Showing papers on "Slab published in 1968"

Finite Strip Method Analysis of Elastic Slabs

Abstract: Rectangular elastic isotropic and orthotropic slabs for a variety of plate loadings and boundary conditions are analyzed by the finite strip method, in which a combination of trigonometric and hyperbolic series satisfying the boundary conditions in the longitudinal direction is used together with a simple polynomial function in the transverse direction. By using variational principles, the stiffness and load matrices of each strip are readily derived. The stiffness and load matrices for the whole slab are then assembled and solved to give the displacements, from which the moments can be calculated. Excellent accuracy has been achieved for various numerical examples using only a relatively small number of discrete computational variables. Beam-slab structures such as bridges should be readily amenable to the application of this method.

Magnetostatic surface waves on a y.i.g. slab

Abstract: Magnetostatic surface waves are identified in microwave-frequency experiments with a single-crystal y.i.g. slab. Slow travelling waves having k numbers that are high in the magnetostatic range are studied in a pulse experiment, and fast waves with k numbers low in the range are observed in a c.w. test.

Phonon Modes of an Ionic Crystal Slab

Abstract: The vibrational problem of a slab‐shape diatomic ionic crystal is studied within the harmonic approximation and neglecting retardation effects. The interest is centered on a proper treatment of the physical boundary conditions existing at the free surfaces of the slab. By taking advantage of the translational symmetry of the slab for lattice translations parallel to the free surfaces, the problem is first reduced to finding the normal modes of a linear model consisting of two parallel diatomic chains coupled together. Using the so‐called planewise summation method developed by deWette and Schacher for computing the Coulomb interaction coefficients, it is shown that the consideration of nearest and n ext‐nearest‐neighbor interactions between the ions of this double‐chain problem is largely sufficient to determine the eigenmodes accurately. This remarkable feature arises from the fact that the Coulomb field created by a plane array of dipoles decreases exponentially with increasing distance from the plane. The double‐chain dynamics is then developed following the general method recently given by Gazis and Wallis. In this paper, we restrict the computation to this class of phonons which propagate perpendicularly to the boundary planes. We found that (i) surface modes of vibrations (with exponentially decreasing amplitude from the surfaces) exist, resulting from the use of physical boundary conditions; (ii) when the slab thickness increases, the “bulk” modes (with a wavelike character) rapidly converge to the solutions obtained with cyclic boundary conditions. It is concluded that, for sufficiently thick ionic slab‐shape crystals (a few tens of layers), the use of periodic boundary conditions does not significantly affect the statistical properties of the crystal (as shown by Ledermann's theorem in the case of short‐range force model) and also accurately provides the true individual eigenfrequencies with the exception, however, of this class of modes involving localized vibrations at the surfaces of the slab.

Transmission of Electromagnetic Waves through a Conducting Slab. II. The Peak at Cyclotron Resonance

Abstract: This is the second in a series of three papers concerned with the propagation of electromagnetic waves through a metallic slab of finite thickness. In the situation studied here, the relation between the current in the slab and the electric field which drives it is highly nonlocal because of the finite electron mean free path. We calculate the transmission amplitude under these conditions, assuming that there is a steady magnetic field normal to the faces, and assuming also that electrons within the slab scatter diffusely at the surfaces. A transmission peak is predicted at cyclotron resonance which, in the limit of slab width much larger than an electron mean free path, has a line shape which approaches the square root of a Lorentzian and a phase which shifts by $\ensuremath{\pi}$ across the line. All of this is superposed on the Gantmakher-Kaner oscillations which are also present. This resonant behavior, which is absent when the electrons are assumed to be scattered specularly from the surface of the slab, can be understood in terms of electron transport from Fresnel zones on the Fermi sphere which expand at resonance so that the first zone covers the entire hemisphere. The absence of this resonance when the electrons are scattered specularly is tentatively ascribed to a fortuitous cancellation which arises because the equatorial electrons, whose response gives rise to currents which shield the interior of the metal, themselves undergo a resonance which excludes the field from the metal. In carrying out these calculations using the two-sided Wiener-Hopf technique for the nonlocal wave equation, we found that the technique itself can be simplified considerably if the quantity of interest is the transmission amplitude (the field at the emergent face of the slab) rather than the full-field amplitude in the slab. We show that this simplification arises when certain short-range parts of the field are eliminated.

