bluuebunny/crossref_metadata_2025 huggingface dataset:
Buckling of a Long, Axially Compressed, Thin Cylindrical Shell With Random Initial Imperfections
Authors: Van Slooten R. A. , Soong T. T.
Published: November 2010

The effect of random geometric imperfections on the maximum load-carrying capacity of an axially compressed thin cylindrical shell is studied. Following a perturbation approach, equations are derived which relate the first and second-order statistics of the maximum load to the statistics of the initial imperfections. Assuming that the imperfections are represented by Gaussian stationary and ergodic random processes, it is shown that the mean maximum load is expressible in quadrature forms involving the power spectral density of the initial imperfection. Furthermore, the maximum load is seen to be equal to its mean value with probability one. A simple asymptotic formula for the maximum load is derived assuming the variance of the initial imperfection is small. In this case the critical load depends only upon the imperfection variance and the power spectral density at a given wave number. For the types of imperfections considered, it is found that random axisymmetric imperfections reduce the load-carrying capacity of the cylindrical shell more than nonaxisymmetric imperfections.
Similarity Solution for the Curved Two-Dimensional Jet
Authors: Fleming G. K. , Alpay S. A.
Published: November 2010

A similarity solution has been obtained for a fluid jet bounded on one side by a separation bubble and on the other by an unbounded region containing the same fluid. The inner boundary has been approximated by a porous pseudowall. The resulting mathematical model reduces to other cases such as the plane wall jet and the free curved jet. A two-parameter family of solutions to the resulting nonlinear equation for the outer half of the jet correlates well with experimental data.
Deformation, Displacement, and Work Bounds for Structures in a State of Creep and Subject to Variable Loading
Authors: Ponter A. R. S.
Published: November 2010

General bounds on the deformation of a structure in a state of creep are derived for an elastic/perfectly plastic/time-hardening creep material, and subject to an arbitrary history of loading. Previously derived bounds for time constant loading are recovered and extended. The bounds are specialized to cyclic histories of loading. A simple example indicates that very accurate bounds are possible in some circumstances.
The Effect of an Axial Force on the Response of an Anisotropic Elastic Half Space to a Rolling Cylinder
Authors: Clements D. L.
Published: November 2010

The problem of an inflated cylindrical tire of infinite length and constant finite width steadily rolling over the surface of an anisotropic elastic half space is examined. The influence of an applied force, acting along the axis of the cylinder, on the width of the region of slip at each end of the tire is determined. In particular, it is shown numerically that when a material exhibits certain anisotropy the presence of an axial force can considerably reduce the width of the zones of slip.
The Stability of Simply Supported Rectangular Surfaces in Uniform Subsonic Flow
Authors: Ellen C. H.
Published: November 2010

A study is made of the stability of a simply supported flat plate set in an infinite rigid baffle when an inviscid fluid flows uniformly at subsonic speed past one side of the surface. The generalized pressures are derived for low frequencies with two and three-dimensional flows. The three-dimensional generalized pressures are expanded asymptotically for high and low aspect ratios, and analytic forms derived for the critical flow velocity at instability. The asymptotic expansions enable the effect of aspect ratio on stability to be determined. It is shown that the incompressible limit, for two-dimensional flows, is singular but the stability criterion is associated with first-mode divergence and is identical with the three-dimensional high aspect ratio stability result, although there are certain detailed differences in the nature of the instability.
General Deformations of Neo-Hookean Membranes
Authors: Yang W. H. , Lu C. H.
Published: November 2010

A set of three nonlinear partial-differential equations is derived for general finite deformations of a thin membrane. The material that composes the membrane is assumed to be hyperelastic. Its mechanical property is represented by the neo-Hookean strain-energy function. The equations reduce to special cases known in the literature. A fast convergent algorithm is developed. The numerical solutions to the finite-difference approximation of the differential equations are computed iteratively with a trivial initial iterant. As an example, the problem of inflating a rectangular membrane with fixed edges by a uniform pressure applied on one side is presented. The solutions and their convergence are displayed and discussed.
The Laminar Boundary Layer Between Parallel Streams of Nonhomogeneous Immiscible Fluids
Authors: Hayakawa N. , Unny T. E.
Published: November 2010

The boundary-layer expansions (inner and outer expansions) of the flow between parallel streams of incompressible, immiscible fluids involve different perturbation parameters (Reynolds numbers) for each layer. Higher-order terms of these expansions have been solved and the correct form of the third boundary condition for the boundary layer (the zeroth order) problem is obtained. Some numerical results based on this condition are presented.
Optimal Design of Plastic Structures for Fixed and Shakedown Loadings
Authors: Cohn M. Z. , Parimi S. R.
Published: November 2010

