bluuebunny/crossref_metadata_2025 huggingface dataset:
On MHD Flow in a Rectangular Duct of Arbitrary Conductivity for Arbitrary Hartman Number
Authors: Chu W. H.
Published: October 2011

The titled problem was solved by a modified Fourier method so that boundary conditions can be fulfilled. The flow parameter, induced magnetic induction, and current were obtained for various conduction parameters and Hartman numbers. For zero and infinite conduction parameters, the calculated values are in good agreement with known theoretical results.
Buckling of Composite and Homogeneous Isotropic Cylindrical Shells Under Axial and Radial Loading
Authors: Lei M. M. , Cheng Shun
Published: October 2011

A theoretical analysis of the buckling of a multilayered thin orthotropic composite circular cylindrical shell of finite length, subjected to (a) uniform axial compression, and (b) axial compression combined with radial pressure, is presented. At each end of the shell, four boundary conditions are satisfied. Four combinations of boundary conditions for simply supported shells, and four combinations of boundary conditions for clamped shells, are treated. These boundary conditions are reduced to the vanishing of a fourth-order determinant. Buckling loads for boron-epoxy composite shells are determined and the results are shown in a series of diagrams. The effect of boundary conditions on the buckling load for various geometrical dimensions of composite cylinders is investigated. Details of the boundary conditions are shown to have strong influence on the buckling load of the shell. The minimum critical axial compression for a simply supported shell with boundary conditions SS1 is as low as 79 percent of the minimum critical axial compression for a shell with classical boundary conditions SS3. As a special case of a composite shell, the minimum critical axial compressive stress for a homogeneous, isotropic, simply supported shell with end conditions SS1 is found to be 43.7 percent of the classical critical stress.
Origin of Generating Functions in Applied Mechanics
Authors: Wilson P. E. , Hook J. F.
Published: October 2011

This Note presents a direct method by which the equations satisfied by generating functions and their relations to the original dependent variables can be deduced. The technique given is applicable to systems of linear partial differential equations with constant coefficients. Examples are presented from the fields of elasticity and shell theory.
Dynamic Membrane Stress in a Circular Viscoelastic Ring
Authors: Forrestal M. J. , Alzheimer W. E.
Published: October 2011

In this Note, wave solutions for the membrane stress in a thin, circular, viscoelastic ring subjected to impulsive loads and internal heat additions are derived. The analysis employs the linear Maxwell material model.
Interaction of a Ring-Reinforced Shell and a Fluid Medium
Authors: Berglund Jerry W. , Klosner Jerome M.
Published: October 2011

This work is concerned with the transient dynamic response of a periodically ring-reinforced, infinitely long, circular cylindrical shell to a uniform pressure suddenly applied through the surrounding acoustic medium. The incident particle velocity is zero, and the rings are assumed to be slightly flexible. A classical theory of the Donnell type is used to analyze the shell while the fluid is described by the linear acoustic field equation. The solution is obtained by assuming a power series expansion in the ring stiffness parameter and utilizing a technique which reduces the transient dynamic problem to an equivalent steady-state formulation. Numerical results are presented for a steel shell immersed in salt water for different ring spacings. For the case of rigid rings, a cylindrical and plane wave approximation was also used to represent the fluid field. It is shown that the cylindrical wave approximation yields reasonably accurate results. Flexible ring results, although limited, indicate that undamped or nonradiating components of the shell vibration are activated.
Impulsive Loading of a Simply Supported Circular Rigid Plastic Plate
Authors: Jones Norman
Published: October 2011

It is clear from a survey of literature on the dynamic deformation of rigid-plastic plates that most work has been focused on plates in which either membrane forces or bending moments alone are considered important, while the combined effect of membrane forces and bending moments on the behavior of plates under static loads and beams under dynamic loads is fairly well established. This paper, therefore, is concerned with the behavior of circular plates loaded dynamically and with deflections in the range where both bending moments and membrane forces are important. A general theoretical procedure is developed from the equations for large deflections of plates and a simplified yield condition due to Hodge. The results obtained when solving the governing equations for the particular case of a simply supported circular plate loaded with a uniform impulsive velocity are found to compare favorably with the corresponding experimental values recorded by Florence.
An Analysis of the Formation of Turbulent Patches in the Transition Boundary Layer
Authors: McCormick M. E.
Published: October 2011

An analysis is presented of the formation and motion of turbulent pressure patches under the transition boundary layer on a flat plate in a zero pressure gradient. The shape of the patch on the surface of the plate is assumed to be triangular with an area that increases as the patch moves downstream from its point of inception. The expressions for the cross-correlation and the cross-spectral density of the surface-pressure fluctuations which are obtained are both space and time dependent. A relation is shown to exist between the transition phenomena and the instabilities in the laminar boundary layer. Finally, the analytical results are used to determine the breakdown points of the laminar instabilities.
An Approximate Theory Governing Symmetric Motions of Elastic Rods of Rectangular or Square Cross Section
Authors: Hertelendy Paul
Published: October 2011