Aluminum reduction cell and system for energy conservation therein

Abstract: A compact electrolytic potcell for the reduction of aluminum in fluoride fusions including a multiplicity of spaced and sized electrical conductors extending from the reduced aluminum pad underlying the fluoride fusion, through the refractory potlining, and to an aluminum slab heat-sink on the potshell, the conductors being molten where in contact with the pad and solid where in contact with the aluminum slab and the temperature and voltage difference of the slab relative to the pad being adjusted to as low as feasible with cell operation to conserve energy for reduction.

Transmission of Electromagnetic Waves through a Conducting Slab. I. The Two‐Sided Wiener‐Hopf Solution

Abstract: This is the first of a series of papers dealing with propagation of electromagnetic waves through a metallic slab of finite thickness. In this first paper, we present a method for solving the integrodifferential equation governing the electric field in the interior of the metal when the electrons in the interior of the metal suffer diffuse reflection at each surface. The method is potentially of use in a wide class of problems, namely, the finite‐slab generalization of all those semi‐infinite‐medium problems which are conventionally studied by the Wiener‐Hopf technique. The solution given here is an iterative one with successive terms converging as e−L/l, where L is the thickness of the slab and l is the range of the kernel of the integral term in the equation.

Diffusion Length and Criticality Problems in Two‐ and Three‐Dimensional, One‐Speed Neutron Transport Theory. I. Rectangular Coordinates

Abstract: Several problems in linear transport theory have been solved involving more than one dimension. We have considered the diffusion‐length problem in a slab system and have studied how the flux in the transverse direction varies as a function of distance from the source. The solution is found to consist of an asymptotic term, composed of a finite number of harmonics, plus a transient which is nonseparable in the x and z coordinates. When the slab is sufficiently thin only the transient term survives and the concept of a diffusion length loses its value. A method for overcoming this difficulty is presented. In another problem, the thickness of the slab is allowed to become semi‐infinite and the effect of decay in the z direction on the emergent angular distribution and surface flux are assessed. By approximating the flux in the y and z directions by a function of the form exp {iByy + iBzz} and solving the resulting one‐dimensional problem in the x direction exactly, it has been possible to obtain a statement of the critical conditions in a bare rectangular parallelepiped system. The application of this method to the diffusion length problem in a system with a rectangular cross section is discussed. Finally, by comparison with the exact solution for the slab, we estimate the accuracy of a reduced Boltzmann equation deduced by the author in a previous publication.

Incoherent backscatter study of electron content and equivalent slab thickness

Abstract: Electron content and equivalent slab thickness from radar backscatter measurements, noting F layer peak height and electron and ion temperatures diurnal variation

Expansion joint for concrete slabs

Abstract: Two concrete slabs separated by a gap are interconnected by an expansion joint formed by a pair of metal profiles which have horizontal flanges flush with the upper slab surfaces and vertical webs projecting upwardly therefrom to the top of a traction layer supported by the slabs; the profiles have confronting projections extending into the gap and supporting a gable-shaped sealing strip of elastomeric material clamped onto these projections.

Concrete slab joint construction

Abstract: A CONSTRUCTION FOR JOINTS BETWEEN CONCRETE SLABS THAT ALLOWS THE ADJACENT SLABS TO SHRINK WITHOUT CRACKING THE SLABS OR DESTROYING WALL STRUCTURES OR OTHER DEVICES THAT MIGHT BE RIGIDLY MOUNTED TO SUCH SLABS. THE JOINT IS SO DESIGNED THAT IT IS REINFORCED AND SELF-SUPPORTING AND ALLOWS OTHER CONSTRUCTION WORK TO CONTINUE WHILE THE NORMAL SHRINKAGE IS TAKING PLACE.

