bluuebunny/crossref_metadata_2025 huggingface dataset:
Axial Impact of Short Cylindrical Bars
Authors: Conway H. D. , Jakubowski M.
Published: October 2011

A modification of the classical Hopkinson-bar apparatus is used to develop a method for investigating wave propagation in axially impacted cylindrical bars of short length. Strain-gage records were obtained which give the axial strains (as a function of time) induced at the curved surfaces of the cylinders. The axial strains and durations of impact were calculated by using Love’s equation to solve the problem of two bars colliding with equal but opposite velocities. Axial strains were also computed from this equation for bars having step and ramp pressure loading on one end. Finally, comparisons made between experimental and analytical results indicate that Love’s equation can give satisfactory results if the end loading is correctly simulated.
Effect of a Suction Upon Laminar Flow Along a Vertical Wall
Authors: Khan M. A. A.
Published: October 2011

The laminar flow of a thin film past a vertical wall subjected to suction is studied. An approximate solution for small porosity is obtained in the accelerated region. A relation between film thickness and distance traveled is presented.
General Properties of Yield-Point Load Surfaces
Authors: Hodge P. G. , Sun Chang-Kuei
Published: October 2011

A structure made of a rigid perfectly plastic material and subjected to more than one independent load is considered. A mode vector is defined for any plastic mechanism and shown to have the same properties relative to the yield-point load interaction surface that the strain-rate vector has to the material yield surface. An application to a circular plate under two independent loads leads to close bounds on the interaction curve.
Application of a Perturbation Technique Based on the Method of Characteristics to Axisymmetric Plasticity
Authors: Richmond O. , Morrison H. L.
Published: October 2011

A perturbation technique is described which may be used for obtaining approximate solutions in plasticity when the field equations are hyperbolic. The characteristic parameters of the exact equations are employed as independent variables. The technique has been used to a limited extent in supersonic fluid mechanics, but not fully exploited. It apparently has not been used before in plasticity. As an example, an upper-bound solution is obtained to an axisymmetric problem: Expansion of a circular hole in a finite flat plate. The accuracy of the technique is illustrated by comparing the stresses with those obtained by a well-known finite-difference method. The advantages of the technique over an earlier perturbation method based on approximate characteristics are demonstrated by a comparison with a solution to the same problem obtained by that method.
Subharmonic Oscillations in an Arbitrary Tank Resulting From Axial Excitation
Authors: Chu Wen-Hwa
Published: October 2011

The problem of subharmonic liquid response in a container subjected to vertical (axial) excitation has been solved to the first approximation by the method of perturbation, employing characteristic functions. In principle, the tank can be arbitrary. However, the computational effort required to construct the characteristic functions and their derivatives may limit the application to tanks of relatively simple geometry such as a compartmented axisymmetric tank. As a check of the theoretical result, the simplest example for a rectangular tank is given, and the results are in good agreement with experiments and a third-order theory by Yarymovych.
Fully Developed Flow in a Permeable Annulus
Authors: Terrill R. M.
Published: October 2011

In a recent paper, Das [1] considered the slow steady flow of a viscous fluid in an annulus with uniform, small, but arbitrary, injection and suction velocities along the walls. The purpose of this Note is to show how to obtain the general fully developed solution for a permeable annulus. It is shown how this solution reduces, when the injection or suction is small, to that given by Das and a few comments are made on Das’ paper.
On the Dynamic Response of a Beam to a Randomly Moving Load
Authors: Knowles J. K.
Published: October 2011

The problem considered is that of an infinitely long elastic beam subject to a moving concentrated force whose position is a stochastic function of time, X(t). The expected deflection and expected bending moment are analyzed, with special attention being given to the case of a stationary process X(t) and to the case in which X(t) is a Wiener process.
Dynamic Plastic Buckling of Cylindrical Shells in Sustained Axial Compressive Flow
Authors: Florence A. L. , Goodier J. N.
Published: October 2011

A theory is postulated to explain the dynamic plastic buckling of cylindrical shells in sustained axial compressive flow. Tube impact experiments are described in which uniform axisymmetric waves were produced. Predicted and experimental wavelengths are in satisfactory agreement. According to the theory presented, wavelengths do not depend strongly on strain-hardening modulus and, based on results for two aluminum alloys, neither do experimental wavelengths. This result is shown to apply also to slow plastic buckling.
Plastic Flow of Rock Under a Pointed Punch in Plane Strain
Authors: Paslay P. R. , Cheatham J. B. , Fulcher C. W. G.
Published: October 2011

Solutions are presented for the plane-strain plastic flow of rock under a pointed punch for two cases. In the first problem the indentation of a half space by a pointed punch is considered, and in the second the influence of a previous indentation on the formation of the next indentation is evaluated. The plasticity theory used in this analysis was developed by the authors earlier for rock mechanics applications. This theory incorporates a yield surface which is dependent on the mean normal stress and normality of the deformation rate vector to the yield surface. Work-hardening and elastic strains are neglected in the theory. These solutions furnish the analytical basis for some elementary experiments which may help to evaluate the theory.
Potential Vortex Flow Adjacent to a Stationary Surface
Authors: Kidd G. J. , Farris G. J.
Published: October 2011

