bluuebunny/crossref_metadata_2025 huggingface dataset:
The End Problem of Rectangular Strips
Authors: Horvay G.
Published: June 2021

J. Fadle was first to derive a solution for the stresses in a rectangular strip subject on one of its narrow edges to a self-equilibrating system of stresses; i.e., stresses which have zero resultant force and zero resultant moment. Fadle’s solution is rather unwieldy because of the use of complex (biharmonic) eigenfunctions. These eigenfunctions are associated with the roots of the equation sin 2γ ± 2γ = 0. The first (nonvanishing) root, as determined to seven decimals by Mittelman and Hillman, is γ2 = 2.1061961 + 1.1253643i. In this paper we derive a variational solution of the same problem in the form φ(x, y) = Σcnφn where, in first approximation, φn = fn(y)gn(x). The series Σcnfn(y) is obtained by expansion of the boundary values φ(0, y) of the Airy function φ into a complete set of self-equilibrating orthogonal polynomials fn(y); the functions gn(x) are then determined from the Euler-Lagrange equations of the associated variational problem. This procedure has the advantage of staying entirely in the real domain. The first approximation corresponds to the physical concept that the longitudinal fibers of the strip are beams on elastic foundation (the adjacent fibers furnish the elastic foundation) subject to end thrusts and lateral loads. Incidental to this idea there are provided quantitative formulas which relate depth of penetration of an applied traction to its shape (number of its wiggles). The eigenvalues γn, the real parts of which furnish the extinction coefficients, are obtained from a quadratic equation in γ2. One finds that the lowest (nonvanishing) eigenvalue is γ2 = 2.075 + 1.143i. In higher approximations coupling effects between derivatives of the orthogonal modes fngn are also taken into account. The jth approximation to a mode φn is obtained by evaluating a 2j − 1-rowed determinantal equation involving the functions fn−j+1 gn−j+1 to fn+j−1 gn+j−1. High modes are calculated with the same facility and accuracy as is the fundamental except that the fundamental mode φ2 not being preceded by other modes, requires, in jth approximation, only a j-rowed determinantal equation. One thus finds that in third approximation γ2 is the root of a 6th degree equation in γ2, and has the value γ2 = 2.1061964 + 1.1253644i.
On Turbulent Flow Between Parallel Plates
Authors: Pai S. I.
Published: June 2021

The Reynolds equations of motion of turbulent flow of incompressible fluid have been studied for turbulent flow between parallel plates. The number of these equations is finally reduced to two. One of these consists of mean velocity and correlation between transverse and longitudinal turbulent-velocity fluctuations u 1 ′ u 2 ′ ¯ only. The other consists of the mean pressure and transverse turbulent-velocity intensity. Some conclusions about the mean pressure distribution and turbulent fluctuations are drawn. These equations are applied to two special cases: One is Poiseuille flow in which both plates are at rest and the other is Couette flow in which one plate is at rest and the other is moving with constant velocity. The mean velocity distribution and the correlation u 1 ′ u 2 ′ ¯ can be expressed in a form of polynomial of the co-ordinate in the direction perpendicular to the plates, with the ratio of shearing stress on the plate to that of the corresponding laminar flow of the same maximum velocity as a parameter. These expressions hold true all the way across the plates, i.e., both the turbulent region and viscous layer including the laminar sublayer. These expressions for Poiseuille flow have been checked with experimental data of Laufer fairly well. It also shows that the logarithmic mean velocity distribution is not a rigorous solution of Reynolds equations.
Elastic Waves Created During Tensile Fracture: The Phenomenon of a Second Fracture
Authors: Miklowitz Julius
Published: June 2021

In some tensile tests with brittle materials, it was noted that fractures were produced at two different cross sections of the specimen when the rupture load was reached. The phenomenon of the second fracture prompted the present investigation. It is believed that the second fracture is caused by the destructive action of the elastic strain waves created during the first of the two fractures. The analytical and experimental work carried out was focused on describing the character of these waves. Consideration of the mechanics involved reduces the problem to that of a vibrating cantilever beam with time-dependent boundary conditions. Two types of waves are shown to exist. The first is a longitudinal unloading wave (compression). The other is a group of flexural strain waves caused by the moment that develops at the initial fracture section. The methods of operational mathematics and the electric-analog computer have been employed in the analytical study.
On the Maximum Numerical Value of the Tangential Stress in Thick-Walled Cylinders
Authors: Ranov T. , Park F. R.
Published: June 2021

Statements in the literature appear to imply that the numerical value of the circumferential stress in thick-walled cylinders is always a maximum at the inner radius. While this is certainly correct in the case of zero external pressure, the presence of both external and internal pressures creates the possibility of a numerically larger tangential stress occurring at the outer radius. This paper investigates this possibility and establishes a criterion for a check on the location of the numerical tangential stress maximum. A chart is presented for its convenient application.
On the Application of the Impedance Method to Continuous Systems
Authors: Chenea P. F.
Published: June 2021