Longitudinal Waves Excited in an Inhomogeneous Magnetized Plasma Slab

Abstract: Excitation of short wavelength longitudinal oscillations in a plasma slab is considered for frequencies near the second harmonic of the electron cyclotron frequency For the uniform plasma slab a long and short wavelength plasma oscillation coupled at the boundary and the relative amplitudes are governed by the boundary conditions In the nonuniform plasma slab these two fields are continuously coupled within the slab as well as at the boundaries When the boundaries are removed, these fields are coupled by the density gradient and the rapidly varying field is of amplitude λ2/L2 less than the long wavelength field where λ is the wavelength and L is the scale size The slab plasma exhibits a series of resonances and antiresonances as a function of field B when B> mω/2e and shows an antiresonance for an excitation frequency slightly greater than the second harmonic An experiment verified this predicted antiresonance

Improvements in or relating to concrete structure

Abstract: The manufacture of a channel-shaped ferroconcrete unit in which a ferroconcrete bottom slab and two ferroconcrete side slabs having pretensioned tendons or passageways passing from the bottom slab to the remote edge of each side slab are arranged in channel formation with the tendons being stressed whereby suitable stress loads in the tendons are realized within the bottom slab and side slabs. The pretensioned tendons pass around radiused bends at each junction between the bottom slab and one of the side slabs.

Model for heat transfer in frost and snow

Abstract: A capillary tube model of frost and snow is used as a basis for developing equations for the temperature distribution in (1) a slab of unventilated material and (2) a slab of ventilated material. The only quantities that need to be known are the properties of ice and air and some knowledge of the density of the material. Using elementary methods of analysis, the model yields approximate results that are useful in clarifying the transfer processes for their important influences. The effects of water vapor diffusion and density stratifications are clearly demonstrated with the model.

Construction element with helically wound anchor lattice

Abstract: A construction element configuration for use in making construction elements for roads or panels for structures and the like and a new joint or anchor therefor. The element comprises a slab or sheet of material, which generally is resilient, having a helical wound lattice partially embedded therein for anchoring the slab or sheet to another material. The anchor means comprises a plurality of metallic wire or rod elements each having a springlike configuration consisting of helically wound turns or coils. The helical convolutions of each element are coaxial about a respective longitudinal axis and the axes of the elements are generally parallel and corresponding coils of next adjacent anchor elements are interlaced so that the elements jointly define a lattice arrangement that can be embedded in another material to anchor the slab or element thereto. The anchoring lattice strengthens the slab and provides excellent distribution of stresses to which the arrangement may be subjected when anchored.

Method for forming a thick thermoplastic slab

Abstract: A METHOD FOR FORMING A THICK THERMOPLASTIC SLAB IS PROVIDED WHEREIN THE SLAB IS EXTRUDED AT A PREDERTIMED SPEED OF AT LEAST 6" PER MINUTE AND THE SLAB EXTRUDATE TEMPERATURE, WHEN DISCHARGED FROM THE EXTRUSION DIE, IS AT LEAST APPROXIMATELY 300*F. THE SLAB EXTRUDATE, UPON BEING DISCHARGED, IS SUPPORTED IN A SUBSTANTIALLY HORIZONTAL PLANE AND, WHILE SO SUPPORTED, IS CONVEYED AWAY FROM THE EXTRUSION DIE AT APPROXUMATELY THE SAME SPEED AS THE SPEED OF DISCHARGE OF THE EXTRUDATE FROM THE DIE.

Slab transfer apparatus

Abstract: There is disclosed herein a plurality of aligned induction heaters which are open at both the top and bottom, lift means for partially ejecting a heated slab from each heater and receiving a cold slab, crane and hoist means for picking up a slab at any heater and transferring it to an outgoing conveyor, and crane and hoist means for picking up a cold slab from an incoming conveyor and delivering the same to a heater

Semiconductor header assembly and method of fabrication thereof

Abstract: 1,215,535. Headers for semi-conductor devices. PHILIPS ELECTRONIC & ASSOCIATED INDUSTRIES Ltd. 20 Feb., 1968 [23 Feb., 1967], No. 8255/68. Heading H1K. A header for a semi-conductor device such as a transistor 12 comprises a thermally conductive plate 2 carrying the device 12 and mounted on a slab 1 of a readily weldable material. The slab 1 has upstanding tubular projections 7, e.g. punched through it, which projections are located in corresponding apertures in the plate 2 and which serve as lead-through apertures for terminal leads 5. The plate 2 may be of Cu, hard-soldered with Ni or a Cu/Ag eutectic alloy to the N-plated soft steel slab 1. The slab 1 may also be of a Fe/Ni/Co alloy. The terminal leads 5 may be of Fe/Ni or Fe/Ni/CO alloy, set in glass beads 6. The melting of the beads 6 to seal the lead-through apertures and the soldering of the plate 2 to the slab 1 may take place simultaneously in a furnace having a slightly reducing atmosphere; e.g. N 2 containing a little H2. Finally a cover 15 is welded to the slab 1 as shown.