The equations describing the flow produced by the interaction of a potential vortex with a stationary surface are solved by means of similarity transformations. In previous attempts at solutions, use was made of the boundary-layer approximations (in which case no solution can be obtained) or a particular form was assumed for one of the velocity components. In this analysis, where the only restriction is that the flow be similar, solutions are obtained for tangential Reynolds numbers up to 4.75. The numerical method employed is based on a recently proposed technique for solving ordinary differential equations with asymptotic boundary conditions.
Optimal Design of an Elastic Column of Thin-Walled Cross Section
Authors: Huang N. C. , Sheu C. Y.
Published: October 2011

This paper treats the optimal design of a vertical column that is built-in at the lower end. In addition to its own weight, the column is to carry an axial compressive load at its unsupported upper end. The column is to be designed as a thin-walled tube. The median line is to be the same for all cross sections; the wall thickness, though constant along the median line of any cross section, is allowed to vary along the length of the tube. Accordingly, the weight per unit length of the tube is proportional to the bending stiffness. For given length and total weight, the variation of the wall thickness along the column is to be determined to maximize the critical value of the compressive load at the upper end. The influence of a maximum allowable compressive stress on the design is also investigated.
On the Unstable Vibrations of a Shaft With Unsymmetrical Stiffness Carrying an Unsymmetrical Rotor
Authors: Yamamoto T. , O¯ta H. , Ko¯no K.
Published: October 2011

In a rotating shaft system carrying an unsymmetrical rotor, or in a rotating shaft system with inequality in stiffness, there are unstable regions in the neighborhood of both the major critical speed ωc and the rotating speed ωd at which the sum of two natural frequencies of the system is equal to twice the rotating speed of the shaft. The unstable vibrations appearing in these unstable regions are treated for the system consisting of a rotor with unsymmetrical inertia and a shaft with unequal stiffness which rotates with the rotor. Simultaneous effects of the unsymmetrical rotor and the unsymmetrical shaft are appreciated and quantitative analytical results are obtained which relate the width of the unstable regions and the negative damping coefficients of the unstable vibrations to the asymmetry in inertia, the inequality in stiffness, and the relative orientation between the inequalities in inertia and stiffness. Furthermore, elimination of two kinds of unstable regions is realized theoretically and experimentally.
Dynamic Expansion of a Spherical Cavity in an Elastic, Perfectly Plastic Material
Authors: Mok Chi-Hung
Published: October 2011

It is shown that initial and boundary-value problems involving high-speed elastic-plastic deformation with spherical symmetry can be solved using a finite-difference numerical technique. Numerical solutions for the dynamic expansion of a spherical cavity under a constant pressure are presented to demonstrate the nature and capability of the numerical scheme. While the solution for an elastic material agrees closely with the exact one, the solution for an elastic, perfectly plastic material also receives support from Green’s analytic predictions concerning the motion of the elastic-plastic boundary. At large times, the asymptotic solution of the dynamic elastic-plastic problem is different from the quasi-static solution. This result indicates that the concept of quasi-static approximation may not hold in dynamic plasticity. A nonlinear dependence of the plastic solution on the boundary condition is also observed.
Notes on Nonlinear Shell Theory
Authors: Budiansky Bernard
Published: October 2011

Exact tensor equations of equilibrium are derived for nonlinear membrane shell theory and small perturbations of pressurized membrane shells. Approximate equations (for sufficiently small initial strains and rotations) for small perturbations of pressurized membrane shells are also given. Exact equations for the general nonlinear shell theory (including bending) are discussed, and approximate equations (again for small initial strains and rotations) are derived for the small perturbations, buckling, and vibration of stressed shells. These last equations are given in an Appendix in lines-of-curvature coordinates in classical notation.
Optimization of a Slot End Configuration in a Finite Plate Subjected to Uniformly Distributed Load
Authors: Durelli A. J. , Parks V. J. , Uribe S.
Published: October 2011

Two-dimensional photoelasticity is used to determine the distribution of stresses at the ends of a transverse slot symmetrically located in the uniform field of a thin birefringent strip subjected to tension. The ends of the slot are ellipses with different axes ratios, ranging from a flat ellipse to a semicircle. The stress-concentration factors are found for different ratios of the transverse width of the slot to the total width of the tensile specimen. Optimum shapes are given for each ratio of the transverse width of the slot to the total width of the tensile specimen. The results obtained may prove useful in the design of solid propellant grains.
The Timoshenko Beam With a Moving Load
Authors: Steele C. R.
Published: October 2011

