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Showing papers on "Beam (structure) published in 1978"


Journal ArticleDOI
TL;DR: In this article, the classical theory of scattering under the Coulomb potential of both charged and neutral particles is used to derive formulae for the energy deposition rate and mean scattering of a beam of charged particles interacting with a cold hydrogen target of arbitrary ionization level as a function of the column density traversed by the beam.
Abstract: The classical theory of scattering under the Coulomb potential of both charged and neutral particles is used to derive formulae for the energy deposition rate and mean scattering of a beam of charged particles interacting with a cold hydrogen target of arbitrary ionization level as a function of the column density traversed by the beam. These general results hold for any form of stable injection energy spectrum, and their relevance to the existing literature on chromospheric heating during solar flares is discussed.

311 citations


Journal ArticleDOI
TL;DR: A pulsed gas valve is described which produces very intense supersonic molecular beam pulses of about 10 micros duration for light gases such as H2 and He, and of somewhat longer duration for heavier gases.
Abstract: We describe a pulsed gas valve which we have developed for use as a molecular beam source. In order to observe the performance of the pulsed beam source, we also have developed an ionization detector with a rise time of about 1 μs. The pulsed valve produces very intense supersonic molecular beam pulses of about 10 μs duration for light gases such as H2 and He, and of somewhat longer duration for heavier gases. As a new tool for the study of molecular collisions, the pulsed beam technique offers substantial advantages over the conventional continuous‐beam method for experiments which are limited by the signal‐to background ratio for scattered products.

256 citations


Book
01 Jan 1978
TL;DR: Theories of stress and strain have been studied in this article, where linear stress-strain-temperature relations have been used to describe the behavior of various materials. But they do not consider the effects of bending of straight beams.
Abstract: Introduction. Theories of Stress and Strain. Linear Stress-Strain-Temperature Relations. Inelastic Material Behavior. Applications of Energy Methods. Torsion. Bending of Straight Beams. Shear Center for Thin-Wall Beam Cross Sections. Curved Beams. Beams of Elastic Foundations. The Thick-Wall Cylinder. Elastic and Inelastic Stability of Columns. Flat Plates. Stress Concentrations. Fracture Mechanics. Fatigue: Progressive Fracture. Contact Stresses. Creep: Time-Dependent Deformation. Appendix A: Average Mechanical Properties of Selected Materials. Appendix B: Second Moment (Moment of Inertia) of a Plane Area. Appendix C: Properties of Steel Cross Sections. Author Index. Subject Index.

231 citations


Journal ArticleDOI
TL;DR: In this article, a relativistic beam of electrons passing through a spatially periodic right-hand circularly polarized magnetic field was considered and the amplification was found to be due to a ponderomotive bunching of the electrons.
Abstract: Stimulated emission from a relativistic beam of electrons passing through a spatially periodic right-hand circularly polarized magnetic field is considered. The amplification is found to be due to a ponderomotive bunching of the electrons. The effect is completely classical and for an infinite interaction distance a dispersion relation, which takes into account space-charge effects, describing the scattered field is derived. Conditions on the pump field amplitude, beam density, and momentum spread of the beam for emission from individual electrons to occur or for emission from plasma oscillations to occur are examined. Also, emission from individual electrons over a finite interaction distance is considered and gain is determined for distances less than an $e$-folding length.

226 citations



Journal ArticleDOI
TL;DR: The holographic plate corresponds to an infinite set of gated viewing systems triggered by the traversing reference beam, and scanning along the processed plate produces a continuous-motion picture of the light in flight.
Abstract: A flat object surface and a hologram plate are both illuminated at an oblique angle by laser light of short pulse duration or short coherence length Only those parts of the object surface are holographically recorded that correspond to a small-pathlength difference between object beam and reference beam The holographic plate therefore corresponds to an infinite set of gated viewing systems triggered by the traversing reference beam Scanning along the processed plate produces a continuous-motion picture of the light in flight This new technique probably represents the ultimate in high-speed photographic recording, as no mechanical or electrical inertia is involved

206 citations


Journal ArticleDOI
TL;DR: In this article, a theory of the cyclotron maser interaction between an annular electron beam and the standing electromagnetic wave in a cavity structure is formulated on the basis of the relativistic Vlasov equation and the Maxwell equations.
Abstract: A theory of the cyclotron maser interaction between an annular electron beam and the standing electromagnetic wave in a cavity structure is formulated on the basis of the relativistic Vlasov equation and the Maxwell equations. Detailed analytical expressions for the beam‐wave coupling coefficient, beam energy gain, and threshold beam power have been derived for the fundamental and higher cyclotron harmonics. Physical interpretations of these results and comparison with cyclotron maser interactions in a waveguide structure are presented. Methods of parameter optimization and their applications to experiments are illustrated through numerical examples.