Variational equations of motion are developed for symmetric motions of linear elastic bars of rectangular cross section. In the finite term approximation, sufficient terms are retained to allow a longitudinal mode, two thickness-stretch modes, and two thickness-shear modes of vibration in an infinite bar of square cross section. Modes for complex wave numbers are also investigated. Adjustment factors in the strain energy and kinetic energy potentials are used to match exact and experimental solutions. Experimental frequency versus wave number results for four modes are reduced by Fourier synthesis and compared both to the approximate theory and to the exact solution for circular cylinders. Theory is intended to predict behavior of thick rectangular bars for which the plane stress solution is not accurate.
Pure Bending of Shallow Helicoidal Shells
Authors: Wan F. Y. M.
Published: October 2011

The solution of the problem of pure bending of shallow helicoidal shells is obtained in terms of elementary functions. Numerical results for the direct and bending stresses as well as for the overall stiffness coefficient of the shell are given for various pitch-to-thickness ratios. An interesting aspect of the analysis is that the displacement state of the shell is multivalued in the polar angle θ while the stress state is unsymmetric but periodic in θ. Moreover, unlike the problem of axial torsion and extension where there is no edge effect, the stress state for the present problem exhibits both an interior state and an edge zone state.
Laminar Flow Along a Vertical Wall
Authors: Haugen R.
Published: October 2011

An analytical study is presented which describes the laminar accelerating flow of a thin film falling along a vertical wall. The approximate mathematical solution is given with emphasis on the growth and decrease of the boundary layer and film thickness, respectively. These resultant solutions are given in closed form and are found dependent upon two-dimensionless variables: φ2=3U0νgh02 and ζ2=1+2gh0x¯U02.
Shrink Fit of a Thick-Walled Cylinder With Contact Shear
Authors: Hill L. R. , Cakmak A. S. , Mark R.
Published: October 2011

The shrink fit of a finite band on an infinite elastic thick-walled circular cylinder is formulated in terms of inhomogeneous dual integral equations. The solution is obtained by the series method for the case of a prescribed uniform radial displacement and an arbitrary contact shear. A three dimensional photoelastic experiment was performed to provide a realistic contact shear condition and to confirm the analytical solution. The model loading fixture was based on the high coefficient of thermal expansion and the two-phase character of epoxy. The resulting stress and displacement fields are compared with those of a similar mixed boundary value problem neglecting the contact shear.
Elastic-Plastic, Axisymmetric Analysis of a Thin-Walled Cylindrical Shell Subjected to a Radial Pressure Difference
Authors: Montague P. , Horne M. R.
Published: October 2011

An analysis is given for the axisymmetric behavior of a thin-walled cylinder with direction-fixed ends subjected to increasing radial pressure, the material being elastic-pure plastic and yielding according to the Tresca (maximum stress difference) criterion. The presence of end pressure as well as radial pressure would involve only an extension to the analysis. A step-by-step, finite-difference technique is adopted, and is illustrated by application to two cylinders, enabling the development of plasticity in the walls of the cylinders to be traced in detail. The two cylinders considered were also tested experimentally and the theoretical pressures necessary to cause full yield conditions over the central sections of the cylinder lengths are shown to be in good agreement with the experimental results. Experimentally, cylindrical shells, which are insufficiently slender to fail by elastic instability when loaded with external pressure, are found to collapse when the central region of the shell length reaches a yield condition, a phenomenon which is not well understood. The theory presented here indicates the load level at which this central yielding takes place and can therefore be used to estimate the experimental collapse load. The relationship of the analysis to the rigid-plastic solution (10) of the same problem is discussed.
The Finite Beam With a Moving Load
Authors: Steele C. R.
Published: October 2011

A “method of images” series solution is obtained which converges rapidly for a simply supported, long beam with a high-velocity, moving concentrated load. Each term of the series is a Fourier integral solution for an appropriate semi-infinite beam problem. The integrals are evaluated in closed form for the beam without a foundation and have a simple asymptotic evaluation for the beam with an elastic foundation. In particular, the asymptotic results provide a solution for the “critical” load velocity, for which a “steady-state” solution does not exist, and for the limiting case of infinite load velocity, for which the beam is given an initial uniform lateral velocity.
Stress-Intensification Near a Semi-Infinite Rigid-Smooth Strip Due to Diffraction of Elastic Waves
Authors: Thau S. A. , Pao Yih-Hsing
Published: October 2011

Scattering of plane harmonic compressional and shear waves (P and SV-waves) by a semi-infinite rigid-smooth strip or ribbon which is a plane barrier with its top and bottom surfaces being confined normally, but free in lateral directions, is treated. Under the condition that displacements must be regular, exact solutions for the combined incident and scattered-wave fields are obtained in terms of Weber’s parabolic cylinder functions. Principal stresses are calculated on both sides of the strip and the stresses are shown to be singular of the order (kr)−1/2, where k is the incident wave number and r the radial distance from the tip.
Neutron Irradiation and the Yield Surfaces of Copper
Authors: Dudderar T. D. , Duffy J.
Published: October 2011