Optimal (minimum weight) solutions for plastic framed structures under shakedown conditions are found by linear programming. Designs that are optimal for two failure criteria (collapse under fixed loads and collapse under variable repeated loads) are then investigated. It is found that these designs are governed by the ratio of the specified factors defining the two failure criteria, i.e., for shakedown, λs and for collapse under fixed loading, λ. Below a certain value (λs/λ)min the optimal solution under fixed loading is also optimal for fixed and shakedown loading. Above a value (λs/λ)max the optimal design for variable loading is also optimal under the two loading conditions. For intermediate values of λs/λ the optimal design that simultaneously satisfies the two criteria is different from the optimal designs for each independent loading condition. An example illustrates the effect of λs/λ on the nature of the design solution.
Response of the Human Spinal Column to Lateral Deceleration
Authors: Soechting J. F.
Published: November 2010

The effects of the musculature of the back and the bending stiffness of the spine are considered in a model for spinal column response to lateral deceleration. It is found that the effect of bending stiffness is negligible except at the ends of the spinal column and a perturbation solution based on this assumption is obtained and typical results are reported.
Impulsive Deformation of Mirsky-Herrmann’s Thick Cylindrical Shells by a Numerical Method
Authors: Ziv M. , Perl M.
Published: November 2010

The transient response of a thick elastic semi-infinite cylindrical shell subjected to impulsive step loads is obtained. This work presents solutions to two boundary-value problems. First, the shell is exposed to an axially step pulse velocity load while second, the pulse is applied radially to the shell. The influence of the transverse normal stress and the transverse normal strain on the deformation is being studied in great detail. The shell theory employed is based on the thick-shell equations derived by Mirsky and Herrmann, which comprise these transversal effects. These equations are solved by the characteristics method, while integration is carried out by the finite-difference technique. The results also present the influence of the thickness parameter (h/R) on the solution. Comparisons are made to solutions of other shell theories which neglect the transversal effects. Major conclusions show the existence of an important influence of the transverse normal strain on the deformation.
Plastic Wave Propagation in Linearly Work-Hardening Materials
Authors: Ting T. C. T.
Published: November 2010

The combined longitudinal and torsional waves in a linearly work-hardening thin-walled tube are studied. Explicit solutions are obtained for the stress paths in the stress space for the simple waves. The stress paths are all “similar”, and hence a proportionality property in the solutions exists for simple waves as well as for a more general initial and boundary-value problem. The same results apply to any type of plane waves of combined stress. Thus the “linearity” in the solutions of one-dimensional plastic waves in a thin rod of a linearly work-hardening material is not completely lost in the solutions of combined stress waves. Depending on whether the plastic wave speed cp is larger, equal, or smaller than c2, the nature of the solutions to a given combined stress wave problem can be quite different. Examples are given to illustrate this point.
Slip Forces for Bodies in Contact With Large Spin and Small Slip Velocities
Authors: Kurtz E. F.
Published: November 2010

Two elastic bodies are treated, which are in contact over an elliptical surface, are subjected to a large spin about an axis normal to the contact surface, and have small slip velocities tangential to that contact surface. It is shown that these slip velocities are proportional to the tangential components of force acting at the contact surface, and that the coefficients of proportionality can be written as simple expressions in terms of complete elliptic integrals of the first and second kind.
A Theory of Elasticity of the Lung
Authors: Fung Y.-C.
Published: November 2010

The stress-strain relationship of the lung parenchymal tissue depends on the alveolar geometry, the elastic property of the alveolar walls (sheets, septa) and the surface tension characteristics. This nonlinear relationship is derived in the present paper.
Dynamic Buckling of the Elastic Cylindrical Shell Subjected to Impulsive Loading
Authors: Hubka W. F.
Published: November 2010

A periodic, Fourier series solution is presented for the nonlinear dynamic response of an impulsively loaded, elastic cylindrical shell. This result has been obtained by a new application of the quadratic form of Newton’s method; in this modification the frequency is considered to be the basic independent variable, and analytic corrections are obtained when solutions of the linear variational equations are nonperiodic. The solution presented here is shown to consist of a slowly varying function modulating a rapidly varying function, and is compared with results obtained by direct numerical integration.
Application of an Eigenfunction Expansion Method in Plasticity
Authors: Wierzbicki T.
Published: November 2010

Possibilities of extending the eigenvalue expansion method to dynamic problems for plastic continua and structures are examined. A model of a pseudo strain rate sensitive material is introduced as an approximation to the concept of rigid-perfectly plastic material. A simple method is then developed which parallels the familiar elastic mode expansion technique but yet retains the main features of rigid-plastic behavior. The accuracy of the method is discussed and comparison with previous theories is made. An illustrative example is presented.
Moving Loads on an Elastic Plate Strip
Authors: Adler A. A. , Reismann H.
Published: November 2010

The response of an infinite plate strip under an arbitrarily distributed transverse moving line load is determined. The line of application of the load is perpendicular to the infinite edges, and the load is assumed to propagate parallel to the infinite edges of the plate at constant speed. The problem is formulated as a boundary-value problem within the framework of a plate theory which includes the effects of shear deformation and rotatory inertia. A closed-form solution, in terms of elementary functions, is obtained for each harmonic component of the line load by the Fourier transform method in conjunction with contour integration.
Transient Bending of a Large Elastic Plate by an Incident Spherical Pressure Wave
Authors: Huang H.
Published: November 2010