162 citations


Journal ArticleDOI
TL;DR: The diagonal compression field theory for symmetrically reinforced concrete beams, which assumes that after cracking the concrete can resist no tension and that the shear will be carried by a field of diagonal compression, is presented in this paper.
Abstract: The diagonal compression field theory for symmetrically reinforced concrete beams monotonically loaded in shear at sections where flexure is unimportant, is presented. This theory assumes that after cracking the concrete can resist no tension and that the shear will be carried by a field of diagonal compression. As well as considering the equilibrium conditions that relate the average stresses in a beam to the applied loads the theory considers the compatibility conditions that exist between the average strains in the various directions. Expressions are given which enable the shear deformations (and thus the effective shear modulus) of diagonally cracked reinforced and prestressed beams to be calculated. Based on a suggested failure criterion for diagonally cracked concrete, equations for the shear capacity of reinforced and prestressed beams are derived. A design chart based on these equations is given.

154 citations


Book
01 Jan 1978
TL;DR: This chapter discusses the analysis of statistically indeterminate structures using the force method - column analogy and the displacement method, and some plane areas commonly used in the method of column analogy.
Abstract: Introduction to the analysis of statistically indeterminate structures force method of analysis displacement method of analysis use of force and displacement methods strain energy and virtual work method of virtual work and its application to trusses further applications of method of virtual work important energy theorems - Betti's and Maxwell's theorems, application of Betti's theorem to transformation of forces and displacements, Engesser's theorem of compatability, Castigliano's theorem of compatability, Catigliano's theorems displacement of elastic structures by special methods application of the force method - column analogy application of the displacement method - slope deflection and moment distribution moment distribution with sway - multistorey and multibay frames influence lines for beams, frames and grids - Muller-Breslau's principle influence lines for arches, trusses and prestressed concrete members effects of axial forces analysis of shear-wall structures method of finite differences analysis of plates by finite differences finite-element method further development of finite-element method plastic analysis of continuous beams and frames yield-line and strip methods for slabs structural dynamics computer analysis of framed structures implementation of computer analysis. Appendices: matrix algebra, displacements of prismatic members, fixed-end forces of prismatic members, end-forces caused by end-displacements of prismatic members, reactions and bending moments of supports of continuous beams due to unit displacement of supports, properties of geometrical figures, torsional constants, values of the integral, deflections of a simple beam of constant EI subjected to unit end-moments, geometrical properties of some plane areas commonly used in the method of column analogy, forces due to prestressing.

145 citations


Journal ArticleDOI
TL;DR: In this article, the authors determined the lead-lag natural frequencies and mode shapes of a radial beam mounted on a rotating disc at a 90° setting angle by means of the finite element technique, a high precision beam element based on a fifth degree polynomial being used as displacement function, with deflection and slope at the ends as common nodal degrees of freedom.

142 citations


Journal ArticleDOI
TL;DR: In this paper, the authors examined the resistive hose instability of a self-pinched relativistic beam with emphasis placed on the important case of the Bennett current profile JB(r) ∝ (1+r2/a2)−2.
Abstract: The resistive hose instability of a self‐pinched relativistic beam is examined with emphasis placed on the important case of the Bennett current profile JB(r) ∝ (1+r2/a2)−2. Previously known results applicable to a general profile are recovered and extended in several directions. An essential new feature in this study is the use of distributed particle mass to model orbital phase‐mixing effects produced by the anharmonic pinch field. Resonant growth is considerably reduced, and the instability when viewed in the beam reference frame is shown to be convective rather than absolute. The peak amplitude of a disturbance wave packet moves from the point of its inception in the beam pulse toward the pulse tail. The disturbance subsequently damps if the pulse length is finite; thus, propagation over distances that are long compared with the particle betatron wavelength is possible. The predicted growth rate and group velocity of the mode are shown to be in fair agreement with the results of numerical simulation.