The problem of a semi-infinite Timoshenko beam of an elastic foundation with a step load moving from the supported end at a constant velocity is discussed. Asymptotic solutions are obtained for all ranges of load speed. The solution is shown to approach the “steady-state” solution, except for three speeds at which the steady state does not exist. Previous investigators have considered only the steady-state solution for the moving concentrated load and have indicated that the three speeds are “critical.” It is shown, however, that only the lowest speed is truly critical in that the response increases with time. For the load speed equal to either the shear or bar velocity, the transients due to the end condition never leave the vicinity of the load discontinuities, so a steady-state condition is never attained. However, the response is shown to be bounded in time for a distributed load. Thus the nonexistence of a steady state does not necessarily indicate a critical condition. Furthermore, the concentrated load solution is shown to have validity at speeds the magnitude of the sonic speeds only for loads of a concentration beyond the limitations of beam theory. Asymptotic results have also been obtained for the beam without a foundation. Since the procedure is similar for beams with, and without, a foundation, only the results are included to show a comparison with the numerical results previously obtained by Florence.
On Inextensional Vibrations of Thin Shells
Authors: Ross E. W.
Published: October 2011

In this paper the nonsymmetric, free, elastic vibrations of thin domes of revolution are studied. It is assumed that the frequency is low. The asymptotic approximations previously given by the writer are used to estimate the general solution to the shell vibration equations at low frequencies. Approximations for the low natural frequencies and modes are derived systematically under a variety of edge conditions. Low natural frequencies are found only when the edge conditions impose no forces tangent to the shell surface. When the edge is free (and only then) Rayleigh’s inextensional frequencies are recovered. For certain other edge conditions, new natural frequencies are found that are above Rayleigh’s frequencies but still low compared, e.g., with the lowest membrane frequency. The displacement modes associated with these new frequencies are mostly of inextensional type. The general results are applied to estimate these new frequencies for spherical domes.
Axially Symmetric Creep Buckling of Circular Cylindrical Shells in
Axial Compression
Authors: Hoff N. J.
Published: October 2011

The creep-buckling phenomenon of circular cylindrical shells subjected to axial compression is studied in the presence of initial imperfections when the creep strain rate is proportional to a power of the stress with the exponent greater than unity. A closed-form solution is obtained for the critical time; that is, for the finite time at which the analysis predicts the development of indefinitely large displacements.
Gyroscopic Drifts Associated With Rotational Vehicle
Vibrations
Authors: Wenglarz R. A. , Kane T. R.
Published: October 2011

Exact dynamical and kinematical equations governing motions of a two-degree-of-freedom gyroscope mounted on a moving vehicle are formulated. From these equations, a set of simpler ones is derived by taking advantage of a number of experimentally verifiable facts, and this set is solved for a vehicle performing oscillations of small amplitude about an axis having an arbitrary orientation. The validity of the resulting drift theory is established by comparing its predictions with those of digital computer solutions of the exact equations of motion, and formulas relating drift rates to system parameters are presented.
Symmetric Arc Solutions of ζ¨ =
ζn
Authors: Atkinson C. P. , Dhoopar B. L.
Published: October 2011

This paper, "Symmetric Arc Solutions of ζ¨ = ζn," presents periodic solutions of this differential equation relating the complex variable ζ(t) = u(t) + iv(t) and its second time derivative ζ¨ The solutions are called symmetric arc solutions since they form such arcs on the ζ = u + iv-plane. The solutions, ζ(t), are “complex modes” of coupled nonlinear differential equations in the complex variables z1 and z2. Symmetric arc solutions are presented for a range of n from n = 3 to n = 101. Approximate solutions are presented and compared with solutions generated by digital computer. Solutions are presented on the ζ-plane and in the time domain as u(t) and v(t).
Collapse of a Gas-Filled Spherical Cavity
Authors: Jahsman W. E.
Published: October 2011

The PLK coordinate perturbation technique [10] is used to obtain a solution to the problem of collapse of gas-filled spherical cavity in an infinite compressible liquid. The gas is assumed to undergo quasi-static adiabatic compression and the liquid equation of state is taken to follow the modified Tate form [11]. The approach was first outlined by Benjamin [9] and in the present paper expressions for cavity wall history and fluid pressure, density, and particle velocity are carried out in complete detail for the first three terms in the expansions. It is found that the solutions for the variables can all be written as products of functions which depend on only one of the perturbed coordinates. For the coordinate corresponding to outward traveling characteristics (first used by Whitham [12]), only two functions are required; they are associated with cavity wall position and with velocity and satisfy second-order ordinary differential equations which are readily solved by digital computer. For the remaining coordinate (perturbed radius) the functions are all polynomials. A numerical example is presented and curves of cavity wall position, pressure, and velocity histories are given for the period associated with collapse and rebound of the cavity. Results are compared with earlier work based on the Gilmore adaptation of the Kirkwood-Bethe formulation [8], and good agreement is found.
Vibratory Motion of a Body on an Elastic Half Plane
Authors: Karasudhi P. , Keer L. M. , Lee S. L.
Published: October 2011

