bluuebunny/crossref_metadata_2025 huggingface dataset:
Physicochemical, mineral and sensory properties of set‐type yoghurts produced by addition of grape, mulberry and carob molasses (Pekmez) at different ratios
Authors: KARACA OYA BERKAY , SAYDAM IBRAHIM BAŞAR , GÜVEN MEHMET
Published: October 2011

This study investigated the effects of adding grape, mulberry and carob molasses (Pekmez) at 6%, 10% or 14% on titratable acidity, pH, viscosity, whey separation, water holding capacity (WHC), gel firmness, acetaldehyde, volatile fatty acids, colour values, mineral profile and sensory properties of set‐type yoghurts. Increasing concentration of the molasses decreased whiteness value, viscosity and WHC, but increased redness/greenness and yellowness/blueness values, whey separation and mineral contents of the samples significantly (P < 0.05). Nevertheless, the yoghurts produced by adding grape molasses had the highest points in the sensory evaluation, followed by mulberry and carob molasses.
Science, self, and immortality
Authors: Haught John F.
Published: October 2011

The following considers the concept of scientific naturalism in relation to life after death and contrasts three alternative perspectives on immortality of the soul, including naturalistic fatalism, otherworldly optimism, and long‐suffering hope.
Quid pro quo: the ecology of the self
Authors: Paulson Steve , Flanagan Owen , Bloom Paul , Baumeister Roy
Published: October 2011

Moderated by Steve Paulson, producer and interviewer for public radio's To the Best of Our Knowledge, philosopher and neurobiologist Owen Flanagan (Duke University), and psychologists Paul Bloom (Yale University) and Roy Baumeister (Florida State University) examine current biological, psychological, and anthropological research on the complex interaction between the self and others, and consider the roots of empathy and morality. The following is an edited transcript of the discussion that occurred February 23, 2011, 7:00–8:15 PM, at the New York Academy of Sciences in New York City.
Me, myself, and I: the rise of the modern self
Authors: Hanna Robert , Izenberg Gerald , Martin Raymond , Wiley Norbert , Seigel Jerrold
Published: October 2011

Moderated by Robert Hanna (University of Colorado), historians Gerald Izenberg (Washington University, St. Louis) and Jerrold Seigel (New York University), philosopher Raymond Martin (University of Maryland and Union College), and sociologist Norbert Wiley (University of Illinois) trace the evolution of the meaning of self from antiquity to the present and consider how the self described by classical philosophers matches the reality of what we know about ourselves from human experience and research.
“Much ado to know myself…”: Insight in the talking cures
Authors: Jopling David A.
Published: October 2011

Psychoanalysis, psychodynamic psychotherapy, and the other talking cures claim to help clients acquire insight into their selves. With insight, the unruly forces that govern lives and that make people strangers to themselves finally come to be understood and rendered subject to conscious control. These insights, it is claimed, are true, and fit the facts like a key fits a lock; they are not merely coherent fictions or confabulated cause‐and‐effect stories designed to please clients. But is this credible? The argument developed here is that some of the therapeutic changes in the talking cures are functions of placebos that rally the mind's native healing powers in much the same way that placebo pills rally the body's native healing powers and that some of these placebos are insight placebos. The talking cures rightfully claim that it is only talking with others that unlocks the soul and opens it up to ways of self‐knowing and to caring for self that would otherwise be unavailable, but they fail to acknowledge the presence of placebo effects, and they operate with restrictive models of dialogue that may unintentionally encourage placebo effects and cognitive suggestibility.
The American self and the long march to legal equality
Authors: Wiley Norbert
Published: October 2011

Legally, women, Native Americans, and African‐Americans were defined by the American Constitution as inferior. The pragmatists gradually showed that all selves are equal. These ideas helped the minorities to attain nearly full legal status. But economic status is going in the other direction, toward inequality. It threatens to overcome the hard‐won legal equality and make it meaningless.
Physiological evidence for a trans‐basal ganglia pathway linking extrastriate visual cortex and the superior colliculus
Authors: Jiang Huai , Stein Barry E. , McHaffie John G.
Published: October 2011

Non‐technical summary  The superior colliculus (SC) is a subcortical brain structure critically involved in the production of eye and head movements to novel or salient visual cues. But to accomplish its function, an input from visual cortex also is required. Because visual cortex projects directly to the SC, this route is typically viewed as the predominant way by which cortex exerts higher‐level control over SC‐mediated behaviours. However, anatomical studies suggest that other multi‐neuronal circuits through the basal ganglia, a collection of interconnected structures involved in decision making, might provide an alternative way for cortex to influence the SC. The present study provides physiological evidence for such an alternative route and affords additional insights into how the brain initiates and controls movements in response to visual cues. Such knowledge could be important for developing therapies to lessen the effects of visual deficits in patients experiencing loss of function following head trauma or stroke.
The Effect of General Imperfections on the Buckling of Cylindrical Shells
Authors: A´rbocz Johann , Babcock Charles D.
Published: October 2011