Journal ArticleDOI
TL;DR: In this paper, a technique is developed to give the optimal dynamic vibration absorber parameters for the elimination of excessive vibration in sinusoidally forced Bernoulli-Euler beams.

Journal ArticleDOI
TL;DR: In this article, a graphical algorithm is developed for predicting the power flux spectra of whistler and upper hybrid noise for a wide range of ionospheric and beam parameters, which is in good agreement with observations of VLF hiss.
Abstract: Refraction of electrostatic noise in the whistler and upper hybrid modes out of the spatially limited amplification region of the auroral electron beam limits the amplitude of the noise produced. Power flux spectra are calculated by using the linear electrostatic growth rate and allowing for ray refraction in the direction perpendicular to the auroral arc. A graphical algorithm is developed for predicting the power flux spectra of whistler and upper hybrid noise for a wide range of ionospheric and beam parameters. Predicted power flux spectral shapes and intensities for the whistler mode are in good agreement with observations of VLF hiss. The power flux in the upper hybrid mode can exceed the whistler mode power flux in the region of the ionosphere where the electron plasma frequency is larger than the electron cyclotron frequency. A distinction based on the beam intensity is made between quiet and intense arcs. Quasi-linear and nonlinear processes are not important in quiet arcs but may produce observable effects in intense arcs. In particular, intense electrostatic noise near the plasma frequency may produce deep density cavities that radiate electromagnetic kilometric radiation.

Journal ArticleDOI
TL;DR: The effects of the skull in degrading the properties of the ultrasonic pulse would be lessened if the amplitude of the first cycle of the pulse and the directionality of its energy could be used for imaging.
Abstract: Many investigators have stated that the difficulties of imaging with acoustical energy through the skull result from the marked attenuation of the energy by the skull. In the literature measurements of total attenuation have been confused with those for absorption. Measurements made by us show that absorption by compact bone varies between 2–3 dB cm −1 MHz −1 and, in the low megaHertz region appears to be directly proportional to frequency. It has also between shown that the convoluted inner surface of the ivory bone of the inner table of the skull may degrade the collimation and directionality of the beam by refraction. Cancellous bone, such as is present in the dipole of the skull, greatly attenuates the energy. It is postulated that this largely results from scattering. It is also postulated that the energy propagates through cancellous bone as two components, one in the soft tissues and the other partly in the bony spicules. Observations suggest that attenuation due to scattering much more markedly affects the latter of these components and scatters more greatly the higher frequencies in a pulse of broad bandwidth. The energy in each component has varying propagation paths so that the later cycles in the pulse of each component are subject to increasing interference as a result of the variations in propagation times. The two components moreover may have different propagation times so that interference may occur between the pulses of each component as well. All of these phenomena degrade the collimation, coherence, directionality, beam width, pulse length, frequency and other properties of the ultrasonic energy upon which imaging through the skull depends. The interference effects described above are least for the first cycle in the pulse which usually is not the cycle of highest amplitude. Since, in the free field, most of the energy is concentrated around the beam axis, most of the energy in the field which is deflected from its normal propagation path is deflected away from the beam axis. Thus the directionality of the beam is least degraded in the beam axis. The effects of the skull in degrading the properties of the ultrasonic pulse would therefore be lessened if the amplitude of the first cycle of the pulse and the directionality of its energy could be used for imaging.

Journal ArticleDOI
TL;DR: Quantitative measurements on the correction of severely aberrated laser beams using stimulated Brillouin scattering (SBS) at 0.69 microm are obtained and it is shown that under certain conditions SBS can be used to restore an aberrated optical beam to its original unaberrated condition.
Abstract: We have obtained quantitative measurements on the correction of severely aberrated laser beams using stimulated Brillouin scattering (SBS) at 0.69 μm. We have shown that under certain conditions SBS can be used to restore an aberrated optical beam to its original unaberrated condition. When an optical beam double passes an aberrating region after reflecting from an “ordinary” mirror (i.e., a plane mirror) the aberration is twice that obtained from a single pass. However, when the aberrated beam enters a medium that allows SBS to occur, it emerges from its second pass through the aberrating medium in the same condition as that in which it originally entered. Quantitative experiments are described in which a single-mode ruby laser beam is intentionally aberrated by passing it through an etched plate. When the beam is allowed to double-pass the plate using an ordinary reflector (i.e., plane mirror), the beam divergence is more than 10 times the diffraction-limited divergence. However, when we replace the ordinary reflector with a cell in which SBS can take place, the SBS reflected beam is restored to diffraction-limited divergence when it is allowed to pass back through the aberrating medium. Applications of this time-reversal or phase-reversal technique for correcting aberrations in optical trains and atmospheric turbulence are discussed.