The transient response of a large elastic plate to the impact of an incident spherical pressure wave is studied. The interaction problem is formulated with the aid of the Laplace and Hankel transform techniques and the inverse transform is asymptotically evaluated by the method of Laplace. The transient solution for early time immediately after the impact is obtained. It demonstrates that the convex incident wave front could cause bending stress at the plate many times higher than the incident wave front pressure.
Dynamic Buckling of Axisymmetric Shells
Authors: Kalnins A.
Published: November 2010

A procedure for the analysis of dynamic buckling of axisymmetric shells subjected to axisymmetric, periodic loads of long duration is proposed that is based on the calculation of the nonsymmetric modes of free vibration and associated mode integrals over the reference surface of the shell. Numerical results are presented for the evaluation of dynamic stability of an actual shell that is designed for the cooling system of a nuclear power plant.
Velocity Fields in a Sphere Subjected to Large Deformations
Authors: Durelli A. J. , Chen T. L. , Parks V. J.
Published: November 2010

This paper deals with the experimental determination of velocities of displacement in a sphere subjected to a diametral load. The maximum applied load reduced the diameter of this sphere by 27 percent. The velocities are given for each step of loading and were determined from a model made of polyurethane rubber that behaves linearly. The velocities were obtained by superposition of photographs of 500 lpi gratings embedded in the meridian plane of the sphere. The evaluation was made both point-by-point and by photographic recording of the whole field of isotachics. The errors produced as a consequence of the motion of points are evaluated and criteria are given on the best method to use and on whether corrections are necessary or not.
Stabilization of Turbulent Axisymmetric Rotating Flows
Authors: Narain J. P.
Published: November 2010

The turbulent entrainment mechanism of a swirling plume surrounded by a potential vortex and a swirling jet and a wake in a uniform stream has been discussed. With the assumption of the stream-wise similarity of various flow variables, the integrated conservation equations yield a rate of entrainment function which explicitly shows that the external potential vortex retards the rate of entrainment whereas the positive density gradients across the plume interact with the surrounding vortex to weakly increase the rate of entrainment. In a uniform stream, the swirling jets and wakes show distinctly opposite behavior. An increasing initial swirl delays the dissipation of the swirling wake whereas it promotes the dissipation of a swirling jet. The coaxial uniform free stream always retards the rate of entrainment across the swirling jet.
Plane Turbulent Couette Flow With Zero Net Flow
Authors: Huey L. J. , Williamson J. W.
Published: November 2010

This paper examines analytically and experimentally the case of turbulent plane Couette flow with a sufficient adverse pressure gradient to cause zero net flow. This is the limiting case of flow in bearings with small spacing-to-radius ratios and large eccentricities. It is a fairly exact representation of the flow in the pockets of deep pocket hydrostatic bearings. Temporal characteristics and certain turbulence data are presented for this type of flow over a Reynolds number range of 9650 to 27,300.
On Membranes, Tension Fields, and the Human Skin
Authors: Danielson D. A.
Published: November 2010

In this Note we extend and simplify the theory of the deformation of human skin developed in two previous reports. We show that the equations of membranes constrained to slide over deformable mandrels can be written in terms of the unknown law of transformation between coordinate systems on the undeformed and deformed membranes. We also derive the precise equations of tension field theory for membranes undergoing arbitrarily large deformations.
Schlierenoptical Stress Analysis of Short Duration Pulses in Elastic Plates
Authors: Beinert J. M.
Published: November 2010

Applying a quantitative schlieren optical method, the shape and the stress amplitudes of elastic pulses traveling through a plate are determined experimentally. The short duration pulses are generated by loading an edge of the plate with an exploding wire. The influence of several experimental parameters is shown. The primary dilatational pulse splits up into a train of equally spaced pulses.
Endochronic Representation of Cyclic Creep and Relaxation of Metals
Authors: Valanis K. C. , Wu H.-C.
Published: November 2010

In this paper we have used the endochronic theory of plasticity to model one of the most complex phenomena of mechanical behavior of materials, that of cyclic creep and relaxation. We have shown that the theory provides a consistent analytical representation for the observed behavior of metals under conditions of cyclic deformation. This we have done using a simple form of the theory. In particular the hereditary response of the materials has been represented by two heredity functions, E(z) and ν(z). It was found that in the case of copper E(z) may be approximated by a single exponential term while ν(z) is approximately constant in the range of interest.
Axisymmetric Stokes Flow Past Cones Including the Case of the Needle
Authors: Ghia K. N. , Mikhail A. G.
Published: November 2010