Tests were conducted to determine the effects of irradiation and plastic deformation on the yield surfaces of polycrystalline copper. It was found that the principal effect of plastic deformation on unirradiated copper was to translate the yield surface without appreciably changing its size or shape. Irradiation, on the other hand, produced a very large change in the overall size of the initial yield surface; in other words, it produced an effect phenomenologically similar to extensive isotropic strain-hardening. In addition, the shape of the initial yield surface after irradiation was dependent on the plastic strain offset chosen to define yield. This effect was not observed for the unirradiated metal. Extensive plastic deformation after irradiation caused the yield surface to translate and grow smaller without significantly changing shape.
An Alternate Approach to the Problem of Stokes’ Flow
Authors: Pollock F. , Struzynski R. E.
Published: October 2011

The problem of Stokes’ flow for a sphere in arbitrary external flow pattern is solved using a particular scalar Green’s function. By this method, the uniqueness of solution is clearly shown, and arbitrary flows (linear shear flow, Poiseuille flow, and so on) are seen to be as straightforward as simple uniform flow.
Bending Athwart a Parallel-Stiffened Plate
Authors: Huffington N. J.
Published: October 2011

Consideration is given to the problem of predicting the flexural rigidity of plates reinforced by parallel, equally spaced stiffeners for the direction (in the plane of the plate) normal to the stiffener orientation, as well as the stresses induced by a bending moment acting in this direction. The determination of this lateral flexural rigidity is formulated in terms of a problem in plane elasticity which may be solved by the finite-difference method for specific cases. Results obtained by this method are compared with those obtained by a simpler approximate procedure. An explicit relation is derived for the flexural rigidity associated with Poisson contraction. Experimental results are introduced and compared with theoretical predictions.
A Note on Taylor Instability in Circular Couette Flow
Authors: Coles D.
Published: October 2011

The problem of Taylor instability is reexamined, and it is shown that the effect of geometry (radius ratio) can be very nearly suppressed by a proper choice of variables. The two cases of cylinders rotating in the same direction and in opposite directions are treated separately.
On Dispersion of Longitudinal Waves in Rectangular Bars
Authors: Medick M. A.
Published: October 2011

Dispersion of longitudinal or extensional waves in isotropic, linear elastic bars of rectangular cross section is discussed within the framework of several approximate bar theories. A critique of three first-order theories and one second-order theory is given. The variation of cutoff frequencies with section geometry is established, and the singular nature of the bar response for a square section is noted.
Optimum Plastic Design of a Portal Frame for Alternative Loads
Authors: Prager W.
Published: October 2011

Minimum-weight design of a portal frame for alternative combinations of horizontal and vertical loads is discussed. It is shown that the usual proof of the existence of a Foulkes mechanism as a necessary condition for minimum weight cannot be carried over to this problem.
Kinematic Reversibility of Free Surfaces in Plane Viscous Creep
Authors: Berg C. A.
Published: October 2011

The plane creep of a free surface in an isotropic incompressible viscous fluid is shown to be kinematically reversible under cyclic loading about zero mean. It is concluded that, when kinematically irreversible free surface motion is experimentally observed in materials which show no apparent history effects, the phenomenon must be caused by three-dimensional deformation.
Rotating Flows Over a Rotating Disk for a Class of non-Newtonian Fluids
Authors: Lugt H. J. , Schwiderski E. W.
Published: October 2011

Axisymmetric rotating flows over a rotating disk for non-Newtonian fluids of Reiner-Rivlin type are calculated by means of an adjustable local boundary-layer approximation, which was recently introduced by the authors. Variation of the dynamic similarity parameter, which characterizes the non-Newtonian fluid, shows that secondary motions of stagnation, wake, or cell type can exist. The beginning of instability in Bo¨dewadt-type motions, which indicates laminar flow separation from the surface of the disk is shifted to higher Reynolds numbers for non-Newtonian fluids. Furthermore, the largest tangential shear stress at the surface is exhibited by laminar flows of Newtonian fluids.
Oscillatory Characteristics of Unsteady MHD Channel Flows Under Heaviside-Type Applied Magnetic Fields
Authors: Eraslan Arsev H.
Published: October 2011

The unsteady, fully developed MHD channel flow of a viscous, electrically conducting fluid is investigated under Heaviside-type applied magnetic fields. The fluid is assumed to be of constant properties and the Hall effect is neglected. The exact solutions, for the velocity and the induced magnetic fields, are obtained by Laplace and finite Fourier transforms for the ideally conducting wall conditions. It is shown that, during the transition from hydrodynamic to magnetohydrodynamic conditions, the flow undergoes strong oscillations, depending on the characteristic parameters, magnetic Prandtl number, and the Hartmann number, in contrast to the nonoscillatory transition from magnetohydrodynamic to hydrodynamic conditions.
Anisotropic Relaxation of Internal Forces in a Wound Reel of Magnetic Tape
Authors: Tramposch H.
Published: October 2011