It is shown how the concept of impedance may be extended to apply to those continuous systems whose vibratory behavior leads to the wave equation. The use of the method is demonstrated by three examples which include the free and forced vibration of an elastic bar in longitudinal oscillation and torsional oscillation of a tapered shaft.
Natural Frequencies of Twisted Cantilever Beams
Authors: Rosard D. D.
Published: June 2021

When a cantilever beam, an aircraft propeller, a turbine or compressor blade, is twisted, the natural frequencies of vibration may be changed appreciably. The effect of twist depends on the width-to-thickness ratio. An experimental and analytical investigation was made of the effect of twist for various width-to-thickness ratios.
The Shearing of a Rectangular Block Between Rough Plates
Authors: Craggs J. W.
Published: June 2021

In a recently published paper, W. T. Read gives an approximate solution of a problem in elasticity which occurs in the testing of materials. This is the problem of determining the stresses in a rectangular block when a pair of opposite faces are mutually displaced in the direction of an edge. The conditions are not those of uniform shear, for that would imply shear stresses on the free faces of the block. In the present paper an analytical solution of the same problem is obtained and the results are compared for a particular case. The method used is a particular case of the general method described by G. Pickett.
Bending of Circular and Ring-Shaped Plates on an Elastic Foundation
Authors: Reismann Herbert
Published: June 2021

This paper develops a method for the evaluation of deflections, moments, shears, and stresses of a circular or ring-shaped plate on an elastic foundation under transverse loads. A series solution is derived for plates subjected to edge and/or concentrated loads and is given in terms of tabulated functions. It is exact within the assumptions underlying the classical theory of plates and includes, as a particular case, the known solution of the corresponding radially symmetric problem. Two examples displaying radial asymmetry are worked. A solution is given for (a) a circular plate resting on an elastic foundation, clamped at the boundary and subjected to an arbitrarily placed concentrated load, and (b) a plate of infinite extent, resting on an elastic foundation and clamped to the boundary of a rigid circular disk to which a pure moment is applied.
Stress Concentration Due to a Hemispherical Pit at a Free Surface
Authors: Eubanks R. A.
Published: June 2021

This paper contains a solution in series form for the stresses and displacements around a hemispherical pit at a free surface of an elastic body. The problem is idealized by considering a semi-infinite medium which otherwise is bounded by a plane. At infinity the body is assumed to be in a state of plane hydrostatic tension perpendicular to the axis of symmetry of the pit. The present method of solution may be generalized to loadings which are not rotationally symmetric. Numerical results are given for the variation along the axis of symmetry of the normal stress which is parallel to the tractions at infinity; these results are compared with the known corresponding numerical values appropriate to the two-dimensional analog of the present problem.
Coulomb Friction, Plasticity, and Limit Loads
Authors: Drucker D. C.
Published: June 2021

Additional attention is given to the somewhat subtle but extremely important difference between Coulomb friction and the apparently corresponding resistance to plastic deformation. It is shown that the limit theorems previously proved for assemblages of perfectly plastic bodies do not always apply when there is finite sliding friction. Theorems are developed which relate the limit loads with finite Coulomb friction to the extreme cases of zero friction and of complete attachment, and also to the case where the frictional interfaces are “cemented” together with a cohesionless soil.
The Stresses in a Flat Curved Bar Resulting From Concentrated Tangential Boundary Loads
Authors: Wu Ning-Gau , Nelson C. W.
Published: June 2021

The Fourier integral method is applied to plane-stress problems of a curved bar bounded by two concentric circles and loaded by concentrated tangential boundary loads. The solutions presented may be combined with results given in previous papers (1, 2) dealing with radial boundary loads so as to obtain the stresses in a curved bar loaded by any combination of concentrated boundary loads inclined at any angle to the radial direction.
Forced Motions of Elastic Rods
Authors: Herrmann G.
Published: June 2021

In a recent paper by Mindlin and Herrmann, a one-dimensional theory of compressional waves in an elastic rod was described. This theory takes into account both radial inertia and radial shear stress and, accordingly, contains two dependent variables instead of the one axial displacement of classical rod theory. The solution of the equations for the case of forced motions thus involves complications not usually encountered. The difficulties may be surmounted in several ways, one of which is presented in this paper. The method described makes use of Lagrange’s equation of motion and reduces the most general problem of forced motion to a free vibration problem and a quadrature.
A Method for Determining the Internal Damping of Machine Members
Authors: Cochardt A. W.
Published: June 2021

A method is described by which the internal damping of a machine member can be evaluated in a simple way. It is shown that the results of a conventional damping test on a simple shaped specimen of the chosen material can be combined with a newly introduced quantity, the stress-distribution function, to yield the internal damping of a particular member. The suggested method eliminates the necessity for testing expensive specimens as was often the practice.
The Existence and Stability of Ultraharmonics and Subharmonics in Forced Nonlinear Oscillations
Authors: Caughey T. K.
Published: June 2021