Journal ArticleDOI
TL;DR: In this article, the directionality of beams produced by gaussian Schell-model planar sources is investigated by calculating the root-mean-square beam radius as a function of the distance propagated.

Journal ArticleDOI
TL;DR: In this article, the stiffness and mass matrices of a twisted beam element with linearly varying breadth and depth are derived, where the angle of twist is assumed to vary linearly along the length of the beam.

Journal ArticleDOI
TL;DR: In this paper, a column of enhanced density plasma, exceeding the density expected from ionization by primary beam electrons, was observed in a large vacuum system at low magnetic fields (1 to 1.5 G) and low ambient pressures (10 to minus 6 to 10 to the minus 5 torr).
Abstract: The paper describes electron beam injection experiments which clarify observational results obtained in rocket flights. A column of enhanced density plasma, exceeding the density expected from ionization by primary beam electrons, was observed in a large vacuum system at low magnetic fields (1 to 1.5 G) and low ambient pressures (10 to the minus 6 to 10 to the minus 5 torr). The peak luminosity of the discharge was about 10 times that of the beam alone, and the radius increased by a factor of three. In the absence of the discharge, RF emission is observed at 1.1 to 1.2 times the cyclotron frequency, and a strong band of RF noise with upper frequency cutoff at about the cyclotron frequency is observed in the discharge mode, along with higher frequency noise at or near the plasma frequency. The onset of the plasma discharge is critically dependent on beam current. The described results agree with observations obtained at much higher densities and magnetic fields in fusion research studies.

Patent
07 Dec 1978
TL;DR: In this article, a beam of light is split and introduced into different ends of a light path whose rotation is to be sensed, and at least one frequency shifter is placed in the light path to affect the frequency difference of the two beams so as to introduce or adjust a non-reciprocal phase shift.
Abstract: A beam of light is split and introduced into different ends of a light path whose rotation is to be sensed. At least one frequency shifter is placed in the light path to affect the frequency difference of the two beams so as to introduce or adjust a nonreciprocal phase shift. The beams are then mixed back together and the resultant beam is detected and analyzed by suitable circuitry to provide an output indicative of rotation of the light path.

PatentDOI
TL;DR: An acoustic lens having nonuniform cross sectional thickness is disposed in the path of an ultrasonic energy search beam traveling from a transducer probe to an object to be examined as discussed by the authors.
Abstract: An acoustic lens having nonuniform cross sectional thickness is disposed in the path of an ultrasonic energy search beam traveling from a transducer probe to an object to be examined. In an alternative embodiment the lens has at least one contoured surface. As the lens undergoes motion in a plane substantially normal to the direction of the search beam, the search beam exhibits a varying focal zone depth and beam path for providing real time ultrasonic scanning of the examined object.

Journal ArticleDOI
A. Hofmann1
TL;DR: In this paper, the spectrum of a weak undulator field is calculated by going into a moving frame and the spectrum consists of one line with its width depending on the solid angle of the accepted radiation.

Journal ArticleDOI
TL;DR: In this article, the results of detailed numerical calculations are presented for small scale beam breakup due to nonlinear self-focusing in Cyclops, a high power Nd-glass laser amplifier.
Abstract: Experimental data and the results of detailed numerical calculations are presented for small scale beam breakup due to non-linear self-focusing in Cyclops, a high power Nd-glass laser amplifier. Both perturbed plane wave and nonlinear whole beam calculations were carried out. The whole beam calculations were carried out using a dust particle model of beam perturbations.