Equations were developed to describe the relaxation of the internal stresses of a wound reel of magnetic tape, with allowances for the effects of surface roughness between tape layers and unequal thermal expansion of hub and tape-layer body. Numerical examples obtained with the aid of a high-speed digital computer indicated that the surface roughness as well as the unequal thermal expansion of hub and tape-layer body greatly affect the internal stress distribution. Essentially independent of the surface roughness, a typical reel, when stored at 120 F after being wound at 70 F and when the coefficient of thermal expansion of the hub is three times the value of the tape material, will approach stress-free conditions about 80 percent earlier than when it is stored at the winding temperature.
On the Axisymmetric Thermoelastic Problem in Bispherical Coordinates
Authors: Warren W. E. , Weese J. A.
Published: October 2011

Results of the thermoelastic analysis of an infinite elastic medium containing two arbitrary-sized spherical cavities with arbitrary separation distance are presented graphically. Of particular interest is the interference effect of one cavity on the other. The cavity surfaces are assumed to be held at uniform temperature while zero temperature prevails at infinity. Examples treated include those for which the cavity surfaces are stress-free and those for which individually self-equilibrated rigid liners are bonded to the cavity surfaces.
Torsional Instability of Cantilevered Bars Subjected to Nonconservative Loading
Authors: Nemat-Nasser S. , Herrmann G.
Published: October 2011

A cantilevered bar of uniform cross section and subjected at the free end to distributed, non-conservative, compressive loads is considered. It is shown that, for certain cross sections, stability may be lost by either torsional divergence (torsional buckling) or torsional flutter, depending upon the load distribution at the end section. In addition, transverse flutter also can occur, however, not transverse buckling.
Plane Waves in an Elastic-Plastic Half-Space Due to Combined Surface Pressure and Shear
Authors: Bleich H. H. , Nelson Ivan
Published: October 2011

The most general case of plane wave propagation, when normal and shear stresses occur simultaneously, is considered in a material obeying the von Mises yield condition. The resulting nonlinear differential equations have not been solved previously for any boundary-value problem, except for special situations where the differential equations degenerate into linear ones. In the present paper, the stresses in a half-space, due to a uniformly distributed step load of pressure and shear on the surface, are obtained in closed form.
The Measurement of Dynamic Strains Using Birefringent Strips
Authors: Frasier J. T. , Robinson D. N.
Published: October 2011

An experimental study is presented of the bonded birefringent strip as a means of observing transient deformations on the surfaces of opaque bodies. The particular situation investigated consists of a birefringent sheet bonded to a metal rod in which a strain pulse is initiated by a small explosive charge. Major emphasis is placed upon the study of two problems associated with the use of the technique. The first is the development of a reliable method of interpreting the observed photoelastic fringe patterns. The second is an evaluation of the influence the sheet has on the strain pulse in the bar. Satisfactory agreement is obtained between the strain profile at the rod-sheet interface determined by using a birefringent strip and the profile given by resistance-wire strain gages.
On the Almost Sure Stability of Linear Stochastic Distributed-Parameter Dynamical Systems
Authors: Wang P. K. C.
Published: October 2011

In this paper, sufficient conditions for almost sure stability and asymptotic stability of certain classes of linear stochastic distributed-parameter dynamical systems are derived. These systems are described by a set of linear partial differential or differential-integral equations with stochastic parameters. Various examples are given to illustrate the application of the main results.
The Effect of a Riveted Stringer on the Stress in a Sheet With a Circular Cutout
Authors: Bloom J. M.
Published: October 2011

A theoretical investigation was made into the effect of a rivet-attached stringer on the stress concentrations in a thin elastic sheet with a circular cutout. The sheet and stringer are loaded (at infinity) by a uniform tensile stress parallel to the stringer. The results are expressed in terms of a “correction factor.”
On Certain Approximations in Sandwich Plate Analysis
Authors: Cook R. D.
Published: October 2011

This paper presents quantitative information regarding the validity of certain approximations applicable to sandwich plate analysis. Equations are developed for each approximate theory. Results given by the approximate theories are compared with results given by a more general theory, for several values of pertinent geometric and elastic properties.
Some Fundamental Thermoelastic Problems in Orthotropic Slabs
Authors: Baker B. R.
Published: October 2011

Steady-state problems of stresses in orthotropic slabs subjected to forces and temperature distribution on the faces are solved by means of Fourier transforms. The usual direct applications in the literature are shown for simple examples to lead to divergent integrals but, by introduction of generalized transforms, a very broad class of problems can be handled. As a part of these considerations, a more definite form of Saint-Venant’s principle is obtained. For a certain class of material constants, it is possible to obtain closed-form solutions for stresses when concentrated loads or temperature sources are applied to the faces of the slab. Results are presented for several examples in the form of complex stress potentials and graphs of the corresponding stress components.
One-Dimensional Theories of Wave Propagation and Vibrations in Elastic Bars of Rectangular Cross Section
Authors: Medick M. A.
Published: October 2011

