bluuebunny/crossref_metadata_2025_split huggingface dataset:
Water-Channel Analog to High-Velocity Combustion
Authors: Oppenheim A. K. 
Published: June 2021

Abstract
This paper is a sequel to one presented in 1951, by the author (1). It was shown that during the development of detonation, the combustion zone which appears first in a unidimensional flow field as a single discontinuity, is later transformed into an unsteady, double discontinuity system, and it was demonstrated that such a transformation is necessary because of the restrictions imposed on the system by the dynamic boundary conditions. In the water channel the combustion-front discontinuity is simulated by a unidimensional source formed by admitting water from the bottom. By a proper selection of state parameters analogous relationships are derived to those between pressure and specific volume in a gaseous combustion system. Thus the consequences of restrictions imposed by dynamic boundary conditions on the propagation of combustion are illustrated in an analogous system which, being simpler in nature, is easier to understand. Moreover, the water-channel analog is utilized as an illustrative model of a system where controlled, stationary detonation could be achieved.
Frequencies of Longitudinal Vibration for a Slender Rod of Variable Section
Authors: Lubkin James L. , Luke Yudell L. 
Published: June 2021

Abstract
The natural frequencies of a slender, homogeneous, fixed-free rod of variable section are studied in a one-dimensional theory. The rod is uniform at the fixed end for a certain distance L1, and then tapers for a distance L2 so that the cross-sectional area varies linearly. The frequency equation is derived and its first five zeros are tabulated for several ratios of L1 to L2, and various tapers. The first few terms of asymptotic expansions for the roots of the frequency equation are presented and discussed.
An Invariant Membrane Stress Function for Shells
Authors: Langhaar H. L. 
Published: June 2021

Abstract
Inextensional shells that have no thickness are idealized representations of real shells that have small bending stresses and small deformations. With certain restrictions, the stresses in these shells are derivable from a generalized Airy function. For shells of constant Gaussian curvature, the stress function is unrestricted, but, for other shells, it is expressed as a function of the Gaussian curvature. Although, in this respect, it is less general than Pucher’s stress function, it has the advantage that it may be used with any surface co-ordinates.
Pure Bending of an Incomplete Torus
Authors: Sadowsky M. A. , Sternberg E. 
Published: June 2021

Abstract
An exact solution in series form is presented for the stresses and displacements in an incomplete torus of circular center line and circular cross section under conditions of pure bending. The solution is preceded by a formal treatment of the case in which the shape of the cross section is arbitrary. This more general problem is reduced to one of axisymmetry, which is in turn attacked by a modification of the stress-function approach of Timpe to rotationally symmetric problems in elasticity theory. The modified stress-function approach, which may be of interest beyond the present application, is referred to general orthogonal axisymmetric co-ordinates, and the solution of the specific problem considered here is based on the use of toroidal co-ordinates. The normal stresses acting on the circular cross sections of the torus are evaluated numerically in an illustrative example and are compared with the results of previous approximate solutions of the same problem. The adaptation of the present solution to the determination of the initial stresses in a complete torus from which a wedge-shaped portion has been removed is indicated.
On an Iterative Method for Nonlinear Vibrations
Authors: Roberson R. E. 
Published: June 2021

Abstract
An iterative method for nonlinear vibrations, previously discussed by Brock, is treated from a primarily analytic point of view. In this light, it is a modification of a Picard-like process for two-point boundary conditions mentioned by Gwoh-Fan Djang. It is generalized from previous treatments to systems with more than one degree of freedom and to dissipative systems. Despite its quite different rationale, the results are only slight modifications of those obtained by the application of Duffing’s method, indicating that the two are facets of the same fundamental process.
Remarks on Combined Bending and Twisting of Thin Tubes in the Plastic Range
Authors: Onat E. T. , Shield R. T. 
Published: June 2021