A study is made of the forced oscillations of a second-order system having a small cubic nonlinearity in the restoring force. It is shown that under suitable conditions ultraharmonic or subharmonic motion exists in addition to the harmonic motion which a linearized theory would predict. By studying the stability of such motions it is shown that at points on the amplitude frequency-response curves having vertical tangents, instability and consequently “jumps” occur. A study of the dependence of the motion on the initial conditions reveals that while ultra-harmonic and harmonic motions are rather insensitive to initial conditions, the existence of subharmonic motion can be achieved only for a restricted set of initial conditions.
Oil Streamlines in Bearings
Authors: Kettleborough C. F.
Published: June 2021

A semigraphical method is given for tracing oil-flow streamlines in bearings. This is illustrated by a typical calculation.
Application of the Electronic Differential Analyzer to the Oscillation of Beams, Including Shear and Rotary Inertia
Authors: Howe C. E. , Howe R. M.
Published: June 2021

The equations for normal modes of lateral vibration of beams are set up on the electronic differential analyzer. Beam deflections due to transverse shear and rotary-inertia forces are included. The differential analyzer is shown to be a fast and accurate method for solving the problem. Analyzer outputs include mode shape, slope, bending moment, and shear force along the beam. Curves showing the normal-mode frequencies for the first three modes of vibration of a uniform free-free beam are presented for a wide range of transverse shear and rotary-inertia parameters. The electronic differential analyzer also is utilized to solve the problem of lateral vibration of nonuniform beams.
Two-Dimensional Flow About Half Bodies Between Parallel Walls
Authors: Breslin John P.
Published: June 2021

Two new families of blunt half bodies are derived from the combination of source distributions and a uniform stream. One is obtained from a source lamina placed normal to an infinitely broad free stream, the other family is obtained by using the same source distribution between parallel walls. Formulas for the half-body profiles and the velocity and pressure distributions are given. Results of a calculation for selected values of the parameters are presented in graphical form and applications of the formulas are made to give the pressure distributions on the profile and the walls. The influence of the walls on the pressure distribution and body shape is studied. An approximate relationship (obtained by neglecting the small change in body shape for large wall distances) is derived for the half-body size which may be placed between given walls with a prescribed error in the pressure at one point of the profile. It is concluded that the influence of walls should be considered carefully in the design or use of two-dimensional facilities for study of flows which are of the half-body type.
Axially Symmetric Flexural Vibrations of a Circular Disk
Authors: Deresiewicz H. , Mindlin R. D.
Published: June 2021

At high frequencies, the flexural vibrations of a plate are described very poorly by the classical (Lagrange) theory because of neglect of the influence of coupling with thickness-shear vibrations. The latter may be taken into account by inclusion of rotatory inertia and shear-deformation terms in the equations. The resulting frequency spectrum is given, in this paper, for the case of axially symmetric vibrations of a circular disk with free edges and is compared with the spectrum predicted by the classical theory.
Clamped Semicircular Plate Under Uniform Bending Load
Authors: Woinowsky-Krieger S.
Published: June 2021

The semicircular plate subjected to bending usually is considered as a particular case of a sectorial plate and one introduces polar co-ordinates to discuss the deflection of the plate and the corresponding distribution of stresses. If the semicircular plate is clamped along the boundary the application of approximate methods becomes necessary to this end. It is worthy of note that a rather simple exact solution can be given in this latter case by making use of bipolar instead of polar co-ordinates.
The Formation of a Conical Crater in a Thin Plastic Sheet
Authors: Thomson W. T.
Published: June 2021

The deformation of a thin plastic sheet forced by a conical mandrel of any angle is analyzed. Dimensions of the conical crater formed are presented in nondimensional form for various cone angles.
Stress-Concentration Factors in Shafts With Transverse Holes as Found by the Electroplating Method
Authors: Ōkubo H. , Satō S.
Published: June 2021

In this paper the torsion of shafts with transverse holes has been investigated experimentally. Usual methods for stress measurements, such as the method of brittle coatings and the use of sensitive extensometers, are not applied effectively to the present problem because the maximum stress occurs in the bore and does not occur on the outer surface of the shaft. The stress may be measured by the stress-freezing and slicing method but we cannot expect too much from this method for the accurate determination of the stress when the diameter of the hole is comparatively small. In treating the problem theoretically, considerable mathematical difficulties are encountered on account of its axially nonsymmetrical nature. The electroplating method recently developed by one of the authors (1), however, has been proved to be useful in this case, so the maximum stresses in shafts are measured by this method and the stress-concentration factors are found for various diameters of the hole.
Laminar-Diffusion Boundary Layer—A Review
Authors: Berman Kurt
Published: June 2021

Diffusion theory has not assumed as yet the degree of organizational elegance accorded to fluid-flow and heat-transfer theories. In this paper mass-transport phenomena and their nondimensional correlation are summarized. In order that the similarities between energy, momentum, and mass-transport phenomena may be exhibited, the discussion of diffusion is preceded by brief summaries of dynamic and temperature boundary-layer theories.
Buckling of Continuous Columns
Authors: Perkins H. C.
Published: June 2021

The following brief note describes an interesting procedure for setting up the characteristic equation of a continuous column, using the method of superposition.
Representation of Three-Dimensional Stress Distributions by Mohr Circles
Authors: Zizicas G. A.
Published: June 2021