The vertical, horizontal and rocking vibrations of a body on the surface of an otherwise unloaded half plane are studied. The problems are formulated so that one stress vanishes over the entire surface, and an oscillating displacement is prescribed in the loaded region. The problems are mixed with respect to the prescribed displacement and the remaining stress. Each case leads to a mixed boundary value problem represented by dual integral equations which are reduced to a single Fredholm integral equation. Although numerical methods are used to solve the integral equation, the contact stresses are found to be presentable in closed form to good accuracy. An estimate of the stiffnesses for coupled horizontal and rocking vibration is also suggested and it is found that the coupling effect is significant.
On the Diffusion of Load From a Transverse Tension Bar Into a Semi-Infinite Elastic Sheet
Authors: Muki R. , Sternberg E.
Published: October 2011

This paper deals with the load diffusion from a tension bar of finite length and uniform cross section into a semi-infinite sheet, the axis of the bar being perpendicular to the edge of the sheet. The bar is regarded as a one-dimensional elastic continuum, whereas the elastic sheet is treated within the two-dimensional theory of generalized plane stress. Three alternative models for the stringer-attachment are considered: (a) line-contact, (b) area-contact based on matching the axial stringer-strain and the corresponding average sheet-strain across the width of the strip of adhesion, and (c) area-contact based on matching the stringer strain and the corresponding sheet-strain along the center line of the strip of adhesion. It is shown that the line-contact model, in contrast to both area-contact models, does not admit the transmission of portions of the applied load through forces concentrated at the ends of the adhering bar segment. Further, asymptotic estimates are deduced for the end slopes of the load-diffusion curves appropriate to the three models under consideration. The integro-differential equation for the stringer-force in Case (b) and Case (c) is reduced to a standard Fredholm integral equation, which is solved numerically. The results thus obtained are compared with available experimental findings.
Photoelastic Study of High-Frequency Stress Waves Propagating in Bars and Plates
Authors: Clark J. A. , Durelli A. J. , Parks V. J.
Published: October 2011

This paper deals with the photoelastic analysis of stress waves in bars and plates subjected to damped sinusoidal loading. The device used to apply the loading is a piezoelectric transducer which produces about 10 cycles of a decaying sine wave. The wavelength of the stress wave which propagates along the square bar is comparable to the thickness of the bar. A strobotac, or a microflash, is used as light source flashing with a continuously variable delay. The isochromatics and isoclinics can be seen directly by eye as static patterns. More than 100 repetitions of illumination can be used, permitting the use of fine grain film. The specimens are relatively thick, but by using embedded polarizers and analyzers, two-dimensional solutions can be obtained. Good correlations with theoretical computations are shown for phase and group velocities. Stress distributions are determined along the center line and the edge of the bar.
Perturbation Solutions for the Buckling Problems of Axially Compressed Thin Cylindrical Shells of Infinite or Finite Length
Authors: Dym C. L. , Hoff N. J.
Published: October 2011

A study is presented of the effect of initial deviations on the load carrying capacity of thin circular cylindrical shells under uniform axial compression. A perturbation expansion is used to reduce the nonlinear equations of von Karman and Donnell to an infinite set of linear equations, of which only the first few need be solved to obtain a reasonably accurate solution. The results for both infinite shells and shells of finite length indicate that a small imperfection can sharply reduce the maximum load that a thin-walled cylinder will sustain. In addition, for a particular set of boundary conditions, it is shown that the effect of the length of a finite shell is small as far as the load carrying capacity is concerned, but significant when the number of waves around the circumference has to be determined. A further result of the study is that axisymmetric initial deviations reduce the load carrying capacity only slightly more than deviations characterized by a product of trigonometric functions of the axial and circumferential coordinates if the wave lengths are properly chosen.
Approximate Solutions for Impulsively Loaded Elastic-Plastic Beams
Authors: Martin J. B. , Lee L. S.-S.
Published: October 2011

A unified method of approximating the response of rigid-plastic and elastic, perfectly plastic beams subjected to impulsive loading is described. The method is based on the uniqueness proof for such problems. A simply supported beam subjected to a uniform impulse is given as an illustrative example.
Theory of the Bathtub Vortex
Authors: Marris A. W.
Published: October 2011

The paper gives an analysis of the temporal growth of vorticity when water contained in a large vertical cylindrical tank flows out through a small hole in the base of the tank. The results indicate both an exponential growth of vorticity from the rotation of the frame of reference and an exponential growth of the residual vorticity in the water. Two main cases are considered; (a) the case when the initial swirl component does not vary in the vertical direction, (b) the case when the swirl component decreases downwards. The latter case simulates the effect of a tank bottom boundary layer or other vertical shear layer on the vorticity growth. While the analysis relates to a simplified model of the physical situation and also entails approximations, it nevertheless indicates that when a downwardly decreasing gradient of swirl velocity exists, a reversal from an initial clockwise residual swirl to a final counterclockwise rotation (in the Northern Hemisphere) may be anticipated. This is in accord with cited experimental results.
Plane Thermal Stress at an Insulated Hole Under Uniform Heat Flow in an Orthotropic Medium
Authors: Chen W. T.
Published: October 2011