Abstract
The influence of the loading program on the agreement between the predictions of the Hencky and the Prandtl-Reuss stress-strain relations for a perfectly plastic material is investigated in the case of the combined bending and twisting of thin-walled tubes. The agreement in the values of the bending and twisting moments is found to vary considerably with the particular loading program chosen. The analysis is extended to tubes composed of a work-hardening material. The bending and twisting moments are obtained numerically using the incremental approach for a square tube which is bent and then twisted. Owing to the large amount of labor involved in this solution, an approximate method using the concept of a “composite” beam is developed, and good agreement in the results is found with those obtained from the incremental solution.
Analysis of Viscous Laminar Incompressible Flow Through Axial-Flow Turbomachines With Infinitesimal Blade Spacing
Authors: Torda T. P. , Hilton H. H. , Hall F. C. 
Published: June 2021

Abstract
The Lorenz theory has been extended to the viscous, laminar, incompressible flow through axial-flow turbo-machines with infinitesimal blade spacing. Expressions are derived for the velocity components, pressure, power input and output for arbitrary blade surfaces. A numerical example is presented and the flow variables and blade surfaces are plotted.
Temperature Distribution in the Wake of a Heated Sphere
Authors: Baer D. H. , Schlinger W. G. , Berry V. J. , Sage B. H. 
Published: June 2021

Abstract
The temperature distribution in the wake of a heated sphere 0.5 in. diam was determined at a gross stream velocity of 30 fps. Measurements were carried out in a channel 0.70 in. in height and 12 in. in width. The surface temperature of the sphere and the energy dissipation from it were determined as a function of gross stream velocities between 10 and 90 fps. The temperature distribution in the wake was correlated on the basis of methods developed for cylinders and satisfactory agreement was obtained.
The Measurement of Acceleration Pulses With the Multifrequency Reed Gage
Authors: Shapiro Henry , Hudson D. E. 
Published: June 2021

Abstract
It is shown that the data recorded by a multifrequency reed gage can be used to derive information concerning the time history of the exciting motion. If the general shape of an exciting acceleration-time pulse is known approximately, then reed-gage data alone will permit calculations of peak acceleration, time duration of pulse, and time to peak acceleration. A study of response curves for typical pulses will give design data on the proper frequencies, frequency distributions, and damping for the individual elements of the gage. Response curves for a series of typical pulse shapes are determined by electric-analog-computer methods, and are presented in dimensionless form.
Design of Helical and Leaf Springs for Minimum Weight
Authors: Spotts M. F. 
Published: June 2021

Abstract
This paper presents equations for the direct determination of the proportions of a helical spring which will contain the least possible amount of material. In general, it is possible by this method to effect considerable economies over a spring whose dimensions have been selected arbitrarily. The advantages are illustrated by numerical examples. The method also has been applied to leaf springs and design equations are presented.
Measurements of Torsional Stiffness Changes and Instability Due to Tension, Compression, and Bending
Authors: Engel H. L. , Goodier J. N. 
Published: June 2021

Abstract
The measurements reported verify theoretically predicted effects of tension, compression, and bending, on the torsional stiffness of uniform bars of thin-walled open section. Related modes of buckling and types of nonlinear behavior in torsion are indicated analytically and exhibited in tests, some of these being apparently new.
Reflection of Flexural Waves at the Edge of a Plate
Authors: Kane T. R. 
Published: June 2021

Abstract
The reflection of straight-crested flexural waves at the edge of a semi-infinite plate is studied in terms of a two-dimensional plate theory. It is found that, in general, a flexural wave propagated toward the edge at an arbitrary angle of incidence gives rise to three reflected waves: two flexural waves and a shear wave. A number of special cases, involving degenerate forms of these motions, are investigated in detail.
Impulsive Response of Beams in the Elastic and Plastic Regions
Authors: Thomson W. T. 
Published: June 2021