O. Mohr has developed a diagram representing the normal stress component snn = σn and the total shearing stress component τn on an element of surface of any prescribed orientation with respect to the directions of the principal stresses. His procedure, however, does not give the orientation of the shearing stress τn within the element or, which is equivalent, the components of this shearing stress in a plane co-ordinate system within the element under consideration. An extension of the Mohr method that overcomes this limitation is presented in this note.
Heat-Transfer Measurements in an Inexpensive Supersonic Wind Tunnel: 1—Apparatus and Results for a Laminar Boundary Layer Based on a Simple One-Dimensional Flow Model
Authors: Kaye Joseph , Keenan J. H. , Brown G. A. , Shoulberg R. H.
Published: June 2021

Reliable experimental data, obtained at relatively low cost, are presented in the form of heat-transfer coefficients for air moving at supersonic speeds in a round tube. These data are analyzed, interpreted, and compared with available data in the literature. The experimental local heat-transfer coefficients are for laminar, transitional, and turbulent boundary layers. The data for a laminar boundary layer, comprising 17 runs, are discussed here for Mach numbers at tube inlet of 2.8 and 3.0. The range of values of diameter Reynolds number covered is from 20,000 to 100,000 for these laminar-flow tests, while the length Reynolds number extends to about 4,000,000. The computed quantities are obtained on the basis of a simple one-dimensional flow model, but a companion paper will analyze the same data in greater detail on the basis of a two-dimensional flow model.
The Accuracy of Donnell’s Equations
Authors: Hoff N. J.
Published: June 2021

Solutions of Donnell’s equations of the small deformations of the perfectly elastic thin-walled circular cylindrical shell are compared with those obtainable from Flügge’s equations. The range of the basic parameters is found within which the two solutions are approximately equal.
Bending of Pretwisted Beams
Authors: Zickel J.
Published: June 2021

The general theory of pretwisted beams and columns is applied to the bending of an initially straight and uniformly pretwisted beam of doubly symmetric thin-walled section. Pretwisting brings planes of various bending stiffness into play with a resulting stiffness which in a sense averages the stiffness of the beam in its principal directions. It is shown that compared with bending of an untwisted beam in its most flexible direction a thin strip can have its deflection in the plane of bending reduced 72 per cent by an initial twist of 0.83π. Simultaneously, however, lateral deflections of almost equal magnitude are induced. For pretwists above 2π, the lateral deflections become practically negligible and the deflections in the plane of bending are still reduced as much as 44 per cent. With increasing initial twist, however, the pretwisted beam becomes more flexible, and for an initial twist of 6.5π it is as flexible as the untwisted beam in its most flexible direction. Beams of equal flexibility in all directions simply become more flexible with initial twist, a fact which corresponds to the observations made by Den Hartog in some of his experiments.
Nutation of a Free Gyro Subjected to an Impulse
Authors: Plymale B. T. , Goodstein R.
Published: June 2021

It is the purpose of this paper to call attention to a particular gyro motion which has been observed and studied in our laboratories. The phenomenon is of extreme practical importance for all instruments which use a gyro as a space-stable element, and no published usable information has been found concerning it. A description and explanation of the motion will be presented. An Appendix contains the basic equations for the system and the results of approximate solutions.
The Permanent Deflection of a Plastic Plate Under Blast Loading
Authors: Wang A. J.
Published: June 2021

This paper is concerned with a simply supported circular plastic plate that is exposed to a strong blast. Equations of deformation are developed.
Simplified Formulas for Boundary-Value Problems of the Thin-Walled Circular Cylinder
Authors: Pohle Frederick V. , Nardo S. V.
Published: June 2021

N. J. Hoff has presented formulas which can be used in the solution of boundary-value problems of circular cylinders. The purpose of this note is to express these results in exact simplified form; a more detailed investigation appears elsewhere. The notation will be that of Hoff, unless otherwise stated.
Combined Tension-Torsion Tests With Fixed Principal Directions
Authors: Davis E. A.
Published: June 2021

A series of combined tension-torsion-internal pressure tests, each with a different amount of torsion present, are discussed. The specimens were tested in such a manner that the principal directions of the increments of natural plastic strain were kept constant. These increments can be summed in various ways, the simplest of which would yield finite strains with fixed principal directions. The octahedral shearing-stress versus octahedral shearing-strain diagrams for the four specimens tested coincide quite closely. The principal directions of stress were measured at each increment of strain and found to agree well with those of the increments of strain.
Experiments Concerning the Yield Surface and the Assumption of Linearity in the Plastic Stress-Strain Relations
Authors: Naghdi P. M. , Rowley J. C. , Beadle C. W.
Published: June 2021

Combined tension and torsion experiments for six tubular 24S-T4 aluminum-alloy specimens with considerable initial anisotropy are reported. In all cases the results reveal the existence of corners on the yield loci of the material.
A Criterion for Minimum Scatter in Fatigue Testing
Authors: McClintock F. A.
Published: June 2021