A method for constructing rational, one-dimensional theories of various orders of approximation, descriptive of wave propagation and vibrations in anisotropic elastic bars of rectangular cross section, is presented. As illustrations, several approximate theories are derived which are applicable to extensional motion in rectangular bars of isotropic material.
On Wave Propagation in Thermoplastic Media
Authors: Fine A. D. , Kraus H.
Published: October 2011

The dynamic behavior of a medium, according to the uncoupled thermoplastic theory, is presented and is compared to the behavior that would be obtained from an uncoupled quasi-static analysis. Since the inertia terms are retained in the equations of motion, wave fronts (or surfaces of discontinuity) are produced in the medium. The normal velocity of the wave front separating the elastic and plastic regions is determined. General closed-form solutions of the displacement (according to both the dynamic and the quasi-static approaches) are obtained; their unique forms are found for the semi-infinite region, and an illustrative numerical example is then presented.
The Effect of a Riveted Stringer on the Stress in a Cracked Sheet
Authors: Bloom J. M. , Sanders J. L.
Published: October 2011

This paper is a theoretical investigation into the effect of a rivet-attached stringer on the stress concentrations in a thin elastic sheet with a crack. The sheet and stringer are loaded (at infinity) by a uniform tensile stress parallel to the stringer. The sheet contains a finite crack perpendicular to the stringer. The problem is formulated in terms of an infinite set of algebraic equations for the unknown rivet loads which are truncated and then solved on the IBM 7094 digital computer. The results are used to calculate the effect of the stringer on the strength of the stress intensity at the crack tip.
Interaction of Critical Pressures and Critical Concentrated Loads Acting on Shallow Spherical Shells
Authors: Loo Ta-Cheng , Evan-Iwanowski R. M.
Published: October 2011

In this paper the critical combinations of uniform pressures and concentrated loads at the apex acting on shallow spherical shells have been determined analytically and experimentally. The Dini-Bessel expansion of unknown functions, proposed first in [4], have been applied to the problem on hand. Test specimens void of initial geometrical imperfections and negligible residual stresses have been fabricated in the laboratory by using the die-pressing technique. The analytically calculated critical combinations are in good agreement with those determined experimentally. The theoretical lower-bound, or the cut-off values, of the geometry parameter, μ, is found to be near the experimental values. The existence of the analytical and experimental cut-off values of γ2 indicates that there is a lower bound of the values of uniform pressures such that a shell does not exhibit a snap-through instability when subjected for any combinations of concentrated loads and uniform pressures below its cut-off value.
The Dynamics of Real Air From Subcritical Temperatures to 1500 K
Authors: Pinkus O.
Published: October 2011

Analytical expressions for the calculation of the thermodynamic properties of real air are presented. The expressions are derived from an equation of state proposed by Hirschfelder, et al. Although the region of interest is primarily that of low temperatures, the contribution of the vibrational energy is included, making the equations applicable to temperatures ranging from subcritical to 1500 K. Based on these equations, expressions are derived for the expansion of real air from fixed or variable plenum conditions, with the expansion of the air in the supply chamber ranging from isothermal to isentropic. It is shown that, compared with calculations based on perfect gas relations, the expansion of real air yields lower mass rate flows.
Hydrodynamic Gyroscope
Authors: Then J. W.
Published: October 2011

The apparatus is a gyroscope in which the rotor consists of a circulating stream of water contained in four loops of transparent plastic tubing, 1 in. ID. The circulation is maintained by a d-c centrifugal pump and motor as a single unit, the speed of which is variable. It exhibits all the qualitative characteristics of a regular gyroscope. A description of the apparatus, its performance, and operating data are included.
Large Deflection in Elastoplastic Bending of a Simply Supported Circular Plate Under a Uniform Load
Authors: Ohashi Y. , Murakami S.
Published: October 2011

The present paper is concerned with the analysis of the large elastoplastic deflection of a simply supported plate subjected to a uniform load. The analysis is performed under the assumptions of von Mises’ yield condition, Hencky’s stress-strain relation, and nonhardening of the material. The corresponding experiment is also made with a mild steel specimen to ascertain the appropriateness of the assumptions and the procedure of the analysis. Results of the analysis are compared with the available analytical results based on the limit analysis or the theory neglecting the effects of membrane force as well as with experimental data. Also discussed is the physical validity of the deformation theory used in the present analysis.
Normal Modal Vibrations for Some Damped n-Degree-of-Freedom Nonlinear Systems
Authors: Morgenthaler George W.
Published: October 2011

T. K. Caughey1 has shown that a necessary and sufficient condition that a damped, linear, n-degree-of-freedom system possess classical linear normal modes is that the damping matrix be diagonalized by the same transformation which uncouples the undamped system. Rosenberg2 has defined normal modes for nonlinear n-degree-of-freedom undamped systems and has shown the existence of such modes for various classes of nonlinear systems. In linear systems, the frequency is independent of the amplitude and, if a set of masses is vibrating in unison, it is not surprising that in some cases they continue to do so as the motion damps out. In nonlinear vibrations, however, frequency depends upon amplitude so that a series of masses vibrating at different amplitudes in a Rosenberg normal mode might generally be expected to lose synchronization as their amplitudes damp out. Two classes of systems are discussed here in which normal modes are preserved under damping, and several examples are given.
Upper and Lower Bounds of Frequencies for Cantilever Bars of Variable Cross Sections
Authors: Gaines J. H. , Volterra Enrico
Published: October 2011