Patent
20 Nov 1978
TL;DR: A light, portable laser beam level instrument has an optical path which includes a solid state light source; a pendulous, positive lens; a rotatable pentaprism or mirror equivalent; and a glass plate which is tilted to provide fine tuning as discussed by the authors.
Abstract: A lightweight, portable laser beam level instrument has an optical path which includes a solid state light source; a pendulous, positive lens; a rotatable pentaprism or mirror equivalent; and a glass plate which is tilted to provide fine tuning. The level instrument also includes a damping mechanism, a waterproof enclosure and a clip-in battery pack. The solid state light source is a diode in a specific embodiment and produces an intense beam of rapidly diverging infrared laser light. The postiive lens is suspended below the diode at approximately the focal length of the lens from the diode to collimate the light. The pendulous suspension lens maintains the beam in a truly vertical position with respect to the earth to provide self-leveling in a limited range of movement of the instrument. The pentaprism or equivalent converts this vertical beam to a horizontal beam. The glass plate is positioned between the diode and the lens and can be tilted in two orthogonal degrees of adjustment to provide a fine tuning for optical centering of the diode and the lens. Oscillation of the pendulous lens is damped by magnetic or air damping.

Journal ArticleDOI
TL;DR: Lawson as discussed by the authors presents a general discussion of effects, such as beam focusing, self-fields, collisions, and interaction with finitely conducting walls, which are important to most beam devices.
Abstract: J D Lawson London: Clarendon/Oxford University Press 1977 pp xxi + 462 price £16.50 The practical applications of charged particle beams become increasingly wide and varied. This book presents a general discussion of effects, such as beam focusing, self–fields, collisions, and interaction with finitely conducting walls, which are important to most beam devices.

01 Jan 1978
TL;DR: In this paper, the second-degree nonlinear equations of motion for the coupled flapwise bending, lagwise bending and axial extension of an untwisted, torsionally rigid, nonuniform, rotating beam having an arbitrary angle of precone with the plane perpendicular to the axis of rotation are derived using Hamilton's principle.
Abstract: In an attempt both to unify and extend the analytical basis of several aspects of the dynamic behavior of flexible rotating beams, the second-degree nonlinear equations of motion for the coupled flapwise bending, lagwise bending, and axial extension of an untwisted, torsionally rigid, nonuniform, rotating beam having an arbitrary angle of precone with the plane perpendicular to the axis of rotation are derived using Hamilton's principle. The derivation of the equations is based on the geometric nonlinear theory of elasticity and the resulting equations are consistent with the assumption that the strains are negligible compared to unity. No restrictions are imposed on the relative displacements or angular rotations of the cross sections of the beam other than those implied by the assumption of small strains. Illustrative numerical results, obtained by using an integrating matrix as the basis for the method of solution, are presented both for the purpose of validating the present method of solution and indicating the range of applicability of the equations of motion and the method of solution.