Abstract
The problem of the impulsive response of a beam in the elastic and plastic regions is discussed. The beam in the plastic region is simulated by yield hinges where the moment reaches a constant yield value. Transition from the elastic to the plastic beam, including the satisfaction of the initial conditions imposed on the plastic beam, is accomplished automatically in terms of the normal mode solution of each. A practical computing scheme making use of the electronic analog computer is described. Some elastic-plastic solutions obtained by the computer are presented.
The Anticlastic Curvature of a Strip With Lateral Thickness Variation
Authors: Fung Y. C. , Wittrick W. H. 
Published: June 2021

Abstract
The large deflection equations of von Kármán have been extended to apply to plates of variable thickness with initial deviations of the middle surface from a plane. These are used to determine the distortion of the cross section of a strip with lateral thickness variation, when bent uniformly in the longitudinal direction. Numerical calculations are made for the case of a strip whose cross section is of double-wedge shape and it is shown that when the longitudinal curvature becomes large the distortion of the cross section is quite different from that of a strip of uniform thickness.
Plastic-Rigid Analysis of a Special Class of Problems Involving Beams Subject to Dynamic Transverse Loading
Authors: Conroy Margaret F. 
Published: June 2021

Abstract
The object of this paper is to show that in certain circumstances the plastic deformation of beams, made of a material with linear strain hardening and subject to dynamic transverse loading, can be determined by the techniques used in solving elastic problems. In particular, the differential equation of motion for such beams is in some instances of the same form as in the corresponding linear elastic case, and so any of the methods employed for solving elastic-beam problems, such as the normal-mode method, Laplace-transform method, or Boussinesq’s solutions for infinite beams, can be used. Because of this linear character of the differential equation of motion encountered in the analysis presented here, it also is shown that some initial-motion problems for beams undergoing large plastic deformations due to transverse loading can be solved by superposing solutions. In these problems the disturbance part of the solution is obtained by some elasticity technique and is then superposed on the initial motion of the beam. The method of solution is demonstrated by means of several examples involving finite beams. The first example is an initial-motion problem and illustrates the method of superposition. The second example is an initial-stress problem for a simply supported beam. Again, the method of superposition is used. The last example is a free-boundary problem for a cantilever beam. This problem is solved by an inverse method whereby the form of the solution is assumed and the physical problem associated with this solution is then determined.
Forced Motions of Timoshenko Beams
Authors: Herrmann G. 
Published: June 2021

Abstract
Timoshenko’s theory of flexural motions in an elastic beam takes into account both rotatory inertia and transverse-shear deformation and, accordingly, contains two dependent variables instead of the one transverse displacement of classical theory of flexure. For the case of forced motions, the solution 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 the property of orthogonality of the principal modes of free vibration and uses the procedure of R. D. Mindlin and L. E. Goodman in dealing with time-dependent boundary conditions. Thus the most general problem of forced motion is reduced to a free-vibration problem and a quadrature.
The Effect of Elliptic Holes on the Bending of Thick Plates
Authors: Naghdi P. M. 
Published: June 2021

Abstract
The effects of an elliptic hole on both plain bending and pure twist of an elastic plate are investigated by application of the recent theory for bending of plates due to E. Reissner, where the influence of shear deformation and transverse-normal stress is taken into account. The stress-concentration factors are given for both cases mentioned. The solution, which is approximate in character, involves modified Mathieu functions of the second kind. In limiting cases, the results reduce exactly to the solution of corresponding problems with circular hole, as well as to the predictions of the classical theory of plates.
Fracture of Inoculated Iron Under Biaxial Stresses
Authors: Cornet I. , Grassi R. C. 
Published: June 2021

Abstract
Data are presented on the fracture of inoculated-iron thin-wall tubes, investigated under various ratios of axial to tangential stress, ranging from pure tension to pure compression. These data are consistent with published data on gray cast iron. It may be assumed that in cast-iron, plates of friable graphite in an iron matrix, act like solid iron with respect to compressive stresses, but they act as stress-concentrating cavities with respect to tensile stresses. This gives a stress-concentration factor, which is easily determined experimentally. Stress-concentration factors obtained were 3.2–3.3 for gray cast iron, and 2.4–2.5 for inoculated cast iron. A distortion-energy criterion for fracture, modified by this stress-concentration factor, is consistent with the experimental data. It appears that the concentration of the dispersed graphite, and the shape and size of this brittle phase, affect the fracture strength under combined stresses.
Determination of Thermal Stresses in Three-Ply Laminates
Authors: Durelli A. J. , Tsao C. H. 
Published: June 2021