Upper and lower bounds of frequencies of transverse vibrations of cantilever bars of variable cross sections are presented, taking into account the effects of transverse shear and of rotatory inertia. Numerical results for the first four natural frequencies are presented in tabular form for different inertia characteristics of the bars.
Ablation of Reinforced Plastic for Heat Protection
Authors: Kauzlarich J. J.
Published: October 2011

The steady-state ablation of reinforced plastic is analyzed, and a new solution for the pyrolysis-zone equations is presented. Attention is directed to the effect of combustion of gases of ablation in the boundary layer at low free-stream, total-enthalpy conditions with a numerical example. The solution may be used to predict ablation rate, surface temperature, temperature distribution in the plastic, and the effect of physical and chemical properties of the materials.
Stress Interference in Three-Dimensional Torsion
Authors: Eubanks R. A.
Published: October 2011

An explicit series solution is presented for the stress and displacement fields in an elastic body of infinite extent containing two equidiameter spherical cavities. At large distances from the cavities the displacement field coincides with that which arises from pure torsion about the axis of symmetry. Numerical results are presented in graphs which demonstrate the interference of the two sources of stress concentration.
Stress Distribution in Anisotropic Viscoelastic Hollow Sphere
Authors: Moghe S. R. , Hsiao C. C.
Published: October 2011

The stress and deformation analysis of an anisotropic linear viscoelastic hollow sphere under a symmetrical loading on the boundaries is considered. In order to reduce some of the mathematical difficulties, assumptions of small strain with quasistatic stress-strain conditions are consistently made. The solution is found for a system of non-homogeneous anisotropic viscoelastic media, and subsequently reduced to that for a homogeneous medium. Numerical results for both short-time and long-time behavior are presented for a number of simple model media in the anisotropic viscoelastic case and compared with the result for the elastic or viscoelastic medium in the isotropic case.
Stress Distribution Near Internal Crack Tips for Longitudinal Shear Problems
Authors: Sih G. C.
Published: October 2011

A method is developed for finding the stress distribution in a cracked body under longitudinal shear and applied to solve a number of problems. Stress solutions are obtained in closed form and discussed in connection with the Griffith-Irwin theory of fracture. The results indicate that current fracture-mechanics theories may be applied directly to longitudinal shear problems. More specifically, the character of the stress distribution near the vertex of a sector cylinder in shear is examined. The inverse half-power law of the stress singularity at a crack tip may be verified by taking a vertex angle of 2π. In addition, crack-tip, stress-intensity factors are defined and evaluated from a complex stress function in a manner similar to those previously given for extension and plate-bending problems. Results of such studies clarified the behavior of branched cracks and other crack systems of interest.
A Direct-Stress Analysis of Orthotropic Cantilever Plates
Authors: Coull A.
Published: October 2011

A method is given for the direct-stress analysis of orthotropic cantilever plates, without the usual need for intermediate deflection calculations. The partial differential equation of plate theory is reduced to a set of ordinary linear differential equations by assuming Fourier-series distributions of stress couples and shear-stress resultants in the plate: The coefficients of these series are determined by the principle of least work.
On Detached Shocks for Blunt Bodies at Small Angles of Attack
Authors: Yeh Hsuan , Doby Raymond
Published: October 2011

This paper is addressed to the problem of determining the subsonic flow field that exists between the shock and the associated blunt body at small angles of attack. An inverse perturbation procedure is used whereby the shock itself is caused to rotate and the body that supports the perturbed shock is determined. It is found that the perturbed body does not possess a rigid-body-rotation relation relative to the primary flow body. Curves and tables are presented which represent the results of the numerical computations.
On the Destabilizing Effect of Damping in Nonconservative Elastic Systems
Authors: Herrmann G. , Jong Ing-Chang
Published: October 2011

The destabilizing effect of linear viscous damping in a nonconservative elastic system is investigated by studying the roots of the characteristic equation in addition to the stability criteria and by introducing the concept of degree of instability. A generic relationship between critical loadings for no damping and for slight damping as well as vanishing damping is established. It is found that while the presence of small damping may have a destabilizing effect, proper interpretation of the limiting process of vanishing damping leads to the same critical load as for no damping.
Analysis of a Magnetohydrodynamic Ejector
Authors: Heiser W. H.
Published: October 2011