When a uniform heat flow in an infinite orthotropic solid is disturbed by the presence of a long circular insulated cavity, local intensification of the temperature gradient occurs in the neighborhood of the cavity. This report describes a study of the stress field induced by the temperature distribution. The linear plane (plane stress or plane strain) thermoelastic problem is solved by using the complex variable technique. The analysis may also be used for other steady-state thermal stress problems in an orthotropic medium.
Asymptotic Solution for Infinite Cylinder Reinforced by Radially Loaded Ring
Authors: Vafakos W. P.
Published: October 2011

An asymptotic expansion procedure proposed by E. Reissner is applied to the simple Donnell equations for circular cylindrical shells, and a simple explicit solution is obtained for the interaction problem of an infinite cylinder reinforced by a central ring subjected to a nonuniform radial load. It is shown that the sign of the dominant stresses depends entirely upon whether the shell is reinforced by inside or outside rings. In addition, even when only the lower harmonic contributions are retained, good agreement with an exact solution for the case of concentrated loads is achieved.
Journal-Bearing Velocity Profiles for Small-Eccentricity and Moderate Modified Reynolds Numbers
Authors: Kulinski E. S. , Ostrach S.
Published: October 2011

The velocity profiles for an infinite, cylindrical bearing are obtained by means of a small-eccentricity perturbation calculation. The modified Reynolds number appears as a parameter, and velocity profiles are presented for modified Reynolds numbers of 10−3, 10−2, 10−1, 1, 10, and 102. The most significant difference in the velocity profiles for the various Reynolds numbers is the appearance of components which are 90 deg out of phase with the film thickness at the larger values of the modified Reynolds number. The consequences of these components are discussed.
On Nonlinear Analysis of Elastic Shells of Revolution
Authors: Kalnins A. , Lestingi J. F.
Published: October 2011

A multisegment method is developed for the solution of two-point boundary-value problems governed by a system of first-order ordinary nonlinear differential equations. By means of this method, rotationally symmetric shells of arbitrary shape under axisymmetric loads can be analyzed with any available nonlinear bending theory of shells. The basic equations required by the method are given for one particular theory of shells, and numerical examples of a shallow spherical cap and a complete torus subjected to external pressure are presented in detail. The main advantage of this method over the finite-difference approach is that the solution is obtained everywhere with uniform accuracy, and the iteration process with respect to the mesh size, which is required with the finite-difference method, is eliminated.
An Experimental Investigation of Elastic-Plastic Pulse Propagation in Aluminum Rods
Authors: Bodner S. R. , Clifton R. J.
Published: October 2011

Experiments are reported involving elastic-plastic pulses due to explosive loading at one end of long, annealed, commercially pure, aluminum rods at room temperature and at elevated temperatures up to 750 deg F. The stress waves were detected by a condenser microphone at the far end of the rod and, in some cases, by strain gages at a cross section distant from the impact end. The essential features of the recorded velocity-time profiles and strain-time profiles are found to be in agreement with the predictions of rate independent elastic-plastic theory which takes a Bauschinger effect into account. At room temperature, the reference dynamic stress-strain curve does not differ appreciably from the quasi-static stress-strain curve whereas at elevated temperatures there appears to be a marked difference between the dynamic and quasi-static stress-strain curves. The experiments also serve to determine the dynamic proportional limit which is found to be fairly insensitive to temperature. Since the maximum plastic strains are small at cross sections remote from the impact end, the measurements, and consequently the conclusions, are limited to small strains beyond the proportional limit.
Lower Bounds to the Critical Rayleigh Number in Completely Confined Regions
Authors: Sherman M. , Ostrach S.
Published: October 2011

A method is presented for estimating lower bounds to the minimum Rayleigh number that will induce a state of convective motion in a quasi-incompressible (Boussinesq) fluid where the temperature gradient is in the direction of the body force. The fluid is completely confined by fixed-temperature, rigid bounding walls. For any arbitrary region, the critical Rayleigh number is greater than 1558(h/D)4 where h is the maximum dimension of the given region in the direction of the body force and D is the diameter of an equal volume sphere. In certain simple geometrical configurations, improved lower-bound estimates are calculated.
Response of a Rigid-Plastic Ring to Impulse Loading
Authors: Cline G. B. , Jahsman W. E.
Published: October 2011

Formulas are derived which describe the dynamic response of a ring of rigid-plastic material which is subjected to an arbitrarily distributed impulse load. When the impulse is distributed over half the ring in a cosine fashion, the final deformation is proportional to the square of the maximum magnitude of the applied impulse. Although the predominant deformation is in a bending or “ovaling” mode, one half of the incident energy is dissipated in the “membrane” or direct stress mode. The remainder is divided equally between bending (plastic work at the hinges) and kinetic energy.
A Theory of Torsional and Coupled Bending Torsional Waves in Thin-Walled Open Section Beams
Authors: Aggarwal H. R. , Cranch E. T.
Published: October 2011