An experimental and theoretical investigation of the effect of general imperfections on the buckling load of a circular cylindrical shell under axial compression was carried out. A noncontact probe has been used to make complete imperfection surveys on electro-formed copper shells before and during the loading process up to the buckling load. The data recording process has been fully automated and the data reduction was done on an IBM 7094. Three-dimensional plots were obtained of the measured initial imperfection surfaces and of the growth of these imperfections under increasing axial load. The modal components of the measured imperfection surfaces were also obtained. The theoretical solution located the limit points of the postbuckled states. A simplified imperfection model was used consisting of one axisymmetric and two asymmetric components. For global buckling the correlation between the theoretical buckling loads and the experimental values was found to be good.
An Asymptotic Method to Analyze the Vibrations of an Elastic Layer
Authors: Achenbach J. D.
Published: October 2011

The displacement components for both free and forced vibrations are sought as power series of the dimensionless wave number ε, where ε = 2π × layer thickness/wavelength. For the free vibration problem the object is to determine the frequencies, which are also sought as power series of the dimensionless wave number. The displacement and frequency expansions are substituted in the displacement equations of motion and in the boundary conditions. By collecting terms of the same order εn, a system of second-order, inhomogeneous, ordinary differential equations of the Helmholtz type is obtained, with the thickness variable as independent variable, and with associated boundary conditions. For free vibrations, subsequent integration yields the coefficients of εn for the displacements and the frequencies for all modes, and in the whole range of frequencies, but in a range of dimensionless wave numbers 0 < ε < ε* < 1, where ε* increases as more terms are retained in the expansions. For forced vibrations, the amplitudes are determined in an analogous manner if the external surface tractions are of sinusoidal dependence on the in-plane coordinates and on time. The response to surface tractions of more general spatial dependence is obtained by Fourier superposition.
Analysis of Heterogeneous Anisotropic Plates
Authors: Whitney J. M. , Leissa A. W.
Published: October 2011

Using the basic assumptions of thin-plate theory, including nonlinear terms in the von Karman sense, the governing equations of a laminated anisotropic plate are formulated. In particular, the type of plate under discussion consists of n layers of orthotropic sheets bonded together. Each layer has arbitrary thickness, elastic properties, and orientation of orthotropic axes with respect to the plate axes. The governing equations are obtained by integrating the equations of nonlinear elasticity. Inertia terms and thermal stresses are included. Closed-form solutions to the linearized equations are obtained for bending, flexural vibration, and buckling of special, but important, classes of laminates for which coupling between bending and stretching is unavoidable.
Equivalent Circuit Representation of Web Conveyance Systems
Authors: Dunn H. Searl
Published: October 2011

Typical web conveyance components are described by equivalent electrical circuits with web tension and velocity analogous to voltage and current, respectively. Such phenomena as waves and resonances in web handling system are easily understood in terms of the analogous electrical networks.
Approximate Roots of Flu¨gge’s Characteristic Equation for the Closed Cylindrical Shell
Authors: Colbourne J. R.
Published: October 2011

Two approximate solutions are given for Flu¨gge’s closed cylindrical shell characteristic equation, valid for the lower and higher harmonics, respectively. It is shown that as the harmonic number increases, the roots of Donnell’s characteristic equation do not behave asymptotically like those of the Flu¨gge equation.
On the Stability of the Vibrations of Two Coupled Particles in the Plane
Authors: Rand R. H. , Tseng S. F.
Published: October 2011

The stability of the vibrations of two identical particles constrained to a plane and restrained by three identical linear springs with initial stress is studied by uncoupling the first variational equations and applying Floquet theory and perturbations. A new stability parameter is introduced which indicates stability by virtue of its sign.
On Evaluation of Natural Frequencies for a System of Equal Inertias and Equal Spring Stiffnesses
Authors: Chen Fan Y.
Published: October 2011

Based on mathematical induction, an expedient method of computation of natural frequencies for a close-coupled linear vibrational system of equal inertias and equal spring stiffnesses is devised.
End Effect Bending Stresses in Cables
Authors: DeRuntz J. A.
Published: October 2011

An analysis of bending stresses in flexible cables has been carried out. It has been found that stresses which arise due to fixity at the boundaries or other points of discontinuity, decay in an exponential manner from such boundaries, similar to the edge effect solutions of shell theory. Such a phenomenon makes it possible to analyze a finite cable of sufficient length using solutions which are applicable only to infinite or very long cables. In this way the cumbersome but otherwise exact solutions of the elastica are replaced by much simpler ones of sufficient engineering accuracy. The term “sufficient length” is defined as part of the analysis.
Forced Transverse Vibration of a Solid Viscoelastic Cylinder Bonded to a Thin Casing
Authors: Shaffer Bernard W. , Sann Robert I.
Published: October 2011

