse elastic wave by an elastic sphere in an infinite isotropic homogeneous elastic solid. Analytic expressions are derived for the matrix elements indicated by Einspruch, Witterholt, and Truell, and the resulting matrix equations are solved numerically. The dependence of the scattering cross section upon K1a (K1 is the transverse propagation constant, a is the obstacle radius) over the range 0.01–10 is computed for various combinations of host and scatterer materials. The sensitivity of the cross section and its component terms to the elastic properties of the host and scatterer materials, and their behavior in the Rayleigh limit approximation are discussed. The calculations include the case of a constant host with a varying obstacle, and a constant scatterer in a varying host medium. It is found that most of the examples tested can be grouped conveniently into four classes, with a fifth category containing unstable results; this classificat...

A qualitative description of the transverse motion of axial channeled particles in thin crystals

Abstract: The qualitative features of the angular distribution of particles emergent from thin ∼ 1μ, uniform single crystals of silicon and germanium for incidence at small angles to axial directions are discussed in terms of the continuum picture of particle channeling. Blocking of axially channeled particles in the transverse plane is demonstrated. Implications and possibilities arising from observation of non-equilibrium of the transverse momentum vector are discussed. The use of the radial spreading of the angular distribution to investigate the average inter-atomic potential distribution in the plane transverse to the axial direction is explored and perturbations due to multiple scattering in surface films or inside the crystal and to beam divergence are qualitatively considered.

Razor with adjustable blade cartridge

Abstract: The specific disclosure provides a safety razor system comprising a cartridge having at least one single cutting edge blade and a guard member having a transverse blade guard surface, and a holder including means for releasably engaging the cartridge. The system also includes means for movably supporting the guard member of the cartridge, and means mounted on the holder and releasably interlocked with the guard member for selectively adjusting the guard surface with respect to the cutting edge of the blade.

Translational Mobility of Hard Ferromagnetic Bubbles

Abstract: We show that steady translation of a magnetic bubble possessing Bloch lines requires the application of both longitudinal and transverse field gradients. The predicted longitudinal gradient obeys the usual relation valid for a normal bubble. The transverse gradient is proportional to the product of velocity and number of Bloch lines. Experiments of Tabor et al. support the theory.

Thermal breakdown in chalcogenide glasses

Abstract: The time-dependent heat balance equation has been solved numerically for a material having the measured low-field conductivity of amorphous As30Te48Ge10Si12. For a 60 μm thick infinite slab, with boundaries held at ambient temperature and a constant electric field applied parallel to the slab faces, the temperature and current distributions remain relatively uniform until a critical field is exceeded. The current then becomes progressively channelled in the region of the central plane and, for a field of 5.9 × 107 V m−1, it increases by two orders of magnitude within 100 psec as the centre temperature rises from 750 to 1000 K. Time-dependent solutions have also been obtained for a cylindrical block geometry, where heat flow is considered simultaneously both parallel and transverse to the axis. For sufficiently large applied potentials a current channel forms with the hottest point initially at the centre of the block. Hot spots, with associated channel constriction, then grow and move out towards the electrodes.

Actuating cap for an aerosol device

Abstract: This invention relates to a device for dispensing a liquified gas propellant including one or more active ingredients such as is used for insecticides or exterminating purposes. More particularly, the device, which is commonly known as an ''''Aerosol Bomb'''', comprises a container of conventional type having a discharge nozzle which is actuated by pressing or tilting to release the contents of the container as a spray. The container has an annular flange near its upper end to which a cap is releasably connected. The cap has a transversely extending wall between its ends which is longitudinally displaced more from one end of the cap than from the other, so that in one position of the cap on the flange, the transverse wall will be spaced from the nozzle and in the reverse position of the cap, the transverse wall will abut against the nozzle to actuate the latter to release the pressurized contents of the container through an aperture in the transverse wall.

Corrugated film having increased stiffness

Abstract: Corrugated polymeric film can be stiffened in the direction transverse to corrugation lines by creating flattened, i.e., noncorrugated, narrow width lanes in that transverse direction.

The stability of plane Poiseuille flow between flexible walls

Abstract: This paper examines the linear stability of antisymmetric disturbances in incompressible plane Poiseuille flow between identical flexible walls which undergo transverse displacements. Using a variational approach, an approximate solution of the problem is formulated in a form suitable for computational evaluation of the (complex) wave speeds of the system. A feature of this formulation is that the varying boundary conditions (and the Orr-Sommerfeld equation) are satisfied only in the mean; this reduces the labour involved in determining the approximate solution for a variety of wall conditions without increasing the difficulty of obtaining solutions to a given accuracy. In this paper the symmetric stream function distribution across the channel is represented by a series of cosines whose coefficients are determined by the variational solution. Comparisons with previous work, both for the flexible-wall and rigid-wall problems, show that the method gives results as accurate as those obtained previously by other methods while new results, for flexible walls, indicate the presence of a higher wave-number stability boundary which joins the distorted Tollmien-Schlichting stability boundary at lower wave-numbers. In some cases this upper unstable region, which is characterized by large amplification rates, may determine the critical Reynolds number of the system.

Grooved structural element

Abstract: A structural element has elongated, parallel, transverselyspaced grooves which can accommodate the edges of transverselyspaced panels. That structural element coacts with other similar structural elements to constitute a plural-sided frame which has substantially-continuous, elongated, parallel, transverselyspaced, inwardly-directed grooves. A plurality of panels have their upper and lower edges extending into and held by one of those elongated, parallel, transversely-spaced, inwardly-directed grooves to define a structural plane; and a further plurality of panels have their upper and lower edges extending into and held by the other of those elongated, parallel, transversely-spaced, inwardly-directed grooves to define a second structural plane which is spaced transversely from the first structural plane. Connector members of generally H-shaped cross section have grooves which accommodate the side edges of the first plurality and second plurality of panels and which prevent transverse movement of those side edges relative to each other and relative to those structural planes.