When a number of fatigue tests are run on specimens with a longitudinal radius of curvature, there results a scatter in both the number of cycles to failure and the position of failure. A previous statistical analysis showed that if the variations in life are due solely to local inhomogeneities in the specimen, then there is a definite relation between the scatter in position of failure and the scatter in the number of cycles to failure. If the scatter in life significantly exceeds that corresponding to the scatter in position of failure, then there is some factor other than local inhomogeneities contributing to the scatter in life. Such other factors can be eliminated by improving the experimental technique. The usefulness of this criterion is illustrated by its application to crack detection tests on polycrystalline ingot iron.
A New Approach to the Analysis of Large Deflections of Plates
Authors: Berger H. M.
Published: June 2021

Simplified nonlinear equations for a flat plate with large deflections are derived by assuming that the strain energy due to the second invariant of the middle-surface strains can be neglected. Computations using the solution of these simplified equations are carried out for the deflection of uniformly loaded circular and rectangular plates with various boundary conditions. Comparisons are made with available numerical solutions of the exact equations. The deflections found by this approach are then used to obtain the stresses for the circular plate and the resulting stresses are compared with existing solutions. In all the cases where comparisons could be made, the deflections and stresses agree with the exact solutions within the accuracy required for engineering purposes.
Perturbation Methods Applied to Nonlinear Dynamics
Authors: Bellman Richard
Published: June 2021

We wish to present a simple technique which will in many cases increase the range of effectiveness of perturbation and power-series methods in situations in which the equations treated contain parameters which assume only positive values.
Integral Methods in Natural-Convection Flow
Authors: Levy Salomon
Published: June 2021

This paper presents an evaluation of the range of application, accuracy, and usefulness of integral methods in natural-convection flow. The study reveals (a) that integral methods may be utilized to obtain approximate answers to free-convection problems whenever exact analytical solutions become too involved. Specific-flow examples considered here (natural convection from inclined plate, horizontal cylinder, arbitrary body, or within enclosed channels) confirm their adaptability to complicated configurations. (b) Over-all accuracy of the solutions is good. For inclined plates the derived equations reduce at high Grashof numbers to the correlation proposed and verified by Rich (1) while in the case of horizontal cylinders the results compare satisfactorily with the theoretical values of Hermann (2) and the accepted experimental relations (12). (c) The integral method of solution may be extended to apply to low Prandtl number fluids, laminar or turbulent flow, variable wall temperature, and convection within confined spaces.
Stress Distribution in Square Plates With Hydrostatically Loaded Central Circular Holes
Authors: Durelli A. J. , Barriage J.
Published: June 2021

The stress distribution in square plates with hydrostatically loaded central circular holes was determined using photoelasticity and brittle coatings. Photoelasticity was used to determine the maximum shear lines (isochromatics) and a brittle coating was used to determine the directions of the principal stresses (isostatics). The investigation was conducted for plates with holes producing seven ratios of the diameter to the square side (D/a). Curves are presented which show the distribution of the maximum shear stress along the axis and along the diagonal of the square plate, as a function of D/a, Figs. 3 and 4. The maximum principal stress along the exterior and interior boundaries as a function of D/a, Figs. 5 and 6, has also been given. A comparison is made of the stress ratios (σ1/P) at a point on the axis of the square at the interior boundary with that calculated for a thick-wall cylinder using Lamé’s equation, Fig. 1. Stress ratios (σ1/P) also are determined for a point on the diagonal of the square plate at the interior boundary, Fig. 8. A diffused-light polariscope was used. The loading jig consisted of rubber tubing in a grooved block. The photoelastic material (CR39) was calibrated automatically. No new methods are developed in the paper but it is felt that the use of the presently available methods has been simplified appreciably.
Free Vibrations of Thin Cylindrical Shells Having Finite Lengths With Freely Supported and Clamped Edges
Authors: Yu Yi-Yuan
Published: June 2021

Free vibrations of thin cylindrical shells having finite lengths are investigated on the basis of a set of three differential equations which are derived in a similar manner as Donnell obtained his equations for the bending and buckling problems. The equations can be solved readily after a simplifying assumption is introduced. In this manner the frequency equations are obtained for cylindrical shells with both edges freely supported, with both edges clamped, and with one edge freely supported and the other edge clamped. It is found that the lowest frequency given by the frequency equation is the smallest in the first case, larger in the third, and the largest in the second. The other two frequencies yielded by the frequency equation are approximately the same in all cases. As a result of the approximations, the characteristic equations for the three cases are found to be similar to the frequency equations for the lateral vibration of beams with similar end conditions. For the case of freely supported edges the normal functions obtained are identical in form with those assumed by Flügge and by Arnold and Warburton. For the same case, natural frequencies of one numerical example are computed by means of the present method, and the results are in good agreement with those obtained by these previous authors.
Some Solutions of the Timoshenko Beam Equations
Authors: Boley B. A. , Chao C. C.
Published: June 2021