The amplitude versus frequency-response spectra of stress and displacement components within a solid viscoelastic cylinder bonded to a thin elastic casing are obtained when arbitrary normal and tangential stresses are applied to the outer surface of the casing. Special consideration is given to assemblies whose cores are made either of a Voigt material or a Maxwell material. A quantitative comparison of the bond stress amplitude spectrum at the lowest circumferential wave number reveals for both Voigt and Maxwell cores, and for small values of retardation time and relaxation time, respectively, that the amplitude ratio between the radial bond stress and the lateral pressure decreases with increasing values of the time constant. As the time constants get larger, the resonant amplitude increases for the Maxwell material, and decreases for the Voigt material. The Voigt core essentially behaves like an elastic solid at small values of its retardation time, and like a viscous fluid at large values of its retardation time. The Maxwell core essentially behaves like a nonviscous fluid at small values of its relaxation time and like an elastic solid at large values of its relaxation time.
Circular Cylindrical Shell Supported Along a Generator
Authors: Sarkadi-Szabo Istvan
Published: October 2011

The circular cylindrical shell is subjected to arbitrary forces. The boundaries can be free, simply supported, or fixed. The shell is supported also along a generator. This problem was solved by the use of the finite Fourier transform and the results simplified by the Euler sum formula. A numerical example is presented.
On the Dynamic Response of an Infinite Rod to a Randomly Moving Torque
Authors: Recker W. W.
Published: October 2011

The problem of an infinitely long elastic rod subject to a moving concentrated twisting moment with position determined by the stationary process X(t) is analyzed. Information concerning the expected value of the angle of torsion is found.
Generalized Vector Derivatives for Systems With Multiple Relative Motion
Authors: Sherby T. A. , Chmielewski J. F.
Published: October 2011

For the analysis of relative motion, classical vector mathematics is limited to the use of one moving reference frame when taking vector derivatives. However, many dynamical systems consist of a number of rigid bodies in motion relative to one another. The classical procedure requires the specification of the position of each body relative to a single “main body.” The use of relative coordinates allows a natural specification of the position of one moving body relative to another moving body in network fashion. To use relative coordinates in dynamic and kinematic analyses, it is necessary to use relative vector derivatives involving more than one moving reference frame. This paper presents general expressions for the kth-order derivative of a relative position and angular velocity vector measured in any moving reference frame in a system of m reference frames with multiple relative motion. These expressions are used to develop a procedure which generates the differential equations of motion for the system by routine substitution of the relative coordinates and their scalar derivatives. This procedure offers promise as an algorithm for machine generation of the system equations and eliminates the possibility of neglecting subtle accelerations due to relative motion. The use of the procedure is demonstrated by generating the equations of motion of an offset unsymmetrical gyroscope.
Dynamics of Synchronous-Precessing Turborotors With Particular Reference to Balancing. Part 2—Application
Authors: Tang T. M. , Trumpler P. R.
Published: October 2011

The theory of Part 1 is applied to a flexible rotor in which bearing forces are taken as linear functions of journal displacement. The balancing problem is viewed as the optimization (by digital computer) of the angular orientations of all disk masses at rotor assembly, after a rough balance of each mass is achieved and the location of its mass center experimentally established. A “disk sensitivity” criterion is suggested for determining which disk locations show the greatest effect of balance change on rotor performance. Finally, an example of the predicted difference in bearing force for a typical rotor with arbitrary disk orientation, and with improved orientation, is presented.
Plane-Strain Dynamic Response of a Cylindrical Shell—A Comparison Study of Three Different Shell Theories
Authors: Reismann H. , Pawlik P. S.
Published: October 2011

An analytical study of the plane-strain dynamic response of a circular, cylindrical shell is presented. The shell is subjected to a radially directed concentrated impulse acting on its surface. Solutions are presented within the framework of (a) membrane theory, (b) Flu¨gge theory, and (c) improved theory (including shear deformation and rotatory inertia). A quantitative study of the initial motion of the shell indicates major differences in response prediction of the three theories. An explanation of these differences is offered.
Transient Axially Symmetric Excitation of a Circular Elastic Rod in Plane Strain
Authors: Nelson C. W.
Published: October 2011

Consider a long cylindrical bar (of a homogeneous, isotropic, linearly elastic material) that is initially in static equilibrium under the action of uniform radial pressure on its cylindrical surface and axial stress as required to maintain plane strain. At zero time the radial pressure is suddenly removed, but plane-strain conditions are maintained. A finite Hankel transform solution is presented for the ensuing radial displacement and for the radial, circumferential, and axial stresses—all as functions of the radial coordinate and time. Results of computations for Poisson’s ratio equal to 0.3 are presented graphically.
Finite Deflections of a Rigid-Viscoplastic Strain-Hardening Annular Plate Loaded Impulsively
Authors: Jones Norman
Published: October 2011