Prestress loss and creep camber in a highway bridge with reinforced concrete slab on pretensioned prestressed concrete beams

Abstract: A NUMERICAL PROCEDURE USING A STEP-BY-STEP METHOD IS USED FOR COMPUTING BOTH ELASTIC AND TIME DEPENDENT STRAINS, DEFLECTIONS, AND PRESTRESS LOSSES IN FULL SIZE PRETENSIONED PRESTRESSED CONCRETE HIGHWAY BRIDGE BEAMS. BOTH LIGHTWEIGHT AND NORMAL WEIGHT STRUCTURAL CONCRETES ARE USED. THE METHOD USES CREEP AND SHRINKAGE FUNCTIONS, DERIVED FROM CONTROL SPECIMENS, FOR MAKING PREDICTIONS. THE COMPUTED STRAINS, DEFLECTIONS, AND PRESTRESS LOSSES AGREED WELL, FOR THE MOST PART, WITH MEASURED VALUES DURING THE TIME INTERVAL FROM DATE OF CASTING OF THE SLABS TO END OF TESTS. THE BEAMS WERE ABOUT 320 DAYS OLD WHEN THE SLAB WAS CAST, AND TESTS TERMINATED AT 660 DAY BEAM AGE. MEASURED ELASTIC BEAM DEFLECTIONS UNDER THE WEIGHT OF THE PLASTIC SLAB WERE A LITTLE OVER 50% OF THE DEFLECTIONS COMPUTED BY THEORY. PRESTRESS LOSSES WERE ABOUT 15% IN 40 FT. LONG LIGHTWEIGHT CONCRETE BEAMS AT 660 DAYS. THE 56 FT. LW BEAMS LOSS AT THE SAME AGE WAS ABOUT 21% AND THE NW BEAM 14-1/2%. THE CHANGES IN CAMBER AND PRESTRESS LOSSES AFTER THE SLAB WAS CAST WERE MINOR. /BPR/

Monolithic concrete slab construction

Abstract: A SLAB CONSTRUCTION FOR USE IN MULTISTORY BUILDINGS WHICH INCLUDES A PAIR OF SPACED SLABS BEING INTEGRALLY JOINED BY A PLURALITY OF VERTICALLY SPACED CYLINDRICAL MEMBERS. AN OMNI-DIRECTIONAL VOID IS PROVIDED BETWEEN THE SLAB MEMBERS FOR ACCOMMODATING ELECTRICAL WIRING, AIR CONDITIONING, PASSAGEWAYS, ETC. THE ENTIRE SLAB CONSTRUCTION IS POURED MONOLITHICALLY IN CONCRETE, SO AS TO INCREASE THE SHEAR STRENGTH OF THE CYLINDRICAL CONNECTORS.

Illuminated display apparatus

Abstract: 1,130,601. Display signs. CALORIFIC APPLIANCES Ltd. 19 Oct., 1965 [30 April, 1965], No. 18392/65. Heading G5C. An edge-illuminated display comprises a lightreflecting faceted surface 1 illuminated in predetermined variable manner, to give, e.g., an effect of animation, by a source of light 6 at the thick edge or edges 5 of a generally wedgeshaped transparent slab 2. The source 6 may comprise sequentially illuminated lamps, or continuously lit lamps may be rotated around a slab with a circular periphery and a rear face shaped as a cone of large apical angle (Fig. 5). Alternatively continuously lit lamps or fluorescent tubing may be placed around the slab periphery, or selected edges, and an endless band with alternate opaque and transparent portions be rotated about the slab (Fig. 4) or the light source. Figs. 6, 7 (not shown), show a continuously lit source 6 extending axially through a cylindrical hole in the thick edge 5 and surrounded by a rotatable helical band of opaque material. The slab may be a block of acrylic plastics, or comprise a liquid-filled shell. Its rear face may be concave and its front face may be coated with a transparent substance having a different critical angle from that of the slab to reduce light loss. The thick edge 5 may have a concave, convex, and/or straight bevel along its length to obtain a more uniform illumination (Figs. 10, 15-21, not shown). The reflecting surface may be divided into two or more areas spaced apart by transparent sheets (Fig. 15, not shown), or a plurality of individual slabs may be arranged one behind the other (Fig. 12) with the reflecting surface divided into areas one behind each slab.