An appropriate torsion or coupled bending torsion theory is developed for the dynamic behavior of thin-walled open section beams. A new, more accurate set of governing equations is established which eliminate the short-wavelength defects of both the Saint-Venant and Timoshenko torsion theories. This theory, which includes warping and associated effects of longitudinal inertia and transverse shear deformation, while agreeing with previous theories for large wavelengths, leads to satisfactory finite wave velocities for short wavelengths and high frequencies. Dispersion and group velocity curves for wide-flanged and channel sections are displayed.
The Effects of Various Parameters on the Dynamic Stability of a Shallow Arch
Authors: Hsu C. S.
Published: October 2011

The effects of various parameters on the dynamic stability of shallow arches against snap-through when subjected to impulsive loads are investigated in this paper. The parameters are the amplitudes of the higher harmonics in the arch shape, the initial thrust, and the stiffness of the elastic supports at the arch ends. The results are expressed in terms of sufficiency regions of stability in a phase space of infinite dimensions, which, in turn, lead to simple and practical energy criteria. The study of the effects of the higher harmonics in the arch shape shows that the sufficiency stability criterion is sensitive only to the second harmonic. Moreover, for a sinusoidal arch with small amounts of imperfection, it is possible to give an explicit formula for the sufficiency criterion. The analysis presented here takes into account all modes in the response; consequently, the results are free from any uncertainties usually associated with most of the approximate analyses.
Effect of Embedding Medium Viscoelasticity on the Transient Response to Plane Waves of Arbitrarily Thick Circular Cylinders
Authors: Crouzet-Pascal Jacques , Garnet Hyman , Pifko Allan
Published: October 2011

The transient response of a circular cylinder of arbitrary thickness, embedded in a viscoelastic medium and impinged upon by plane waves, is obtained. Dilatational and shear incident waves are considered. The solution is valid within the scope of the linear theories of elasticity and viscoelasticity. The method of solution, which circumvents the difficulties encountered in the customary transform approaches, relies upon (a) the construction of a train of incident pulses from steady-state components, where each pulse represents the time history of the transient stress in the incident wave and (b) the existence of a physical mechanism that, between pulses, restores the disturbed particles of the cylinder and the surrounding medium to an unstrained state of rest. The influence on the major stress and displacement response of variations in the viscoelastic properties of the medium is investigated for the case of incident step waves. The results for the viscoelastic media are compared with corresponding results for the limiting cases of elastic-unrelaxed and elastic-relaxed media.
Initial Studies in Three-Dimensional Dynamic Photoelasticity
Authors: Dally J. W. , Riley W. F.
Published: October 2011

An initial study of stress waves propagating in a half space due to a point load on the surface has been accomplished by employing dynamic three-dimensional photoelasticity. The central plane of the half-space model was isolated for investigation by employing an embedded polariscope. Auxiliary experiments show that the thin elements of the polariscope do not significantly distort the stress wave as it propagates across the joints of the model containing the elements. Photographs of the dynamic fringe patterns were recorded with a Cranz-Schardin multiple spark gap camera operating at 400,000 fps. Three different waves were identified from the fringe patterns; namely, the incident dilatational and distortional waves and the reflected shear wave known as the von Schmidt wave. The data obtained for the shear wave in the form of isochromatic fringe orders were converted to individual values of the principal stresses along the axis of symmetry in the model. The method developed for separation of the principal stresses is only applicable when the distortional wave occurs alone along the axis of symmetry.
Normality Relations and Convexity of Yield Surfaces for Unstable Materials or Structural Elements
Authors: Palmer A. C. , Maier G. , Drucker D. C.
Published: October 2011

The stress-strain relations for materials and the load-deflection relations for structural elements play corresponding roles in the analysis of three-dimensional continua and of structures, respectively. Mathematically equivalent and phenomenologically quite similar, they are treated simultaneously here. As in previous treatments of stable (rising) plastic stress-strain curves, unstable (falling) curves in simple shear or tension are generalized to all states of stress through the exploration of the work done in a cycle of stress (Drucker) and in a cycle of strain (Ilyushin). The plastic increment of strain is found to be normal to the current yield surface for a wide class of unstable materials in which a continuous variation of strain produces a unique continuous variation of stress and of the shape and position of the yield surface. In the absence of any significant alteration in the (stable) elastic response, each yield surface then is shown to be convex. The degree of concavity possible when the elastic response is stable but is nonlinear and does alter appreciably due to plastic deformation is illustrated by a nonlinear elastic spring and a plastic block in parallel. Such concavity would not be observable in the yield surfaces of common structural metals but might be found for soils, rocks, or concrete and can be quite pronounced for structural elements.
On Plate Theory and Longitudinal Waves in Noncircular Bars
Authors: Medick M. A.
Published: October 2011

Wave propagation in elastic wave guides such as plates and bars of rectangular cross section are related phenomena. This is demonstrated for longitudinal waves within the framework of a first-order bar theory.
Laminar Flow Along a Vertical Wall
Authors: Hassan Nabil A.
Published: October 2011

The problem of laminar flow of thin fluid films is investigated theoretically. An appropriate mathematical solution is given, where surface tension is neglected. The result is one universal curve.
Fluid Drag on a Sphere Rolling in a Tube
Authors: Bauer A. B. , DuPuis R. A.
Published: October 2011