A relatively simple analytical treatment of the behavior of a rigid-plastic annular plate subjected to an initial linear impulsive velocity profile is presented. The influence of finite deflections has been included in addition to strain-hardening and strain-rate sensitivity of the plate material. It is shown, for deflections up to the order of twice the plate thickness, that strain-hardening is unimportant, strain-rate sensitivity has somewhat more effect, while membrane forces play a dominant role in reducing the permanent deflections.
The Strongest Circular Arch—A Perturbation Solution
Authors: Wu C.-H.
Published: October 2011

We consider the problem of determining that shape of circular arch which has the largest critical buckling pressure of all circular arches of given radius, central angle, and volume. The problem is formulated exactly and solved approximately by a perturbation procedure with the corresponding column problem as the fundamental solution. This latter problem was solved exactly by Keller and Tadjbakhsh and Keller. For hinged-hinged circular arches having rectangular cross sections of constant width, the best shaping is found to increase the buckling pressure by approximately 40 percent over that of a uniform arch.
Finite Bending, Stretching, and Shearing of a Block of Orthotropic,
Incompressible Simple Solid
Authors: Carroll M. M.
Published: October 2011

It is shown that a finite deformation history, involving bending, stretching, and shearing, can be supported in every incompressible orthotropic simple solid by the application of suitable surface tractions, if the bending axis is along a material symmetry direction. The corresponding stresses are expressed in terms of the material functionals which characterize the response to homogeneous plane deformations, and these material functionals are calculated explicitly in terms of the constitutive functionals of the material. The surface tractions which are required in order to effect bending and stretching of a rectangular block are also calculated.
Linear Elastic Dipolar Plates
Authors: Kyser E. L.
Published: October 2011

The linear dipolar field equations for an initially flat surface are presented and applied to an elastic isotropic surface. The equations separate into extensional and bending equations, and the extensional equations are discussed in detail. A general representation of the extensional solution is obtained, and is used to solve the stress-concentration problem of an infinite initially flat surface with a circular hole subjected to uniform radial tension at infinity. The stress-concentration factor differs from those obtained or implied by other theories (both classical and nonclassical), and the differences are discussed. Agreement with the classical result is obtained in one limiting case.
Some Properties of the Two-Dimensional, Turbulent Wall Jet in a Moving Stream
Authors: Kacker S. C. , Whitelaw J. H.
Published: October 2011

Measurements of the mean and fluctuating properties of a two-dimensional, constant property, plane turbulent wall jet in a moving stream are presented and their implications discussed.
Flexural Vibrations of an Elastic Plate With Two Symmetric Viscoelastic Coatings
Authors: Hertelendy Paul , Goldsmith Werner
Published: October 2011

The flexural-vibration characteristics of a symmetric, doubly infinite composite plate consisting of two outer layers of a linear viscoelastic material bonded to an elastic core have been examined, the viscous effects in the coating being represented by a complex shear modulus. Calculations of the dispersive and damping effects have been obtained for the lowest three modes by an extension of the exact Rayleigh-Lamb equations. Loss factors of the lowest modes have also been evaluated by two readily computed approximate methods; the results have been compared with those from the exact solution. The material constants were chosen to be representative of a high-polymer coating and an aluminum core. The modal behavior of the systems and coupling effects are discussed.
Response of Cylindrical Sandwich Shells to Moving Loads
Authors: Herrmann G. , Baker E. H.
Published: October 2011

This paper presents an analysis into the dynamic response of a long cylindrical sandwich shell under a moving axially symmetric ring load. The shell is assumed to be orthotropic and subjected to an initial axial stress. The uniform velocity of the load is prescribed and only the steady-state response is considered. Numerical results indicate the effects of various relevant parameters. The behavior of orthotropic sandwich cylinders under initial stress is compared with that of homogeneous isotropic cylindrical shells free of initial stress, and differences are pointed out.
A Numerical Solution for an Axially Symmetric Contact Problem
Authors: Tu Yih-O
Published: October 2011

A numerical scheme for the axially symmetric contact problem of a plate pressed between two identical spheres is given. The axially symmetric contact stress distribution is represented by a finite set of pressure distributions linearly varying with the radius between values defined in a set of concentric circles. The normal displacements of the bodies in contact resulting from these pressure distributions are matched at every radius of the discrete set of radii of these circles. The integral equation for the unkown contact stress distribution is thus approximated by a set of linear algebraic equations whose solution yields the unknown pressure values of the approximate distribution. The contact radius, relative approach, and the maximum contact stress are then computed numerically from this solution and are presented in terms of the total load, the radius of the sphere, and the plate thickness.
Experimental Evaluation of Material Behavior in a Wire Under Transverse Impact
Authors: Schultz A. B. , Tuschak P. A. , Vicario A. A.
Published: October 2011

Results are reported from an experiment involving photographic observation of constant-velocity transverse impact on long wires of annealed pure copper, two pure aluminums, and an aluminum alloy. Predictions of deformation are made assuming the quasi-static stress-strain curve governs behavior. Consistency with experimental observations is examined. Predictions are based on a closed-form solution to the problem, which is shown to be a compounding of two simple wave solutions of the governing equations. Predictions are consistent with observations for the aluminum alloy even under conditions of moderate or high static prestrain. The two pure aluminums and the copper show consistency at low but not at high strain levels. Highest strain levels reached were in the range 0.06–0.14.
Deformation Bounds for Bodies in a State of Creep
Authors: Leckie F. A. , Martin J. B.
Published: October 2011