Solutions are obtained by the method of Laplace transformation for four types of loadings applied to a semi-infinite beam. Numerical results are presented for two of these, both for suddenly applied and gradually varying loads. The effects of shear deformations and rotatory inertia are taken into account according to Timoshenko’s beam model. A comparison with the corresponding results of the Bernoulli-Euler theory are briefly presented.
Asymmetrical Bending of a Cylindrically Aeolotropic Tapered Disk
Authors: Baclig E. S. , Conway H. D.
Published: June 2021

Variations of thickness, anisotropy, and asymmetry of loading usually tend to increase the mathematical difficulty of obtaining solutions to the small-deflection problems of plate bending. However, for the bending of a cylindrically aeolotropic disk twisted about its diameter and having a certain thickness variation, it is possible to obtain a relatively simple solution in closed form. This solution is presented here, numerical results being given for oak and for isotropic material.
Analysis of Short Thin Axisymmetrical Shells Under Axisymmetrical Edge Loading
Authors: Horvay G. , Linkous C. , Born J. S.
Published: June 2021

On the basis of recent work by Hildebrand, formulas are established for the effects of axisymmetrical edge moments and edge shears on short shells of variable wall thickness and variable meridional curvature. While the formulas are inferior in accuracy to those developed for bolted flange assemblies by Waters, Rossheim, Wesstrom, and Williams, in simplicity of use and speed of calculations, they are on a par with the well-known Geckeler formulas, without being subject to many of the limitations of the latter. The formulas are particularly suited for the analysis of the tapered hub portion of a flanged shell. Other uses are also obvious. Particular applications to redundant shell (torus-type) problems will be given in a separate paper.
The Effect of the Earth’s Rotation on Laminar Flow in Pipes
Authors: Benton G. S.
Published: June 2021

The theory of laminar pipe flow has been developed, retaining the effect of the earth’s rotation. A secondary flow is set up in the pipe cross section which results in distortion of the usual parabolic profile. The distortion may be significant in pipes of moderate diameter. Laboratory studies tend to substantiate these conclusions.
Comparison of Slip-Line Solutions With Experiment
Authors: Thomsen E. G.
Published: June 2021

Plane-strain and axially symmetric approximate solutions for a perfect plastic are compared with experimental results obtained from the extrusion of a billet of commercially pure aluminum. The extrusion process was carried out at room temperature under essentially negligible external wall friction with a reduction of area of 87.8 per cent. It is found that the plane-strain solution is in good agreement with the experimental results, if a constant k = σ̄/2 = 20,000 psi (maximum shear stress for Tresca’s criterion) is substituted in the plane-strain solution. The flow stress (σ̄ ≅ 40,000 psi) was determined from a property test for the aluminum billet, at a strain equivalent to the uniform deformation in the extrusion (i.e., same area reduction without shear deformation). It is found that the Haar and von Karman yield condition is not valid for the present case, and further that the axially symmetric solution demonstrates no real advantage over the simpler plane-strain solution in predicting the stress distribution in an axially symmetric extrusion problem.
On the Ideally Plastic Indentation of Inset Rectangular Bands
Authors: Ross E. W.
Published: June 2021

One of the limit design theorems of ideal plasticity is applied to find an upper bound on the initial indentation pressure for the case where a flat, smooth die is pushed into an inset band of rectangular cross section. The dependence of the upper bound on the clearance and width of the band is given, and a possible extension to asymmetrically inset bands is suggested.
Stiffness of Curved Circular Tubes With Internal Pressure
Authors: Kafka P. G. , Dunn M. B.
Published: June 2021

A method is presented for computing the flexibility factor for plane pipe lines with internal-pressure effects considered. Formulas for the first and second approximation to both the flexibility and the stress-intensification factors are given. Comparisons of the second approximations with experimental results are also made.
Bending of a Uniformly Loaded Semicircular Plate Simply Supported Around the Curved Edge and Free Along the Diameter
Authors: Muster D. F. , Sadowsky M. A.
Published: June 2021

Within the limits of classical plate theory, a solution is obtained in series form for the problem of a uniformly loaded, semicircular plate, simply supported around the curved edge and free along the diameter. The solution, although singular at the corners, is otherwise analytic and amenable to numerical evaluation by electronic calculators. The solution results are compared to those obtained experimentally by Robinson and Huggenberger. The agreement is reasonable, when account is taken of the manner in which their empirical results were obtained.
On the Theory of the Acceleration Damper
Authors: Grubin Carl
Published: June 2021

The acceleration damper reduces the vibration of a mechanical system through momentum transfer by collision and conversion of mechanical energy into heat. A typical unit consists of a mass particle moving in a container fixed to the primary vibrating system. The direct problem is to determine the motion of a single-degree-of-freedom system with a damper, when the driving force is simple harmonic. The inverse is to determine the characteristics of a damper for reducing the vibration of the same system to a prescribed value. Numerical results indicate that the damper is most effective at resonance.
Time-Dependent Tangent Modulus Applied to Column Creep Buckling
Authors: Carlson R. L.
Published: June 2021