This paper reports the results of a theoretical first-order analysis of a constant-area ejector for incompressible, inviscid, conducting fluids which uses induced magnetohydrodynamic forces rather than viscous forces for mixing. Performance characteristics in dimensionless form are given in terms of dimensionless parameters which can be controlled by the experimenter. The range of validity of the inviscid model is established in dimensionless form and it is shown by example that experiments for which the analysis is valid are possible.
Natural Frequencies of Transversely Vibrating Uniform Annular Plates
Authors: Vogel S. M. , Skinner D. W.
Published: October 2011

Frequency determinants are derived for various combinations of boundary conditions associated with the transverse vibrations of uniform annular plates. From these equations, the values of the resonant frequencies of the various normal modes are calculated. Graphs and selected tables are included to facilitate the use of this material for design purposes. The results of an experimental investigation of two of the cases are also presented, and the agreement between these findings and the theoretically predicted values is remarkably good.
On the Variational Principle and Lagrange Equations in Studies of Gasdynamic Lubrication
Authors: Tao L. N.
Published: October 2011

The paper is concerned with the variational formulation in studies of gasdynamic lubrication. It is shown that Reynolds’ equation of lubrication is equivalent to a set of Lagrange equations similar to those in classical dynamics. The Lagrangian and the dissipation-production are defined. Furthermore, based on the Hamiltonian principle for the field of a continuum, the Lagrangian density and the dissipation-production density are established. This formulation includes the incompressible problem, which is obtainable from the Helmholtz-Rayleigh principle of minimum energy-dissipation, as a special case. Hence a unification of the variational methods for both gasdynamic and hydrodynamic lubrication is accomplished.
The Plane-Stress Problem for a Doubly Connected Region in Which the Medium Undergoes Elastic and Creep Deformation
Authors: Platus David L.
Published: October 2011

A theoretical method of analysis is revealed for handling the plane-stress problem of a doubly connected region in which the medium undergoes elastic and creep deformation. The solution is developed in small increments of time as a sequence of solutions to elastostatic problems of two types. The first elastostatic problem involves surface forces only and is solved by the alternating method of Schwarz in conjunction with the method of Muskhelishvili. The second elastostatic problem is of the “initial-stress” type and is solved by the use of finite differences and double Fourier series. A numerical example, evaluated with the aid of an IBM 7090 electronic data-processing machine, is presented for the case of a uniformly stretched plate in the shape of a circular annulus.
On the Form of Variationally Derived Shell Equations
Authors: Reissner Eric
Published: October 2011

In the first part of the paper the basic equations of three-dimensional elasticity are formulated as a system of four equilibrium equations and seven stress displacement relations, together with a variational problem which has these eleven equations as Euler equations. In the second part of the paper, the new variational problem is used for a derivation of shell theory which accounts particularly simply for the differences between the resultants N12 and N21 and the couples M12 and M21. In the third part of the paper a solution is given of the torsion problem for circumferentially nonhomogeneous circular cylindrical shells, as an explicit demonstration of the fact that certain terms in the shell equations which are often of negligible influence sometimes are of considerable influence.
Dynamic Stability of Rotating Shafts in Viscous Fluids
Authors: Walston W. H. , Ames W. F. , Clark L. G.
Published: October 2011

Stability characteristics of an overhanging shaft immersed in a viscous fluid are investigated experimentally. The predominance of two effects, damping and virtual mass, are separated and explored as they affect amplitude and critical speed. A correlation equation for amplitude as a function of viscosity, velocity, and mass is developed with the aid of statistical regression analysis. The techniques of regression analysis are summarized in the Appendix.
Solution to Euler’s Gyrodynamics—I
Authors: Harding C. F.
Published: October 2011

A little used parameterization of the three-dimensional rotation group is taken as basis in deriving an easily integrable kinematic relation (a 4-vector linear differential equation) for the attitude rate, in terms of the present attitude and angular velocity of one reference frame relative to another. If the angular velocity is known and well behaved one obtains the exact solution from an iteration procedure explained in detail. The formal solution to a large class of rigid-body problems is thus implied; a particular one being that of an axially symmetric rocket with variable thrust vector and constant moment-of-inertia tensor which as such generalizes Jacobi’s torque-free case.
Lower Bounds to Thermal Instability Criteria of Completely Confined Fluids Inside Cylinders of Arbitrary Cross Section
Authors: Pnueli D.
Published: October 2011

A method is developed to compute the lower bounds for the thermal instability criterion (the critical Rayleigh number) for fluids completely confined inside cylinders of arbitrary cross section; i.e., Rayleigh numbers below which no spontaneous flow may occur in spite of the density gradient being opposite to the body force direction.
Fluid Centering of Pistons
Authors: Raimondi A. A. , Boyd John
Published: October 2011

Conventional piston-in-cylinder designs are liable to high friction, hydraulic lock, and excessive wear. A simple adaptation of fluid compensation which overcomes these faults is described. Design curves for estimating forces and flow requirements are given.
Stress Distribution on the Boundary of a Circular Hole in a Large Plate Due to an Air Shock Wave Traveling Along an Edge of the Plate
Authors: Daniel I. M. , Riley W. F.
Published: October 2011