Abstract
The knowledge of the distribution of stresses produced in three-ply laminates when the temperature changes is very important in the design of airplane windshields. This paper gives the result of a photoelastic investigation on the thermal stresses produced in a three-ply laminate consisting of glass, polyvinyl butyral, glass, when the temperature drops slowly from 70 to −20 F. The maximum stress has been found to be about six and one-half times the average longitudinal stress at the mid-section of the glass. Failure characteristics of the laminates check well with these findings. No new methods have been developed in the paper; however, the presently available techniques had to be applied carefully to determine maximum tensile stresses of about 1300 psi on the interface, at a distance of about 0.007 in. from the edge, at low temperature.
Load Distribution at the Intersection of Several Coaxial Axisymmetric Shells
Authors: Becker H. 
Published: June 2021

Abstract
A relaxation analysis of the load distribution at the intersection of several axisymmetric coaxial shells is presented. The relaxation process leads to an infinite power series, the summation of which yields explicit expressions for the individual shell loads. The shells are all assumed to be unconstrained axially, thus eliminating axial interaction effects among them. The analysis, consequently, is restricted to radial shear forces and distributed moments at the intersection line, which is taken in a plane perpendicular to the common axis of the shells. Methods of treating temperature and pressure effects are described, and an illustrative example of the analysis of a three-shell intersection is included.
Solving Highly Complex Elastic Structures in Easy Stages
Authors: Kron Gabriel 
Published: June 2021

Abstract
A systematic procedure is presented to solve quickly very large elastic structures, containing hundreds of component elements. The method is not competitive with existing techniques of solving sets of linear equations and is to be used only when other methods prove inadequate to cope with the capacity of the available computer (slide rule or electronic). Extension of the method—shown here for beams with one dominant dimension only—to structural components having more general and arbitrary shapes should be obvious to those versed in the art of structural analysis.
Stress Distribution in a Uniformly Rotating Equilateral Triangular Shaft
Authors: Johnson H. T. 
Published: June 2021

Abstract
An approximate solution for the distribution of stresses in a rotating prismatic shaft, of triangular cross section, is presented in this paper. A general method is employed which may be applied in obtaining approximate solutions for the stress distribution for rotating prismatic shapes, for the cases of either generalized plane stress or plane strain. Polynomials are used which exactly satisfy the biharmonic equation and the symmetry conditions, and which approximately satisfy the boundary conditions.
Heat-Transfer Measurements in an Inexpensive Supersonic Wind Tunnel: 2—Results for a Laminar Boundary Layer Based on a Two-Dimensional Flow Model
Authors: Kaye Joseph , Brown G. A. 
Published: June 2021

Abstract
Reliable experimental data on local heat-transfer coefficients for supersonic flow of air in a round tube are reanalyzed in detail with the aid of an approximate two-dimensional flow model. The results are compared with similar results based on a one-dimensional flow model and with the theoretical predictions for supersonic flow over a flat plate and for flow in the entrance region of a tube when a laminar boundary layer is present. The two-dimensional flow model yields a better understanding of the phenomena which occur for diabatic supersonic flow of air in a round tube than that obtained with the aid of the one-dimensional flow model. The two-dimensional flow model shows that the core Mach number is nearly constant along the length of test section for a range of values of the inlet diameter Reynolds number. For a laminar boundary layer the values of the local Stanton number agree within a few per cent with the theoretical values for plate flow at the largest values of the inlet diameter Reynolds number.
The Root Section of a Swept Wing—A Problem of Plane Elasticity
Authors: Hoskin B. C. , Radok J. R. M. 
Published: June 2021