The Stokes flow past sharp axisymmetric cones of acute semivertex angle has been studied using an axisymmetric spherical coordinate system. The Stokes solution consists of associated Legendre functions, of the first kind, of the first-order and fractional degree related to the eigenvalues of the problem. These Legendre functions as well as the lowest eigenvalues of the Stokes solution have been accurately evaluated using two different approaches. The present results for the eigenvalues appear to be more accurate than those obtained earlier by Schwiderski, Lugt and Ugincius [3]. An important limiting case with semivertex angle δ → 0, i.e., the needle has been correctly analyzed and the results show that, as δ → 0, the Stokes flow is valid in a vanishingly small neighborhood of the needle with the skin friction being infinite at the “surface” of the needle.
Boundary-Layer Similarity Near the Edge of a Rotating Disk
Authors: Bodonyi R. J. , Stewartson K.
Published: November 2010

Numerical solutions of the similarity equations governing the flow near the edge of a finite rotating disk are found to be possible only for −2.06626 ≤ α ≤ 1, where α is the ratio of the disk’s angular speed to that of the rigidly rotating fluid far from the disk. Furthermore, for α ≤ −1 the solutions of the boundary-value problem are not unique, and along one of the solution branches a singular structure of the flow field is approached as α → −1. Using the method of matched asymptotic expansions an approximate solution is found along the singular branch which explains some of the problems encountered in finding numerical solutions.
Deformation Bounds for the Bailey-Orowan Theory of Creep
Authors: Ponter A. R. S.
Published: November 2010

In two recent papers [1, 2] constitutive relationships were described which were based upon a theory of creep originally postulated by Bailey [3] and Orowan [4] and which has been subjected to tests by Mitra and McLean [5]. Here displacement and work bounds are derived from the general theory of the authors [6, 7] for a body subjected to variable thermal and mechanical loading. Special cases are discussed, including isotropic-hardening plasticity and the bounds are related to certain elementary continuum problems. For cyclic loading the bounds relate to the exact solution when the cycle time is small compared with characteristic material times.
Compression of Bonded Hollow Cylinders
Authors: Moghe S. R.
Published: November 2010

It is shown, from the analysis of bonded hollow cylinders, that the measured elastic modulus for a hollow cylinder is equal to that of a solid cylinder if the ratio of loaded versus load free areas is the same. Theoretical results also agree well with the experimental data.
Scattering of Water Waves by a Pair of Semi-Infinite Barriers
Authors: Liu P. L.-F.
Published: November 2010

Three-dimensional water waves are incident upon a pair of semi-infinite parallel vertical thin barriers. Assuming that the opening between the barriers is small compared with the incident wavelength, an asymptotic theory is developed for the resulting water motion. Between the barriers uniform progressive waves propagate into the channel. The transmission coefficient is found to be insensitive to the incident wave angle and the separation between the barriers.
Scattering of a Love Wave by the Edge of a Thin Surface Layer
Authors: Simons D. A.
Published: November 2010

The antiplane strain problem of the scattering of an incident Love wave by the edge of a thin surface layer is solved. The effect of the layer is represented by a boundary condition applied at the surface of the substrate. In addition, the condition of vanishing traction on the edge of the layer is explicitly enforced. At large distances from the layer’s edge the scattered field is found to consist of a reflected Love wave and a radiated wave. The power flux identity for the problem is derived, and values of the power reflection coefficient are computed. The power flux identity is verified numerically, and the discrepancy which would arise from a failure to satisfy the condition of vanishing traction on the layer’s edge is evaluated.
A Numerical Method for Computing Plane Plastic Slip-Line Fields
Authors: Bachrach B. I. , Samanta S. K.
Published: November 2010

A numerical method for slip-line field analysis of rigid perfectly plastic material is presented. The method formulates the analysis of metal forming operations as constrained optimization problems. As an example extrusion through curved dies with zero exit angle and nonzero entrance angle is solved using the proposed method. Slip-line fields, hodograph, and flow field are illustrated, and the mean extrusion pressure as a function of reduction ratio is computed.
Fracture Analysis of Adhesively Bonded Sheets
Authors: Keer L. M. , Lin C. T. , Mura T.
Published: November 2010

The problem of adhesively bonded sheets, one of which is cracked, is formulated by the utilization of integral transform methods. The objective of the investigation is to calculate the stress-intensity factor at the crack tip for the cracked sheets. Results are obtained when the cracked sheet has a single crack and an array of identical, equally spaced, coplanar cracks. Results tend to indicate that the growth of crack implies a reduction in the stress-intensity factor.
A Theorem on the Free Vibration of Damped Systems
Authors: Fawzy I.
Published: November 2010

A damped linear system may oscillate freely (with a decaying motion) in “modes” [1]. Certain sufficient conditions have been found [2-4] under which those modes are the principal modes defined in the absence of damping. A simple condition is established in this paper that is both necessary and sufficient for this to be the case. It admits other, hitherto undisclosed, conditions under which this great simplification can validly be adopted.
Steady and Unsteady Flow in Noncircular Straight Ducts
Authors: O’Brien V.
Published: November 2010

A general numerical method to solve for the steady parallel fully developed flow in ducts of arbitrary shape is illustrated and compared to analytic solutions for simple shapes. A straight forward extension of the method is applied also to oscillatory flow solutions. By linear superposition, any pulsatile parallel flow in an arbitrary duct can be synthesized.
Singular Perturbation Theory for Melting or Freezing in Finite Domains Initially Not at the Fusion Temperature
Authors: Weinbaum S. , Jiji L. M.
Published: November 2010