The incompressible fluid drag force on a sphere rolling at constant speed in a closed-end tube has been analyzed for the case where the tube inside diameter is only slightly larger than the sphere diameter. One drag law is found for Reynolds numbers much less than 75π/4λ1/2, where λ is a parameter defined by the sphere and tube diameters. A second drag law is found for Reynolds numbers much larger than 75π/4λ1/2. Experimental results show good agreement with these drag laws. The first law is almost identical with the results of Christopherson and Dowson, and of McNown, et al., for a sphere falling in a vertical tube.
Laminar Source Flow Between Two Parallel Coaxial Disks Rotating at Different Speeds
Authors: Kreith F. , Viviand H.
Published: October 2011

This article presents an analysis of the flow in the gap between two parallel coaxial disks rotating at different velocities, with a source in the center. The Navier-Stokes equations are solved by double series expansion about a known solution at a large radius, and velocity and pressure distributions are calculated for the laminar regime. The interaction between the source flow and the rotational effects is investigated by a method valid for small rotational Taylor numbers of the disks. Several flow configurations are shown to be physically possible, and the magnitude of the parameters delineating the different flow regimes are calculated.
Compound-Compressible Nozzle Flow
Authors: Bernstein A. , Heiser W. H. , Hevenor C.
Published: October 2011

A one-dimensional theory based upon fundamental flow relationships is presented for analyzing the behavior of one or more gas streams flowing through a single nozzle. This compound-compressible flow theory shows that the behavior of each stream is influenced by the presence of the other streams. The theory also shows that the behavior of compound-compressible flow is predicted by determining how changing conditions at the nozzle exit plane affect conditions within the nozzle. It is found that, when choking of the compound-compressible flow nozzle occurs, an interesting phenomenon exists: The compound-compressible flow is shown to be choked at the nozzle throat, although the individual stream Mach numbers there are not equal to one. This phenomenon is verified by a wave analysis which shows that, when choking occurs, a pressure wave cannot be propagated upstream to the nozzle throat even though some of the individual streams have Mach numbers less than one. Algebraic methods based on this compound-compressible flow theory are used to demonstrate the usefulness of this approach in computing the behavior of compound-compressible flow nozzles. A comparison of the compound-compressible flow theory with three-dimensional computer calculations shows that the effects of streamline curvature on nozzle behavior can be disregarded for many practical nozzle configurations. Test results from a typical two-flow nozzle show excellent agreement with the predictions from the theory.
On Magnetohydrodynamics of Rotating Fluids
Authors: Schwiderski Ernst W. , Lugt Hans J.
Published: October 2011

The influence of rather general electromagnetic forces acting upon steady rotating motions of conducting viscous incompressible fluids over a rotating disk is investigated by means of adjustable local boundary-layer approximations of first order. Numerical results for the most important motions of von Ka´rma´n and Bo¨dewadt are displayed and discussed in full detail. The hypothesis of small variations of the imposed magnetic field assumed in other investigations is found to be justified provided the corresponding Hartmann number and magnetic Reynolds number are of sufficiently small magnitude. Considerable distortions of the rotating motions result from strong electromagnetic forces. When the strength of the imposed electromagnetic forces is increased, the secondary motions may change their stagnation character to wake character, and vice versa. This change may proceed through the development of one-cell and two-cell flows as intermediate stages. The spatial instability of wake-type flows can be decreased or increased depending on the strength and the direction of the applied electromagnetic forces. In addition to critical Reynolds numbers, critical Hartmann numbers and magnetic Reynolds numbers are shown to exist beyond which no simple boundary-layer-type motions are possible. The interpretation of the spatial instability of wake-type flows as a separation phenomenon is supported by the “teacup” experiment photographed.
Latent Elastic Strain Energy Due to the Residual Stresses in a Plastically Deformed Polycrystal
Authors: Lin T. H. , Ito Marvin
Published: October 2011

A part of the work done on a plastically deformed metal reappears in the form of heat and the remaining part remains latent in the metal, known as latent energy. Part of this latent energy is the elastic strain energy of the residual stresses of the plastically deformed metal. In this paper, this strain energy in a polycrystal is calculated from the crystallographic slip properties of single crystals. The polycrystalline aggregate is composed of differently oriented cube-shaped crystals, each with one slip plane on which there are three slip directions. Neglecting the inhomogeneity and anisotropy of elastic constants, the polycrystal is taken to be elastically homogeneous and isotropic. The analogy between plastic strain gradient and body force in an infinite elastic medium is used to calculate the residual stress field. The residual stress calculation satisfies the condition of continuity, the equilibrium condition, and the single crystal stress-strain relationship throughout the aggregate. The variation of the latent elastic strain energy with the aggregate stress is shown. A similar method may be used to calculate the latent elastic strain energy of f.c.c. and b.c.c. polycrystals.
Some Interaction Effects in a Problem of Plastic Beam Dynamics—Part 1: Interaction Analysis of a Rigid, Perfectly Plastic Beam
Authors: Nonaka Taijiro
Published: October 2011