Bounds on the energy dissipation and surface displacements are found for bodies undergoing nonlinear creep as a result of step loading. Elastic effects are included in a simple manner, and it is shown that the results are applicable to a variety of generalizations of the primary and secondary creep laws.
Experimental Investigation of Swirling Vortex Motion in Jets
Authors: Chigier N. A. , Chervinsky A.
Published: October 2011

Experiments have been carried out in a series of axisymmetric free turbulent jets with degrees of swirl covering the weak, moderate, and strong ranges, including the case of the onset of reversed flow in the central region of the jet. Measurements are reported of mean axial and swirl velocities, static pressure, and jet width at axial stations up to 15 orifice diameters. Mean velocity and pressure profiles are shown to be effectively similar from an axial distance of four diameters for weak and moderate swirl. For the case of strong swirl, a vortex is generated in the region close to the orifice resulting in a displacement of the axial velocity maximum from the jet axis. After a distance of 10 diameters, the influence of the vortex motion becomes small, and similarity of the profiles is obtained farther downstream. Experimentally determined profiles are described in terms of Gaussian error curves and third-order polynomials. Jet width and mass flow rates of entrained fluid are shown to increase according to the degree of swirl so that, for strong swirl, jet width and rate of entrainment are almost twice those for the nonswirling jet. Results of the decay of velocity and pressure along the axis are compared with values predicted by an approximate theory based on the integration of the Reynolds’ equations of motion. Good agreement is found between results and predictions, and a set of semi-empirical equations is provided from which a complete description of the mean velocity and pressure fields can be obtained for swirling jets.
Experiments on a Type of Shakedown Comprising Cyclic Plastic Deformations in Alternating Directions
Authors: Dietrich T.
Published: October 2011

Flexible foundation structures furnish examples for elastic-plastic systems enduring cyclic plastic deformations in alternating directions under normal working conditions. Such systems have not been considered yet by shakedown theories. The final stationary behavior which they approach is independent, under certain conditions, from the previous loading history, as is demonstrated by model tests with a laterally loaded pile.
The Indentation of an Orthotropic Half Plane Having Inclined Principal Axes
Authors: Conway H. D.
Published: October 2011

This Note concerns the calculation of the contact pressure when an orthotropic half plane is indented by a rigid frictionless indenter, the boundary of the half plane being inclined at an arbitrary angle to the principal axes of orthotropy. Specific results are given for an eccentrically loaded, flat-ended indenter.
Stress Intensity Factors for Semicircular Cracks: Part 2—Semi-Infinite Solid
Authors: Smith F. W. , Emery A. F. , Kobayashi A. S.
Published: October 2011

The stress intensity factor for a semicircular edge crack is derived. Numerical values for axial, bending, and thermal loads in half spaces and plates are presented. The results show that a magnification of the stress intensity factor of about 20 percent occurs at the free surface.
Minimum Weight Design of Beams With Inequality Constraints on Stress and Deflection
Authors: Haug E. J. , Kirmser P. G.
Published: October 2011

A nonlinear optimal design problem, with state variable inequality constraints, is solved. The problem is reduced to a Lagrange problem in the Calculus of Variations and necessary conditions are presented. For a certain class of problems, the necessary conditions are reduced to a system of nonlinear algebraic equations which are solved by an iterative procedure. The computational algorithm is efficient and is easily programmed for use on a digital computer.
Stresses Around an Elliptical Hole in a Finite Plate Subjected to Axial Loading
Authors: Durelli A. J. , Parks V. J. , Feng H. C.
Published: October 2011

A photoelastic solution of the distribution of stresses around a centrally located elliptical hole in a plate of finite width subjected to uniform axial loading is presented in this paper. Stress distributions at the boundaries are given for a wide range of the parameters, and stress-concentration factors have been computed for the points of maximum tensile and of maximum compressive stress. Comparisons are made with available theoretical solutions. Some appreciable discrepancies are pointed out.
Waves in Bars of Mechanically Unstable Materials
Authors: Dillon O. W.
Published: October 2011

This paper provides an analysis of waves in thin bars made of mechanically unstable solids. The concept of a material being unstable leads to a number of experimental observations being unified. The same stress-strain relation is used for very slow rates of unloading and for impact phenomena. In particular, incremental strain waves in the unstable material are predicted to travel at the elastic-bar velocity, because the stress-strain relation usually has a local slope equal to the Young’s modulus even in the plastic range of deformation. At certain discrete stresses, strain waves are predicted to propagate very slowly and as shock waves. Both of these results agree with experimental data obtained from annealed aluminum. A sample of the slowly propagating wave is included. It is also shown that the propagation speed in the unstable material depends on the imposed boundary conditions even though no strain-rate effect is included in the constitutive equation.
On Steady-State Harmonic Vibrations of Nonlinear Systems With Many Degrees of Freedom
Authors: Kinney W. M. , Rosenberg R. M.
Published: October 2011