This paper treats the problem of the inward solidification at large Stefan number 1/ε, ε = CP(Ti − Tf)/L, of a finite slab which is initially at an arbitrary temperature Ti above the melting point. The face at which the heat is removed is maintained at a constant temperature below fusion while the opposite face is either (a) insulated or (b) kept at the initial temperature. Perturbation series solutions in ε are obtained for both the short-time scale characterizing the transient diffusion in the liquid phase and the long-time scale characterizing the interface motion. The asymptotic matching of the two series solutions shows that to O(ε1/2) the short-time series solution for interface motion for the insulated Case (a) is uniformly valid for all time. A singular perturbation theory is, however, required for the isothermal Case (b) since the interface motion is affected to this order by the inhomogeneous temperature distribution in the liquid phase.
The Deflection of an Ice Sheet by a Submerged Gas Source
Authors: Topham D. R.
Published: November 2010

The deflection of an infinite ice sheet by a submerged gas source, as would result from an undersea gas or oil well blowout is analysed utilizing an elastic thin plate model. The results show that fracture may occur either at the bubble center or just beyond the bubble edge, depending upon the bubble depth, the ice thickness, and the material properties assumed for the ice sheet. For ice one meter in thickness and a trapped gas depth greater than 100 mm, fracture at the bubble edge is probable. The critical bubble radius for failure varies rapidly with ice thickness, bubble depth, and the ice properties, which in view of the variability of the latter, makes the prediction of actual bubble radii to cause failure subject to a large degree of uncertainty.
Inverse Solutions for One-Dimensional Seismic Waves in Elastic, Inhomogeneous Media
Authors: Schreyer H. L.
Published: November 2010

An inverse procedure is developed for obtaining exact solutions to the one-dimensional inhomogeneous wave equation. Transformations of the independent spatial variable and the dependent variable are introduced so that the wave equation assumes the form associated with a homogeneous material. The resulting transformation relations are nonlinear but of such a nature that they can be easily integrated if the reciprocal of the wave speed distribution can be expressed in terms of elementary functions. One functional form that yields realistic values for material properties of soil layers is investigated in detail. Amplification factors for a sinusoidal seismic shear wave in inhomogeneous and homogeneous layers are derived and illustrations of significantly different characteristics for the two types of layers are shown.
Modal Method for Free Vibration of Oval Cylindrical Shells With Simply Supported or Clamped Ends
Authors: Chen Y. N. , Kempner J.
Published: November 2010

The free vibration of an oval cylindrical shell of finite length was investigated with the aid of the kinematic relations of the first-order shell theory of Sanders. Transverse and in-plane inertia terms were retained throughout. A method incorporating a type of eigen-function expansion into Hamilton’s principle, was developed and found to be far more convenient than a parallel Fourier analysis. In addition to the determination of the natural frequencies and deformation characteristics, attention was focused on the influence of various types of simple support and clamped end conditions. Two modes of deformation corresponding to a “higher” and a “lower” frequency were observed for every pair of axial and circumferential wave numbers, depending upon the degree of circumferential symmetry in the deformation pattern.
Vibrations and Dynamic Response of Membranes With Arbitrary Shape
Authors: Nagaya K.
Published: November 2010

This paper deals with vibration and dynamic response problems of an arbitrary-shaped membrane subjected to general dynamic loads. The exact solution for an equation of motion in terms of general dynamic loads is used, and the boundary conditions of the membrane are satisfied by means of the Fourier expansion method. The results of free vibration and dynamic response problems are shown in generalized forms for arbitrary-shaped membranes. As examples of these problems, free vibrations of elliptical and crescent-shaped membranes and dynamic responses of elliptical membranes to annular impact loads are discussed by applying the Laplace transform method. For some typical cases, the results obtained are compared with those of the exact method.
The Effect of a Thin Layer Surface Inhomogeneity on Dynamic Surface Response
Authors: Brock L. M.
Published: November 2010

A thin layer surface inhomogeneity consisting of small, evenly distributed rigid bodies is perfectly bonded to an elastic half space. Constant normal and shear line loads are applied to the layer and the dynamic surface response is calculated by Laplace transform techniques. The product of the layer thickness and the rigid body/half-space mass densities proves to be a critical parameter in determining the response. It is found that the layer has a noticeable effect on the half-space surface response in relation to the free-surface behavior. In particular, while no standard surface-interface waves exist, evidence for small values of the critical parameter indicates the presence of pseudo-Rayleigh waves similar to those found in fluid-solid interface analyses.
The End-Values of Distributed Loads in Half Planes by Caustics
Authors: Theocaris P. S. , Razem C. I.
Published: November 2010