The relation of the time-dependent tangent-modulus load—as conceived by Shanley—to actual column capacity is clarified. It may be interpreted as a limiting case of the “allowable-load capacity” which has been shown to be a conservative estimate. The time-dependent tangent-modulus load is, therefore, an approximation to a conservative estimate. The approximation, however, may be either conservative or nonconservative when applied to imperfect or real columns. Typical cases are discussed and experimental results for two alloys are cited.
An Elastoplastic Thermal-Stress Analysis of a Free Plate
Authors: Weiner Jerome
Published: June 2021

The thermal stresses in a free plate of elastoplastic material subjected to a varying heat input over one face are determined. A heuristic solution is first found by suitable modifications of the known elastic solution. It is then verified that the solution satisfies all the conditions of the appropriate uniqueness theorem and represents therefore the unique solution to the problem. Residual stresses are determined and found to depend markedly on the peak magnitude of the heat input.
The Propagation of Fatigue Cracks
Authors: Head A. K.
Published: June 2021

A theory of the rate of growth of fatigue cracks is extended to the case of large stresses. Recent measurements of McClintock and Ryan are discussed.
Impact With Finite Acceleration Time of Elastic and Elastic-Plastic Beams
Authors: Alverson R. C.
Published: June 2021

The purpose of the work described in this paper was to provide information on the elastic and plastic deformation of steel beams subjected to transverse impact. The particular impact problem treated was chosen to correspond to conditions in tests in which a beam initially at rest is struck by a massive hammer, so that a specified change of velocity is imposed at a certain cross section in a small time interval. In the present analysis the initial elastic and subsequent elastic-plastic motions were obtained by methods similar to those used by Bleich and Salvadori (3). As in (3), it is assumed that plastic deformation occurs only at a single stationary plastic hinge (in this case at the struck cross section). Results obtained are compared with those of a “rigid-plastic” solution of the same problem, in which plasticity conditions are correctly taken into account but elastic vibrations are not included.
Flexural Vibrations of Rectangular Plates
Authors: Mindlin R. D. , Schacknow A. , Deresiewicz H.
Published: June 2021

The influence of rotatory inertia and shear deformation on the flexural vibrations of isotropic, rectangular plates is investigated. Three independent families of modes are possible when the edges are simply supported. Coupling of the modes is studied for the case of one pair of parallel edges free and the other pair simply supported. The development of the coupling is traced by means of a solution for elastically supported edges. Special attention is given to the higher modes and frequencies of vibration which are beyond the range of applicability of the classical theory of thin plates.
Plastic Twisting of Thick-Walled Circular Ring Sectors
Authors: Freiberger W. , Prager W.
Published: June 2021

The paper presents a graphical method of determining the fully plastic stress distribution in a twisted circular ring sector with hollow cross section and the warping of the cross sections of this ring in the ensuing plastic flow. The ring is assumed to consist of a rigid, perfectly plastic material.
Three “Neutral” Loading Tests
Authors: Gill S. S.
Published: June 2021

Three tests have been carried out using hollow tubes of alpha brass subjected to combined torsion and internal pressure. An initial torque was applied sufficient to cause plastic deformation, and then the torque was decreased and the internal pressure increased to keep the octahedral shear stress constant in two tests and the maximum shear stress constant in the third test. These loading paths were chosen because they would be neutral loading if the material obeyed the von Mises-Hencky or Guest yield criterion, respectively. Shear strain, axial, and circumferential strain were measured. All three tests gave some plastic strain during the “neutral” loading, but the constant maximum shear-stress loading gave much larger plastic strains than the constant octahedral stress loading. The plastic-strain increment vectors have been plotted to illustrate their direction relative to the loading path.
A Method for Determining the Flexural Effects of Statically Loaded Beams on Multiple Elastic Supports
Authors: Di Taranto R. A.
Published: June 2021

Herein is presented a means for calculating the static deflections, slopes, moments, and shears of a nonuniform beam on two supports for any end conditions and on three simple supports when subjected to concentrated loads and/or concentrated moments. The method is an extension of a simple tabular procedure as used by Myklestad (1) for use on a desk calculator or electronic digital computer. The procedure is such that it may be easily carried out by one who need not have any knowledge of beam theory. Influence coefficients may be easily and directly calculated for nonuniform beams on two and three elastic supports. The two-support beam is formulated for simply supported one overhang, two supports with linear and torsional springs, and fixed-fixed end conditions. Extensions of this method to any other boundary conditions are indicated.
Influence of Large Amplitudes on Free Flexural Vibrations of Rectangular Elastic Plates
Authors: Chu Hu-Nan , Herrmann George
Published: June 2021

In a recent paper (1) a set of plate equations was derived, which governs motions with small elongations and shears, but moderately large rotations, valid for an isotropic material obeying Hooke’s law. The resulting theory, which may be considered the dynamic analog of the von Karman plate theory, is applied presently to the study of free vibrations of a rectangular, elastic plate with hinged, immovable edges. The nonlinear equations are solved approximately by employing a perturbation procedure and also the principle of conservation of energy directly. The influence of large amplitudes on the period of free vibration and on the maximum normal stress is established. The free vibrations of a beam are studied as a special case and the resulting period compared with a previous investigation.
Kinematic Phenomena Observed During the Oblique Impact of a Sphere on a Beam
Authors: Goldsmith Werner , Cunningham D. M.
Published: June 2021