In the research program reported in this paper an experimental solution was obtained for the stress distribution around a circular hole in a large plate during passage of a pressure wave. The pressure wave was generated by passing an air shock wave of fast rise and slow decay along an edge of the plate with a shock tube. The experimental method used for the study was dynamic photoelasticity complemented with the moire method of strain analysis. A transparent, low-modulus, birefringent, urethane rubber was used as the model material. Transient free-field stresses were determined in the plate, at the hole location, prior to machining the hole. These stresses were introduced in the classical Kirsch solution to obtain what is referred to as a static stress distribution around the boundary of the hole. This stress distribution was compared with the dynamic stress distribution obtained directly from photoelastic data. The free-field stresses were also introduced in the theoretical solution by Baron and Matthews to obtain the maximum tangential stress on the boundary of the hole. The theoretical results are in good agreement with the experimentally determined maximum tangential stress. The results also indicate that the dynamic stress-concentration factor is initially lower than the static one, exceeds is at a later time, and finally approaches it asymptotically.
Analysis of Shells of Revolution Subjected to Symmetrical and Nonsymmetrical Loads
Authors: Kalnins A.
Published: October 2011

The boundary-value problem of deformation of a rotationally symmetric shell is stated in terms of a new system of first-order ordinary differential equations which can be derived for any consistent linear bending theory of shells. The dependent variables contained in this system of equations are those quantities which appear in the natural boundary conditions on a rotationally symmetric edge of a shell of revolution. A numerical method of solution which combines the advantages of both the direct integration and the finite-difference approach is developed for the analysis of rotationally symmetric shells. This method eliminates the loss of accuracy encountered in the usual application of the direct integration approach to the analysis of shells. For the purpose of illustration, stresses and displacements of a pressurized torus are calculated and detailed numerical results are presented.
The Dynamic Viscoplastic Expansion of a Cylindrical Tube
Authors: Appleby E. J.
Published: October 2011

The viscoplastic flow of a long thick-walled tube is investigated. The tube is subjected to internal pressure and has its ends restrained from motion in the axial direction. The material of the tube is rigid-viscoplastic and incompressible. The pressure required to produce a specified expansion of the tube is calculated for two examples. In the former the effect of different viscosity coefficients is observed. In the latter example a comparison is made of the effects of perfect plasticity, viscosity, and inertia.
Vibrations of a Rectangular Plate With Concentrated Mass, Spring, and Dashpot
Authors: Das Y. C. , Navaratna D. R.
Published: October 2011

An analytical method, developed by Young [1], is here extended to the determination of the natural frequencies of a composite system which consists of an isotropic rectangular plate with a concentrated mass, spring, and dashpot attached at any point of the plate. This method makes use of a double series expansion in terms of two sets of orthogonal functions which represent the normal modes of the vibration of the plate alone. Numerical examples for a square plate with (a) a combined concentrated mass and spring, (b) two concentrated masses, and (c) an attached dashpot have been presented.
On the Dynamics of Plastic Spherical Shells
Authors: Sankaranarayanan R.
Published: October 2011

This paper discusses the behavior of complete spherical shells and simply supported spherical caps under impulsive loading by uniform external pressure. The pressures are assumed to be greater than the static collapse pressures and to act for a short period of time. The displacements of the shells are presented for particular values of the parameters of the problem.
Transient Analysis of Shear Impact
Authors: Pytel Andrew , Davids Norman
Published: October 2011

This paper carries out a transient analysis of the propagation of stress waves generated by time-dependent tangential surface loadings. The problem is solved by representing the concentrated load as a delta-function singularity and applying the boundary conditions to the general solutions to the equations of motion. Expansion in a power series leads to terms which represent successively reflected waves. The complete expressions for the axial shearing stress and axial displacement for an arbitrary forcing function are obtained and curves are shown for step and exponential pulse inputs for an aluminum plate.
Transient Compressional Waves in an Infinite Elastic Plate or Elastic Layer Overlying a Rigid Half-Space
Authors: Miklowitz Julius
Published: October 2011

The problem treated is that of an infinite free plate excited symmetrically by two equal and normally opposed step point-loads on its faces. The problem is equivalent to that of the surface normal point-load excitation of an infinite elastic layer, half the thickness of the plate, overlying a rigid half-space with lubricated contact. The formal solution is obtained from the equations of motion in linear elasticity with the aid of a double integral transform technique and residue theory. The stationary phase method, and known characteristics of the governing Rayleigh-Lamb frequency equation, are used to analyze and evaluate numerically the far field displacements. It is shown that the head of the disturbance is composed predominantly of the low-frequency long waves from the lowest mode of wave transmission.
On the Annular Damper for a Freely Precessing Gyroscope—II
Authors: Miles J. W.
Published: October 2011

A previous analysis of the annular damper was based on the hypothesis that the motion at any instant could be regarded as quasi-steady. This analysis is revised in the present paper by accounting for all accelerations. The decay times are found to be substantially greater (damping less) than those predicted in the previous analysis. A general result for the dissipation in the laminar boundary layer of a liquid oscillating over a rigid wall is developed.