A nonlinear spring-mass system with many degrees of freedom, and subjected to periodic exciting forces, is examined. The class of admissible systems and forcing functions is defined, and a geometrical method is described for deducing the steady-state forced vibrations having a period equal to that of the forcing functions. The methods used combine the geometrical methods developed earlier in the problem of normal mode vibrations and Rauscher’s method. The stability of these steady-state forced vibrations is examined by Hsu’s method. The results are applied to an example of a system having two degrees of freedom.
Normal and Quasi-Normal Modes in Damped Linear Dynamic Systems
Authors: Maybee J. S.
Published: October 2011

A generalization of the concept of classical normal modes in damped linear systems is presented. It is then shown that a necessary and sufficient condition that such quasi-normal modes exist is that certain matrices associated with the system commute. Necessary and sufficient conditions of the same type are also obtained for the classical normal modes, but under more restrictive conditions.
Single-Edge Crack in Rectangular Sheet Subjected to End Rotations
Authors: Bloom J. M.
Published: October 2011

Stress-intensity factors for single-edge cracks in rectangular sheets subjected to end rotations about the center line of the rectangle are investigated. The problem of the distribution of stress around the crack tip is reduced to the solution of a Riemann-Hilbert problem. Numerical results are presented for varying crack lengths and length/width ratios of the sheet.
Lubrication of a Porous Bearing—Stokes’ Solution
Authors: Joseph D. D. , Tao L. N.
Published: October 2011

Coupling of flows induced by the rotation of an infinite cylinder in an eccentric cylindrical hole in a fluid-saturated porous space is investigated in the context of a coupled boundary-value problem in which the Stokes flow outside porous regions and the Darcy flow inside porous regions are connected by continuity requirements on the pressure and normal component of velocity. The configuration is used to model the effects of a thick porous bearing. The solution simplifies considerably in the Reynolds limit of small clearance, and compact approximations for the pressure distribution and other relevant physical variables are derived. It is shown that transverse pressure gradients in the lubricant which are normally neglected in the Reynolds limit do increase, but not significantly, as a result of bearing flow. It follows that candidate Reynolds’ equations may ordinarily ignore effects of transverse pressure gradients in the lubricant even when the bearing is porous. A principal effect of the porous flow on the coupled motion is a diminution of pressure differences which would develop if all solids were impermeable. Corresponding changes in the shear stress resultant, which is neglected relative to the pressure resultant in the impermeable Reynolds limit, can become dominant because of the diminished pressures which attend porous flow. For large eccentricity ratios, the shear resultant is negative, and the load capacity may fall to zero and even change sign.
Shock Waves Produced by Small Stress Increments in Annealed Aluminum
Authors: Kenig M. J. , Dillon O. W.
Published: October 2011

Experimental data on the propagation of shear waves in annealed aluminum subjected to biaxial prestresses in the plastic range are presented. In addition, experimental evidence of the catastrophic straining at one “point” in a specimen while other “points” are not affected is given for annealed aluminum. Such evidence is not consistent with the material possessing a smooth stress-strain relation, but is compatible with the stair-case type of response. A shock wave theory which is a generalization of our previous work to the case of a biaxial prestress is also described. This theory is applied to the experimentally determined staircase stress-strain relation for aluminum. The same stress-strain relation is used for a wide range of strain rates and predicts a variety of wave speeds which are shown to be consistent with the experimental data. It is found that the biaxial prestress does not lead to any new phenomena but does modify some specific values. Some illustrative boundary-value problems are also discussed.
A Nonlinear Model Study of the Thermal Buckling of Thin Elastic Shells
Authors: Hoff Nicholas J.
Published: October 2011

Analysis of the simple model proposed yields equilibrium curves in agreement with those obtained by other investigators for axially compressed, thin-walled, circular cylindrical shells. A rigorous calculation of the stability of the equilibrium of the model indicates that the snap-through phenomenon can be entirely absent when an imperfect shell is heated in a perfectly rigid testing machine. When the testing machine is sufficiently elastic, snap through will occur. It may take place at a temperature smaller than, equal-to, or greater than T = εcr/α, where εcr is the theoretical critical strain of the perfect shell and α is the coefficient of expansion of the material of the shell, but the maximum stress produced in the imperfect shell will always be less than εcrE, where E is Young’s modulus of the material.
Bending Due to Ring Loading of a Cylindrical Shell With an Elastic Core
Authors: Yao John C.
Published: October 2011

The problem of a long, thin cylindrical shell with a soft core and subjected to a radial ring load is solved with the use of the Boussinesq-Neuber stress function for the core in conjunction with classical shell theory. Numerical results for stress and displacement fields are given for various values of the cylinder geometry parameters and material constants.
Analysis of Lift Augmentation of Vertical Solid Jets in Proximity of the Ground
Authors: Cohen M. J.
Published: October 2011