The optical method of caustics was used for the evaluation of stress fields induced by arbitrarily distributed loadings applied along straight boundaries governed by singular elastic stress functions. Various particular loading distributions, such as uniform, trapezoidal, triangular, parabolic, and others were studied to show the potentialities of the method. A thorough study of the caustics, due to illuminating a specimen near the distributed loading region by a light beam, was undertaken. The caustics formed at the ends of the distributed loading were used to evaluate its end-values. This is of particular interest in contact problems, where the determination of the loading distribution along the contacting surface constitutes the main part of the problem.
A General Theory for Synthesizing Crank-Type Four-Bar Function Generators With Transmission Angle Control
Authors: Gupta Krishna C.
Published: November 2010

In this paper, the author proposes a general theory for synthesizing crank-type (i.e., crank-rocker and double-crank) four-bar function generators in which the transmission angle variation over a full crank revolution is in a specified range. Precision point as well as least-square designs have been considered in the paper. Applications of the theory are illustrated by means of numerical examples.
Wave Propagation and Instability in a Circular Semi-Infinite Liquid Jet Harmonically Forced at the Nozzle
Authors: Bogy D. B.
Published: November 2010

The linearized form of the inviscid, one-dimensional Cosserat jet equations derived by Green [6] are used to study wave propagation in a circular jet with surface tension. The frequency spectra are shown for complex wave numbers for a complete range of Weber numbers. The propagation characteristics of the waves are studied in order to determine which branches of the frequency spectra to use in the semi-infinite jet problem with harmonic forcing at the nozzle. Two of the four branches are eliminated by a radiation condition that energy must be outgoing at infinity; the remaining two branches are used to satisfy the nozzle boundary conditions. The variation of the jet radius along its length is shown graphically for various Weber numbers and forcing frequencies. The stability or instability is explained in terms of the behavior of the two propagating phases.
A Slip Model for Finite-Element Plasticity
Authors: van Rij H. M. , Hodge P. G.
Published: November 2010

Conventional finite-element models are based on displacement or velocity fields which are at least continuous. However, it is known that perfectly plastic materials may exhibit discontinuities of the tangential velocity component along certain lines. In this investigation, a two-dimensional finite-element model is proposed which will allow for such discontinuities. A regular pattern of triangular elements is assumed. The elements are assumed to be rigid, and across the line separating any two adjoining elements the normal displacement component is continuous, but a discontinuity may exist in the tangential component. The defining equations—compatibility, equilibrium, and constitutive—are developed with the aid of the Principle of Virtual Work. Prandtl’s punch problem for contained flow is solved under plane strain conditions. Comparison is made with existing analytical and other numerical solutions, in order to evaluate the merits of allowing for discontinuities.
Optimal Shape of Shallow Circular Arches Against Snap-Buckling
Authors: Amazigo J. C.
Published: November 2010

The optimal shapes of shallow circular arches against snap-buckling are obtained by a combination of perturbation method, variational calculus, and the numerical solution of integral equations. The method that is developed is applicable to the optimization against buckling of structures which undergo limit load buckling. Here, the in-plane extensional deformation of simply supported circular arches with prescribed volume of structural material is considered. The results indicates that the buckling load of arches may be increased by more than 10 percent by a redistribution of the volume of the arch material.
The Effect of Spatial Distribution on Dynamic Snap-Through
Authors: Johnson E. R. , McIvor I. K.
Published: November 2010

The effect of the spatial distribution of impulsive loads on dynamic snap-through of a shallow circular arch is considered in detail. The Budiansky-Roth criterion is used to establish critical magnitudes of the load for many distributions by numerical integration of an approximate set of equations obtained by Galerkin’s method. It is necessary to distinguish between snap-through on the initial oscillation (immediate) and snap-through occurring during a finite time of the response. Critical magnitudes for both cases are compared to a distribution independent lower bound obtained from an analysis of the critical points. For all distributions considered the lower bound is a less conservative estimate of the critical magnitude for finite time snap-through than for immediate snap-through. The effect of small damping on this conclusion, however, remains an open question.
Deflection of a Very Flexible Spinning Disk Due to a Stationary Transverse Load
Authors: Benson R. C. , Bogy D. B.
Published: November 2010

This paper addresses the problem of steady deflection of a very flexible spinning disk due to transverse loads that are fixed in space. We first approach this problem within the context of membrane theory. The membrane differential operator is classified and shown to be hyperbolic in the outer region and elliptic in the inner portion. The characteristics are studied and qualitatively compared with some experimentally observed standing waves in the outer region of a membrane-like disk. The eigenvalue problem is examined and the membrane operator is found to be singular. We therefore conclude that the problem of interest cannot be solved within the context of membrane theory. Finally, the problem is formulated with bending stiffness retained. The concentrated load problem is solved by use of a Fourier series expansion in the angular direction in conjunction with a numerical solution for the radial modes. Graphical results are presented for various values of the stiffness parameter and load location.
A Comparative Study of Liapunov Stability Analyses of Flexible Damped Satellites
Authors: Hablani H. B. , Shrivastava S. K.
Published: November 2010