Book
01 Jan 1978
TL;DR: In this paper, the authors proposed the Torsional Shear Stress Formula, which is a special case of the Tensor Shear Deformation Formula (TSDE) model.
Abstract: Preface 1 Basic Concepts in Strength of Materials The Big Picture 1-1 Objective of This Book - To Ensure Safety 1-2 Objectives of This Chapter 1-3 Problem-solving Procedure 1-4 Basic Unit Systems 1-5 Relationship Among Mass, Force, and Weight 1-6 The Concept of Stress 1-7 Direct Normal Stress 1-8 Stress Elements for Direct Normal Stresses 1-9 The Concept of Strain 1-10 Direct Shear Stress 1-11 Stress Element for Shear Stresses 1-12 Preferred Sizes and Standard Shapes 1-13 Experimental and Computational Stress 2 Design Properties of Materials The Big Picture 2-1 Objectives of This Chapter 2-2 Design Properties of Materials 2-3 Steel 2-4 Cast Iron 2-5 Aluminum 2-6 Copper, Brass, and Bronze 2-7 Zinc, Magnesium, Titanium, and Nickel-Based Alloys 2-8 Nonmetals in Engineering Design 2-9 Wood 2-10 Concrete 2-11 Plastics 2-12 Composites 2-13 Materials Selection 3 Direct Stress, Deformation, and Design The Big Picture and Activity 3-1 Objectives of this Chapter 3-2 Design of Members under Direct Tension or Compression 3-3 Design Normal Stresses 3-4 Design Factor 3-5 Design Approaches and Guidelines for Design Factors 3-6 Methods of Computing Design Stress 3-7 Elastic Deformation in Tension and Compression Members 3-8 Deformation Due to Temperature Changes 3-9 Thermal Stress 3-10 Members Made of More Than One Material 3-11 Stress Concentration Factors for Direct Axial Stresses 3-12 Bearing Stress 3-13 Design Bearing Stress 3-14 Design Shear Stress 4 Torsional Shear Stress and Torsional Deformation The Big Picture 4-1 Objectives of This Chapter 4-2 Torque, Power, and Rotational Speed 4-3 Torsional Shear Stress in Members with Circular Cross Sections 4-4 Development of the Torsional Shear Stress Formula 4-5 Polar Moment of Inertia for Solid Circular Bars 4-6 Torsional Shear Stress and Polar Moment of Inertia for Hollow Circular Bars 4-7 Design of Circular Members under Torsion 4-8 Comparison of Solid and Hollow Circular Members 4-9 Stress Concentrations in Torsionally Loaded Members 4-10 Twisting - Elastic Torsional Deformation 4-11 Torsion in Noncircular Sections 5 Shearing Forces and Bending Moments in Beams The Big Picture 5-1 Objectives of this Chapter 5-2 Beam Loading, Supports, and Types of Beams 5-3 Reactions at Supports 5-4 Shearing Forces and Bending Moments for Concentrated Loads 5-5 Guidelines for Drawing Beam Diagrams for Concentrated Loads 5-6 Shearing Forces and Bending Moments for Distributed Loads 5-7 General Shapes Found in Bending Moment Diagrams 5-8 Shearing Forces and Bending Moments for Cantilever Beams 5-9 Beams with Linearly Varying Distributed Loads 5-10 Free-Body Diagrams of Parts of Structures 5-11 Mathematical Analysis of Beam Diagrams 5-12 Continuous Beams - Theorem of Three Moments 6 Centroids and Moments of Inertia of Areas The Big Picture 6-1 Objectives of This Chapter 6-2 The Concept of Centroid - Simple Shapes 6-3 Centroid of Complex Shapes 6-4 The Concept of Moment of Inertia 6-5 Moment of Inertia for Composite Shapes Whose Parts have the Same Centroidal Axis 6-6 Moment of Inertia for Composite Shapes - General Case - Use of the Parallel Axis Theorem 6-7 Mathematical Definition of Moment of Inertia 6-8 Composite Sections Made from Commercially Available Shapes 6-9 Moment of Inertia for Shapes with all Rectangular Parts 6-10 Radius of Gyration 6-11 Section Modulus 7 Stress Due to Bending The Big Picture 7-1 Objectives of This Chapter 7-2 The Flexure Formula 7-3 Conditions on the Use of the Flexure Formula 7-4 Stress Distribution on a Cross Section of a Beam 7-5 Derivation of the Flexure Formula 7-6 Applications - Beam Analysis 7-7 Applications - Beam Design and Design Stresses 7-8 Section Modulus and Design Procedures 7-9 Stress Concentrations 7-10 Flexural Center or Shear Center 7-11 Preferred Shapes for Beam Cross Sections 7-12 Design of Beams to be Made from Composite Materials 8 Shearing Stresses in Beams The Big Picture 8-1 Objectives of this Chapter 8-2 Importance of Shearing Stresses in Beams 8-3 The General Shear Formula 8-4 Distribution of Shearing Stress in Beams 8-5 Development of the General Shear Formula 8-6 Special Shear Formulas 8-7 Design for Shear 8-8 Shear Flow 9 Deflection of Beams The Big Picture 9-1 Objectives of this Chapter 9-2 The Need for Considering Beam Deflections 9-3 General Principles and Definitions of Terms 9-4 Beam Deflections Using the Formula Method 9-5 Comparison of the Manner of Support for Beams 9-6 Superposition Using Deflection Formulas 9-7 Successive Integration Method 9-8 Moment-Area Method 10 Combined Stresses The Big Picture 10-1 Objectives of this Chapter 10-2 The Stress Element 10-3 Stress Distribution Created by Basic Stresses 10-4 Creating the Initial Stress Element 10-5 Combined Normal Stresses 10-6 Combined Normal and Shear Stresses 10-7 Equations for Stresses in Any Direction 10-8 Maximum Stresses 10-9 Mohr's Circle for Stress 10-10 Stress Condition on Selected Planes 10-11 Special Case in which Both Principal Stresses have the Same Sign 10-12 Use of Strain-Gage Rosettes to Determine Principal Stresses 11 Columns The Big Picture 11-1 Objectives of this Chapter 11-2 Slenderness Ratio 11-3 Transition Slenderness Ratio 11-4 The Euler Formula for Long Columns 11-5 The J. B. Johnson Formula for Short Columns 11-6 Summary - Buckling Formulas 11-7 Design Factors and Allowable Load 11-8 Summary - Method of Analyzing Columns 11-9 Column Analysis Spreadsheet 11-10 Efficient Shapes for Columns 11-11 Specifications of the AISC 11-12 Specifications of the Aluminum Association 11-13 Non-Centrally Loaded Columns 12 Pressure Vessels The Big Picture 12-1 Objectives of this Chapter 12-2 Distinction Between Thin-Walled and Thick-Walled Pressure Vessels 12-3 Thin-Walled Spheres 12-4 Thin-Walled Cylinders 12-5 Thick-Walled Cylinders and Spheres 12-6 Analysis and Design Procedures for Pressure Vessels 12-7 Spreadsheet Aid for Analyzing Thick-Walled Spheres and Cylinders 12-8 Shearing Stress in Cylinders and Spheres 12-9 Other Design Considerations for Pressure Vessels 12-10 Composite Pressure Vessels 13 Connections The Big Picture 13-1 Objectives of this Chapter 13-2 Modes of Failure 13-3 Riveted Connections 13-4 Bolted Connections 13-5 Allowable Stresses for Riveted and Bolted Connections 13-6 Example Problems - Riveted and Bolted Joints 13-7 Eccentrically Loaded Riveted and Bolted Joints 13-8 Welded Joints with Concentric Loads Appendix Answers to Selected Problems Index