An analysis of the lift augmentation properties of a vertical solid two-dimensional subsonic jet due to the presence of the ground is presented. The jet efflux is assumed to behave as an ideal, inviscid fluid, and familiar potential flow techniques are used to solve the resultant problems. The factors controlling the phenomenon are height from the ground, nozzle wall angle, and compressibility. The results in the form of curves of lift augmentation against height from ground show that, whereas the effects of compressibility are very small, the effect of nozzle wall angle is important and can be a useful design-control parameter.
On the Solution to Transient Coupled Thermoelastic Problems by Perturbation Techniques
Authors: Soler A. I. , Brull M. A.
Published: October 2011

The governing equations of coupled thermoelasticity are investigated with the aim of obtaining solutions by means of a perturbation series in the coupling parameter. The perturbation technique is applied to the equations and a simpler set of perturbation equations is obtained. The convergence of the series solution is established, and it is shown that the result is a form of the exact solution to the governing equation for a suitable range of values of the coupling parameter. Numerical results are obtained for a typical problem using only the first two terms of the series solution. A second perturbation technique, well suited to the thermoelasticity problem and based on the method of Krylov and Bogoliuboff, also is presented in this paper. The technique is applied to two problems and the results are compared with the exact solutions.
Dynamic Response of Beams With Lumped Parameters
Authors: Wen Robert K.
Published: October 2011

The dynamic response of two lumped-parameter models for an elastic beam is considered. It is shown that, as compared to the beam with continuous properties, the model of lumped flexibility yields response that is too high, and the model of lumped mass yields response that is too low.
An Integral Method of Liapunov Function Generation for Nonlinear Autonomous Systems
Authors: Walker J. A. , Clark L. G.
Published: October 2011

A method is developed for generating Liapunov functions with which to determine the domain of asymptotic stability for nonlinear autonomous systems of any order, so long as these systems may be represented in phase variable form. The method is illustrated by several examples of higher order.
The Preferred Mode Shape in the Linear Buckling of Circular Cylindrical Shells Under Axial Compression
Authors: Mann-Nachbar P. , Nachbar W.
Published: October 2011

The chessboard buckle pattern in the solution of the linearized Donnell equations for buckling of a thin, cylindrical shell under axial compression is so sensitive to uncertainties in shell dimensions that the number of circumferential waves and the aspect ratio of the buckles is indeterminate. This problem is treated statistically. Shell dimensions are treated as random variables with probability distributions dependent on nominal values and manufacturing tolerances. Distributions for aspect ratio and number of circumferential waves are found by a Monte-Carlo technique. It is found that the linear theory does contain a mechanism for distinguishing among buckle modes. There is always a preferred buckle mode. For thin shells and attainable manufacturing tolerances, the aspect ratio of the preferred mode is closer to one than that of any other possible mode, and the corresponding number of buckles is large.
Vibration Frequencies of Truncated-Cone and Wedge Beams
Authors: Conway H. D. , Dubil J. F.
Published: October 2011

In the first part of a recent paper,2 numerical results were presented for the first five transverse vibrational resonant frequencies of truncated-cone cantilever beams for a number of different geometrics. These results are now extended to include the nine possible combinations of the simply supported, clamped, and free end conditions. The corresponding numerical results for the vibrating truncated wedge are also presented. The foregoing data augment the numerical results for the first five frequencies of uniform cross-section beams given in the recent handbook by Harris and Crede.4
Uniaxial Wave Propagation in Realistic Viscoelastic Materials
Authors: Arenz R. J.
Published: October 2011

The problem of wave propagation in a rod of viscoelastic material with step loading on the end is solved using realistic viscoelastic response characteristics covering approximately ten decades of logarithmic time. To overcome the inherent computational difficulties in the usual transform type of solution, an extension of the Schapery collocation inversion method to dynamic cases is proposed. The results indicate some material dispersion effects not evident in previous treatments using less adequate simple model representations. The present technique is also applicable to problems in two dimensions.
Critical Speeds of Torsional Oscillation of Geared-Shaft Systems Due to the Presence of Displacement Excitation
Authors: Porter B.
Published: October 2011

The system investigated in this paper incorporates a gear-pair which has a velocity ratio which is nominally n: 1 but which in fact varies periodically with rotation, performing p cycles of its variation per revolution of the input shaft. In this analysis, n and p are arbitrary and so the results presented here are effectively a generalization of those previously obtained for a Hooke’s joint system for which n = 1 and p = 2.
A Solution for the Thin Elastic Shell With Surface Loads
Authors: Steele C. R.
Published: October 2011