A literal Liapunov stability analysis of a spacecraft with flexible appendages often requires a division of the associated dynamic potential into as many dependent parts as the number of appendages. First part of this paper exposes the stringency in the stability criteria introduced by such a division and shows it to be removable by a “reunion policy.” The policy enjoins the analyst to piece together the sets of criteria for each part. Employing reunion the paper then compares four methods of the Liapunov stability analysis of hybrid dynamical systems illustrated by an inertially coupled, damped, gravity stabilized, elastic spacecraft with four gravity booms having tip masses and a damper rod, all skewed to the orbital plane. The four methods are the method of test density function, assumed modes, and two and one-integral coordinates. Superiority of one-integral coordinate approach is established here. The design plots demonstrate how elastic effects delimit the satellite boom length.
Modified Governing Equations for Unsteady Compressible Flow in Ducts
Authors: Celmin¸sˇ A.
Published: November 2010

Conventional governing equations for unsteady compressible tube flows are reviewed and it is shown that they neglect first-order terms which can have significant magnitudes. The derivation of correct tube flow equations from general conservation laws is demonstrated for the case of axially symmetric straight tubes. The traditionally neglected terms are computed explicitly for unsteady flows with power law profiles through circular tubes.
Transient Response of Continuous Elastic Structures With Viscous Damping
Authors: Strenkowski J. , Pilkey W.
Published: November 2010

A comprehensive theory is presented for the dynamic response of continuous structural members with viscous damping using a modal analysis. The theoretical development provides a concise set of formulas that may be used for any structural member for which the equations of motion are known. These formulas are appropriate for both self-adjoint and nonself-adjoint systems of equations, which may include viscous damping, nonhomogeneous boundary and in-span conditions, and arbitrary forcing functions. The axisymmetric transient response of a thick elastic cylindrical shell subjected to displacement boundary conditions is included to demonstrate the usefulness of the general formulation in uncoupling the response of complex structural members.
Diffraction of SH-Waves by an Edge Crack
Authors: Datta S. K.
Published: November 2010

Diffraction of an antiplane shear (SH-) wave by an edge crack in a semi-infinite elastic medium is studied here. Asymptotic expansions for the scattered field both near and far from the crack are obtained for the case when the wavelength is large compared to the length of the crack. Near-field expansion is used to compute the dynamic stress-intensity factor at the tip of the crack. Also, the far-field expansion gives the scattered displacement amplitude, which is useful in ultrasonic nondestructive evaluation.
Domains of Stability in a Wind-Induced Oscillation Problem
Authors: Holmes P. J.
Published: November 2010

In two earlier papers, the motion of a structure induced by vortex shedding was investigated for the cases of resonance and order three subharmonic resonance. In both cases classes of unbounded solutions exist and the size and boundary of the domain of stability dividing these from bounded solutions is therefore of great interest. In this paper we show that, for light damping, the domain of stability has an extremely complex boundary due to the presence of heteroclinic orbits. In addition, it may be considerably smaller than might be expected. The method employed is quite general and the conclusions appear significant for a number of other problems in nonlinear oscillations.
Upper Bounds for Amplitudes of Harmonic Components of Excitation
Authors: Haines R. S.
Published: November 2010

The amplitude of the nth harmonic component of a known waveform has upper bounds which can be derived from inspection of the waveform. By indicating when the Fourier analysis of (for example) vibratory excitations can be circumvented, this technique may usefully shorten iterative or desk-top design calculations.
Dynamic Response of a Cylindrical Shell in a Potential Fluid
Authors: Cummings G. E. , Brandt H.
Published: November 2010

A numerical solution technique is presented for determining the dynamic response of a thin, elastic, circular, cylindrical shell of constant wall thickness and density, in a potential fluid. The shell may be excited by any radial forcing function with a specified time history and spatial distribution. In addition, a pressure history may be specified over a segment of the fluid outer boundary. Any of the natural shell end conditions may be prescribed. The numerical results are compared to experimental results for a 1/12-scale model of a nuclear-reactor core-support barrel. Natural frequencies and modes are determined for this model in air, water, and oil. The computed frequencies are within 15 percent of experimental results. A sample application compares the numerical technique to an analytical solution for shell beam modes. The comparison resolves an uncertainty concerning the proper effective mass to use in the analytical technique.
Directionality of Fatigue Properties in Some Textured Sheet Metals
Authors: Le May I. , Nair K. D.
Published: November 2010

The fatigue properties of some face-centred cubic sheet metals with cold rolling and annealing textures are reported. The observed differences between fatigue properties measured in the transverse and longitudinal directions in cold-rolled material are discussed and are related to the pole figures for the material. The study emphasizes that considerable directionality of fatigue properties can occur in rolled sheet metal.
Environmentally Controlled Fatigue Crack-Growth Rates in SAE 4340 Steel—Temperature Effects
Authors: Ryder J. T. , Gallagher J. P.
Published: November 2010