Experimental data relating to the kinetics of oblique impact of 1/2-in-diam steel sphere upon steel beams at initial velocities ranging from 30 to 150 fps are presented. The variation of beam deflection, contact duration, trajectory of the sphere, and contour topography with angle of incidence, beam size, and initial velocity have been determined, and the velocity of propagation of several waves has been ascertained.
Electronic Analog Computer Solutions of Nonlinear Vibratory Systems of Two Degrees of Freedom
Authors: Atkinson C. P.
Published: June 2021

The main contribution of this paper is its account of the use of an electronic differential analyzer for solving the exact differential equations of certain two-degree-of-freedom nonlinear vibrating systems, and the comparison of the differential-analyzer solutions with the approximate analytical solutions obtained from a single-term harmonic approximation (Ritz approximation). The results of these two methods for solving nonlinear differential equations compare favorably over much of the ranges of variables. Where discrepancies arise between the results of the two methods the value of the differential-analyzer approach can be practically appreciated. For example, in the region where superharmonics might be expected, the single-term harmonic approximation ignores them, while the analyzer solutions contain the superharmonic components of the exact solution. A secondary contribution of the paper is the account of the use of the differential analyzer for verification of suspected stability criteria for two-degree-of-freedom nonlinear vibrating systems. Analytical solutions that were reproducible on the analyzer were considered stable; those that were not reproducible were considered unstable. This paper also can be considered as a call for further application of modern computer techniques to the problems of nonlinear mechanics. Since the computer solves the exact or complete differential equations, the results are the complete solutions including transient phenomena, steady state, subharmonics, super-harmonics, and so on. These exact solutions are produced as functions of time which are analogous to the actual vibrations of the physical system studied.
Transient Response of a Nonlinear System by a Bilinear Approximation Method
Authors: Ergin E. I.
Published: June 2021

A line-segment approximation for a nonlinear elastic force has been developed which makes it possible to obtain analytical solutions to a number of transient-load problems which formerly could be solved only by graphical or numerical methods. It is shown that for many problems involving even large nonlinearities, two line segments only are sufficient to give satisfactory accuracy. For some problems where the classical analytical approximate methods of Lindstedt or of Kryloff and Bogoliuboff can be applied, it is shown that the bilinear method leads to an improved accuracy.
Theory and simulation of electroosmotic suppression of acoustic streaming
Authors: Winckelmann Bjørn G. , Bruus Henrik
Published: June 2021

Acoustic handling of nanoparticles in resonating acoustofluidic devices is often impeded by the presence of acoustic streaming. For micrometer-sized acoustic chambers, this acoustic streaming is typically driven by viscous shear in the thin acoustic boundary layer near the fluid-solid interface. Alternating current (ac) electroosmosis is another boundary-driven streaming phenomenon routinely used in microfluidic devices for the handling of particle suspensions in electrolytes. Here, we study how streaming can be suppressed by combining ultrasound acoustics and ac electroosmosis. Based on a theoretical analysis of the electrokinetic problem, we are able to compute numerically a form of the electrical potential at the fluid-solid interface, which is suitable for suppressing the typical acoustic streaming pattern associated with a standing acoustic half-wave. In the linear regime, we even derive an analytical expression for the electroosmotic slip velocity at the fluid-solid interface and use this as a guiding principle for developing models in the experimentally more relevant nonlinear regime that occurs at elevated driving voltages. We present simulation results for an acoustofluidic device, showing how implementing a suitable ac electroosmosis results in a suppression of the resulting electroacoustic streaming in the bulk of the device by 2 orders of magnitude.
Acute cytomegalovirus infections in leukemic mice
Authors: Mayo D R , Rapp F
Published: June 2021

Mice infected with 2 x 10(3) plaque-forming units of mouse cytomegalovirus (MCMV) 3 days after receiving 300 to 400 spleen focus-forming units of Friend leukemia virus developed a more severe MCMV infection than did normal animals. Increased severity was demonstrated by the increased amounts of MCMV recoverable from the salivary glands of leukemic mice 1 to 5 weeks postinfection. In addition, the difference in the number of virus isolations from the kidneys, spleens, livers, and lungs of animals (74 to 120) coinfected with MCMV and Friend leukemia virus compared with animals (49 of 120) infected with MCMV alone was significant (P less than 0.01). Both the 50% lethal dose and 50% infectious dose of MCMV in leukemic mice were lower than in normal animals. MCMV and Friend leukemia virus appear to interact by suppressing the ability of infected spleen cells to respond to mitogen-induced stimulation. The observations of increased severity of MCMV infections in leukemic mice closely parallel the situation observed in human leukemia patients who are at an increased risk of disease due to human cytomegalovirus infections. This mouse model may be useful in assessing the effect of antiviral (cytomegalovirus) therapy.