Patent
10 Apr 1978
TL;DR: In this paper, a method of perforating the sub-surface formation located in the area of an oil or gas well bore hole comprising directing a high powered coherent light beam axially along the bore hole to a predetermined depth from a surface location, deflecting the beam at said depth along a deflected beam axis.
Abstract: A method of perforating the sub-surface formation located in the area of an oil or gas well bore hole comprising directing a high powered coherent light beam axially along the bore hole to a predetermined depth therein from a surface location, deflecting the beam at said depth along a deflected beam axis, and successively focusing the beam at said depth to concentrate the beam at each of a plurality of spaced focal points along the deflected beam axis The method (1) provides a significant increase in the distance (length) to which the calculated oil or gas bearing formations can be perforated (from a present nominal 18 inches to 200 feet or more), thus providing the opportunity for increased yield; and (2) provides an accurate determination of the exact near horizontal plane orientation of such perforations so that each can be aimed in the direction of the most promising formation pay zone

Journal ArticleDOI
TL;DR: In this article, a double plasma device is used to study ion-acoustic solutions in a plasma traversed by a weak ion beam, where large amplitude compressive pulses are amplified and steepened to become solitons of which the amplitude n/n0 is comparable or less than 40%.
Abstract: Ion-acoustic solutions in a plasma traversed by a weak ion beam are studied experimentally by a double plasma device. Large amplitude compressive pulses are amplified and steepened to become solitons of which the amplitude n/n0 is comparable or less than 40%. The amplitude of the soliton is maximum at a beam velocity of Vb/Cs=1.7 while the linear growth rates is maximum at Vb/Cs=1.3. Theoretical explanations are presented with the use of the fluid model.

Journal ArticleDOI
TL;DR: A priori error bound is obtained for the fourth order method to prove the convergence of the finite difference scheme in this article, and a suf- ficient condition guaranteeing the uniqueness of the solution of the boundary value problem is also given.
Abstract: In this paper we develop numerical techniques of order 2, 4 and 6 for the solution of a fourth order linear equation. A priori error bound is obtained for the fourth order method to prove the convergence of the finite difference scheme. A suf- ficient condition guaranteeing the uniqueness of the solution of the boundary value problem is also given. Numerical illustrations are tabulated and results compared with the classical Runge-Kutta method. 1. Introduction. We consider the problem of bending a rectangular clamped beam of length / resting on an elastic foundation. The vertical deflection w of the beam satis- fies the system

Journal ArticleDOI
TL;DR: In this paper, the authors show that a TEM∗01 mode laser beam is convenient to stably levitate either solid or hollow dielectric spheres or metallic ones.