The problem considered is the thin elastic shell described by the equations of Novozhilov with an arbitrary but smooth midsurface that has a surface load and/or temperature distribution which varies rapidly with respect to one curvature coordinate. The particular solution is obtained in the form of an asymptotic series in powers of a parameter which is a measure of the rapidity of variation in the distribution. The wide class of problems, for which only the first term of the asymptotic series need be retained, is analogous to the beam on an elastic foundation. However, the advantage of the complex representation of Novozhilov is demonstrated by an example in which the shell is loaded and heated on strips with several conditions of constraint.
Effect of End Conditions on the Burst Strength of Finite Cylinders
Authors: Costantino C. J. , Salmon M. A. , Weil N. A.
Published: October 2011

Solutions are presented for the bursting strength of thin-walled cylinders of finite length with various end restraints, including (a) two rigid end plates, (b) two hemispherical caps, and (c) one rigid end plate and one hemispherical cap. The deformation theory of plasticity is used, together with the Mises yield criterion, for materials obeying a linear strain-hardening law. Comparisons of the results are made to determine the influence of end restraints on burst pressure with numerical results presented for cylinder lengths from 0 (sphere) to ∞, and for a range of hardening constants. The results show that the effect of shortness is small (less than 8 percent), and the influence of end conditions negligible, in the range l > 3. For shorter cylinders, the finite length of the shell serves to increase burst pressures, to values nearly double those for the infinite cylinder, as l → 0. Also, the effect of end restraints becomes very pronounced, the cylinder with the two rigid end plates being the strongest, and that with two hemispherical caps the weakest; all other types of end closures are assumed to have a strengthening effect intermediate to these two cases.
Rectangular Tensile Sheet With Symmetric Edge Cracks
Authors: Bowie O. L.
Published: October 2011

Complex variable methods are applied to the plane elastic problem of a rectangular tensile sheet with symmetric edge cracks. A mapping function is used which is sufficiently flexible to account for both variations of crack length and length/width ratios of the sheet on the stresses local to the crack tips. The stress-intensity factors are determined numerically for varying crack lengths in sheet with 1 × 1 and 3 × 1 length/width ratios and compared with Irwin’s earlier approximation derived from Westergaard’s collinear crack solution. The results indicate that the approximation is valid for deep cracks but in error by 13 percent for small crack depths.
A Method for the Determination of the Domain of Stability of Second-Order Nonlinear Autonomous Systems
Authors: Infante E. F. , Clark L. G.
Published: October 2011

A method for the determination of the domain of asymptotic stability of second-order nonlinear systems is presented. The essence of the method is the construction of Liapunov-like functions. Several simple but important examples illustrate the application of the method.
Laminar Free Convection From a Vertical Infinite Plate Subject to Transverse Oscillation
Authors: Blankenship Victor D. , Clark John A.
Published: October 2011

The laminar free-convection boundary layer on a vertical plane wall vibrating transversely at high frequencies is analyzed utilizing a perturbation technique. The zeroth-order solutions are that of the well-known steady free-convection flow. First-order harmonic oscillations in velocity and temperature and a second-order time-independent secondary flow and heat transfer are obtained. Series solution for shear stress and Nusselt number are presented having both time-dependent and time-independent terms. Prandtl numbers of 0.72 and 10 are investigated. The time-independent or steady Nusselt number was found to decrease while the shear stress was found to increase under the influence of oscillations.
Longitudinal Impact on Viscoplastic Rods—Approximate Methods and Comparisons
Authors: Symonds P. S. , Ting Thomas C. T.
Published: October 2011

Impact is considered on a rod of finite length whose material exhibits viscoplastic behavior described by a power-law relation between strain rate and dynamic overstress. Strain-hardening and elastic strains are neglected. Solutions previously obtained for the linear case are supplemented by deriving upper and lower bounds for the final strain. The general solution for the nonlinear case, with strain and stress assumed uniform along the rod, is derived and compared with results of the complete solution. The general solution for uniform strain is also compared and contrasted with results of the simplest rigid-plastic (rate independent) theory involving plastic wave propagation.
The Dynamics of Impulsively and Randomly Varying Systems
Authors: Samuels J. C.
Published: October 2011

By a method, related somewhat to a technique used in the theory of he multiple scattering of light, integral equations are derived for the mean and mean-square solution of systems undergoing random changes. These equations are in essential agreement with similar equations derived elsewhere in the literature by completely different methods. The theory developed herein is applied to the analysis of a circular cylindrical shell under random end thrusts. It is found that the shell buckles when the mean-square value of the fluctuation of the end thrusts exceeds a certain critical level determined by damping.
Longitudinal Strain Pulse Propagation in Wide Rectangular Bars: Part 1—Theoretical Considerations
Authors: Jones O. E. , Ellis A. T.
Published: October 2011

The propagation of a longitudinal elastic strain pulse in a wide rectangular bar is considered on the basis of approximate plane-stress equations of motion. Asymptotic expressions are obtained which, for large distances of travel, describe the pulse propagation in a semi-infinite strip with stress-free lateral edges, subject to the conditions that a uniform normal stress with a step-function time dependence is applied to the end and that the end is laterally constrained. Particular emphasis is given to describing the warping of plane sections during passage of the strain pulse.