An analysis is presented to determine the permanent deformation of a rigid-plastic clamped beam with constraints against axial displacements at the ends. The beam carries a concentrated mass at its center and is subjected to large transverse impulsive loading at the mass. Plastic interaction is considered for the combined action of bending moments, axial forces, and shearing forces, based on a fixed yield surface.
Axisymmetric Vibrations of Homogeneous and Sandwich Spherical Caps
Authors: Koplik B. , Yu Yi-Yuan
Published: October 2011

From the generalized variational equation of motion is derived a complete system of equations for sandwich as well as homogeneous spherical shells including the effect of thickness-shear deformation. Based on these equations the exact solution is obtained for the natural frequencies of axisymmetric vibrations of homogeneous and sandwich spherical caps with clamped edges. Emphasis in our investigation is on the transition from the vibrations of a circular disk to those of a spherical cap, for both homogeneous and sandwich cases, with numerical results showing the effects of thickness-shear and of curvature.
Orthotropic Annular Disks in Plane Stress
Authors: Shaffer Bernard W.
Published: October 2011

General solutions are derived for the stresses, strains, and radial displacements in nonhomogeneous orthotropic annular disks subject to stresses at their internal and external boundaries. Nonhomogeneity exists because the directional moduli of elasticity vary with the radius to a power λ. It is found that, when the disk is subject to external tension only, the maximum circumferential stress can occur at either boundary. A relation is derived which can be used to make circumferential stresses equal at both boundaries.
Measurement of Laminar Flow Development in a Square Duct Using a Laser-Doppler Flowmeter
Authors: Goldstein R. J. , Kreid D. K.
Published: October 2011

A system for precision measurement of fluid velocity is developed and applied to determine the laminar flow distribution in a square duct. The experimental technique consists of measuring the Doppler shift of laser radiation scattered by particles moving with the fluid. From this frequency shift, the fluid velocity is inferred. Measurements in the entrance region and fully developed flow region of a square duct indicate that the velocity profile development takes place in a somewhat longer section of the duct than had been predicted. Measurements of the fully developed flow indicate that the optical technique used is capable of measuring velocity within an accuracy of at least 0.1 percent.
Bubble-Growth Calculation Without Neglect of Interfacial Discontinuities
Authors: Bornhorst W. J. , Hatsopoulos G. N.
Published: October 2011

The object of this theoretical investigation is to determine the importance of the nonequilibrium region, which exists at the bubble wall, on the growth of a vapor bubble. All previous investigators concerned with bubble growth have completely neglected this nonequilibrium effect. In another paper [1] Bornhorst and Hatsopoulos investigated the phase-change problem, and the results which were obtained are applied here to solve the special problem of vapor bubble growth. The results are presented in terms of a two-parameter set of curves. These results show that for pressures where experimental results are available, the nonequilibrium effects are within experimental error; however, for pressures which are somewhat lower, the nonequilibrium effects become very important.
A Source Flow Model for Continuum Gas-Particle Flow
Authors: Migdal David , Agosta V. D.
Published: October 2011

A system of differential equations is derived from basic laws of mass conservation dynamics and thermodynamics for a gas-particle reacting system. The concept of two superimposed continua occupying the same control volume is used throughout. A number of terms appearing in the basic equations, physically identified with the presence of particles, are defined as source terms for the gas motion. With the introduction of phenomenological relations for these terms and the thermodynamic variables, a complete set of differential equations is obtained. The equations governing the one-dimensional flow in an arbitrarily shaped duct are presented as a special case.
Compressional Wave Velocity and Compressibility of Aggregates of Particles of Different Materials
Authors: Brandt H.
Published: October 2011

The compressional wave velocity and compressibility of a fluid-saturated aggregate of randomly stacked spherical particles of four sizes are determined. The particles may have different elastic properties so that variations in compressional wave velocity and compressibility can be determined as a function of the material properties of the particles and of the bulk moduli of the saturating fluids. Applications of the theory to problems in seismic exploration and oil production are given.
Impact of a Rigid Sphere on a Viscoelastic Plate
Authors: Phillips J. W. , Calvit H. H.
Published: October 2011

The dynamic, rigid, spherical indenter problem for the case of a thin viscoelastic plate is treated, and a numerical method is developed to handle the resulting equations of motion for a general linear viscoelastic material. Application to a constant tan δ model and comparison with experimental results indicate that the ball-bouncing technique can be extended to thin plate samples by the present theory if the loss tangent for the material is reasonably low.
Deformation of an Elastic Spherical Wedge
Authors: Christensen R. M.
Published: October 2011

Analytical solutions are presented for two separate modes of deformation of an infinite elastic spherical wedge. In part, these solutions take the form of the stresses on the boundaries of the wedge caused by prescribed surface displacements. Full discussion is given to the means of utilizing these two solutions, along with corresponding tests, to determine the complete mechanical-properties characterization of a linear isotropic viscoelastic solid.