The temperature dependence of sustained-loading and corrosion-fatigue crack-propagation behavior of SAE 4340 steel immersed in distilled water was investigated using the fracture mechanics approach. During the load cycle, stress-intensity histories had values higher than the static threshold stress intensity (KIscc). For a stress-intensity range of 20 ksi in., a factor of 30 increase in the corrosion-fatigue crack-growth rate was noted for a temperature increase of 70 deg C. The mechanical variables were found to have much less influence than the environmental reaction rate. In contrast with dry air results, the fatigue crack-growth rate in a distilled water environment was dependent on the mean stress-intensity for stress-intensity histories above KIscc. This dependence varied with temperature level.
Strain Cycling Effects in 1100 Aluminum
Authors: Moreen H. A.
Published: November 2010

The cyclic hysteresis-loop stress-strain behavior, i.e., the hysteresis-loop-shape, of 1100 aluminum was investigated. A power function: ep=K1Sn1+K2Sn2 describes the saturated hysteresis-loop-shape behavior. The exponents n1 and n2 are hysteresis-loop strain-hardening exponents corresponding to the behavior at high and low values of strain and are material properties with the values 0.12 and 0.02, respectively, for annealed material. The flow stress parameters, K1 and K2, depend on cyclic history and plastic anisotropy. A dislocation shuttling model is consistent with the observed behavior.
A New Apparatus to Shear Bulk Materials at Various Rates Under Very High Pressure
Authors: Abey A. E. , Stromberg H. D.
Published: November 2010

The apparatus described will shear bulk materials at strain rates from 2 × 10−5/sec to 5 × 10−1/sec while the materials are under nearly hydrostatic pressures. This apparatus gives complete stress-strain curves in the plastic region at pressures from about 10 kbar to approximately 80 kbar. Data on beryllium are given as an example of the type of data available from this apparatus.
Simultaneous Lateral Skewing in a Three-Dimensional Turbulent Boundary-Layer Flow
Authors: Klinksiek W. F. , Pierce F. J.
Published: November 2010

The results of an experimental program are reported on, wherein the lateral flow in a low-speed, three-dimensional, turbulent, incompressible boundary layer inside a recurving duct was made to reverse itself completely. In such a reversal process there occurs a region of flow where the boundary layer experiences lateral flow in two different lateral directions simultaneously. The physical arguments which support the existence of such flow regions with simultaneous lateral skewing are discussed and supported by the experimental results. Several of the more recent velocity profile models which are intended for use in describing skewed turbulent boundary-layer flows are reviewed as to their applicability to a flow with such simultaneous lateral skewing.
Sensitivity Coefficients Utilized in Nonlinear Estimation With Small Parameters in a Heat Transfer Problem
Authors: Beck J. V.
Published: November 2010

The method of nonlinear estimation for determining parameters in differential equations is extended to treat more efficiently the problem of determining dominant and small parameters. Using the sensitivity coefficients, it is shown how to determine the dominant parameters first using nonlinear estimation and then using linear least squares to find the small parameters. This procedure can save a considerable amount of computer time. Even more important is the application to model-building (identification). The residuals for the difference of the temperatures calculated, assuming the small parameters are zero, and the measured temperatures are shown to yield information for discriminating between alternate mathematical models. A transient heat-conduction example is given to illustrate some of the concepts developed.
The Experimental Design of a Mobile Pressure Suit
Authors: Iberall A. S.
Published: November 2010

An important objective in the development of a pressure suit for a human being is to permit the wearer full mobility, whether pressurized or not, without interfering with physical capability. Although the human skin is stretched during body motion, there is virtually no stretch along certain lines, here called “lines of nonextension.” This fact was utilized as the design basis for a series of experimental pressure suits that were developed to demonstrate that it was possible to achieve natural mobility and minimal ballooning in such suits. The detailed program of investigation pursued during the phase of study being reported on was: (1) to map out these lines of nonextension; (2) to test whether string elements of high elastic modulus, a connected network, could be laid along these lines of nonextension without resulting in any constraint to mobility; (3) to obtain a highly mobile pressure-retaining layer to be constrained by the net; and (4) to construct and demonstrate an entire pressure-retaining garment system that makes use of all necessary layers and string elements in a completely connected netted covering for the body with minimal constraint to mobility at pressures up to 5 psi. The technique, result, and collateral observations relevant to each of these phases are described. A mobile, pressure-retaining garment was developed by building each structural, functional layer into the composite garment in accordance with the basic design theory.
Dynamics of a Proportional Fluidic Amplifier: Part 1
Authors: Humphrey R. A. , Brown F. T.
Published: November 2010

A general experimental procedure is described for determining the complete linearized characteristics of a fluidic component over a wide band of frequencies. The method is applied to a large-scale Corning proportional amplifier with a 0.054-in. throat for frequencies up to over 3 kHz. Similarity was preserved for a 1/4 scale amplifier operating at atmospheric conditions. Since all eight independent complex-number self and transfer admittances are given for linearization about the symmetrical state, the results can be used to predict the behavior of the amplifier in any compatible coupled or uncoupled environment. The paper is continued in Part 2, ASME Paper No. 69-WA/Flcs-3, with an examination of the causes of the observed dynamic behavior in this and other proportional amplifiers.