Abstract
The methods of N. I. Muskhelishvili are used to obtain the stresses in an approximately square plate, subject to concentrated forces at two opposite corners, acting in the direction of the diagonal, and to certain shear-stress distributions along the sides. These shear-stress distributions have been chosen to conform approximately with those observed at the corresponding boundaries during tests on a 45-deg sweptback tube with ribs normal to the leading edge. Numerical results, involving loading parameters, are presented in the form of tables and graphs. Use of the numerical results is illustrated by application to a wing under varying degrees of torsion and bending.
Vibrations of a Helicopter Rotor-Fuselage System Induced by the Main Rotor Blades in Flight
Authors: Morduchow M. , Yuan S. W. , Reissner H. 
Published: June 2021

Abstract
Based on a simplified model of the hub-fuselage structure, a theoretical analysis is made of the response of the hub and fuselage of a helicopter in flight to harmonic forces transmitted by the rotor blades to the hub both in, and normal to, the plane of rotation. The assumed structure is in the form of a plane framework with masses concentrated at the joints. Simple expressions are derived for the vibration amplitudes of the mass points as functions of the masses and natural frequencies of the hub and the fuselage. The pertinent nondimensional parameters are determined, and simple explicit conditions of resonance are derived. Numerical examples are given to illustrate the results.
On the Kinematic Path of Semi-Trailers
Authors: Fazekas G. A. G. 
Published: June 2021

Abstract
A trailer having a rigid axle does not quite follow the path of its tractor. The author describes the basic geometry and kinematics involved. The subject matter is arranged under headings (a) transient trailer path in turn, (b) design criterion, and (c) transient trailer path when straightening out.
Plastic Deformations of a Free Ring Under Concentrated Dynamic Loading
Authors: Owens R. H. , Symonds P. S. 
Published: June 2021

Abstract
A concentrated time-dependent force acts on an unsupported thin ring along a diameter. The problem considered in this paper is to determine the deformations of the ring when the force magnitudes are such that plastic strains large compared with elastic strains occur. By neglecting elastic strains and assuming ideally plastic behavior, approximations to the final deformations of the ring are obtained. The analysis is developed for force pulses of arbitrary shape, but numerical results are obtained only in the special case of a rectangular force pulse. A criterion is stated for conditions when this type of analysis can be expected to provide satisfactory results.
Large Plastic Deformations of Circular Membranes
Authors: Weil N. A. , Newmark N. M. 
Published: June 2021

Abstract
An investigation is presented for the plastic behavior of clamped circular membranes subjected to hydrostatic pressure, based on the Hencky-Mises theory. New strain-displacement relations, valid for finite deformations in the plastic domain, are introduced. The solution is presented in terms of two simultaneous implicit integral equations, which can be solved by numerical methods. The solution also permits the formulation of the instability condition. Experimental work consisted of bulge tests carried out on annealed copper plates of two thicknesses, whose τ-γ curve was previously determined from uniaxial tests. A good correlation is obtained between theoretical predictions and experimental results.
The Affine Transformation for Orthotropic Plane-Stress and Plane-Strain Problems
Authors: Lang H. A. 
Published: June 2021

Abstract
It is demonstrated that a single affine transformation of the type x = ax′, y = by′ immediately extends the solution of any isotropic plane-stress or plane-strain problem to the solution of an orthotropic plane problem where the orthotropic material is characterized by three independent constants. Since orthotropy, defined as elastic symmetry with respect to two orthogonal axes, implies four independent elastic constants, the affine transformation introduces a restriction upon the orthotropic shear modulus. The orthotropic shear modulus differs from that used by previous investigators. This difference alters the equation which the orthotropic stress function must satisfy and, therefore, directly affects the solution to every plane-stress or plane-strain problem. Some arguments are advanced to favor the shear modulus, as here defined, whenever orthotropy must be restricted to three elastic constants. The two solutions of the orthotropic half plane subjected to a normal concentrated load are contrasted to illustrate the effect of the two definitions of orthotropic shear modulus.